To practice Problem-Solving Strategy 25.1 Resistor Circuits. Find the currents through and the potential difference across each resistor in the circuit shown on the diagram (Figure 1) . Use the following values: E = 12.0V , R1 = 15.0Ω , R2 = 45.0Ω , R3 = 20.0Ω , and R4 = 25.0Ω .
Part A
Step by step, reduce the circuit to the smallest possible number of equivalent resistors in order to find the equivalent resistance Req of the entire circuit.
Express you answer in ohms to three significant figures.
Part B
Find Ieq, the current through the equivalent resistor.
Express your answer in amperes to three significant figures.
Answers
Answer:
I₁ = 0.32 A
I₂ = 0.16 A
I₃ = 0.16 A
I₄ = 0.16 A
Explanation:
Part A
The equivalent resistance of the circuit is
Req = R₁ + (R₂||(R₃ + R₄))
Req = 15 + (45||(20 + 25))
Req = 15 + (45||45) = 15 + ((45×45)/(45+45)) = 15 + 22.5 = 37.5 Ω
Part B
From Ohm's law,
V = IR
Ieq = V/(Req) = 12/(37.5) = 0.32 A
Part C
Current through R₁ is the same as Ieq as R₁ is directly in series with the voltage source.
I₁ = 0.32 A
Then, this current flows through the (R₂||(R₃ + R₄)) loop too as the entire loop is in series with R₁
This current is them split into two branches of R₂ and (R₃ + R₄), since these two branches have equal resistances (45 Ω and 45 Ω), 0.32 A is split equally between the R₂ and (R₃ + R₄) branch.
Current through R₂ (using current divider)
I₂ = (45/90) × 0.32 = 0.16 A
Current through (R₃ + R₄) = 0.16 A too.
And because the two resistors are in series, the same current flows through them.
I₃ = I₄ = 0.16 A
First, we resolve the parallel circuits using the formula for resistors in parallel to get the equivalent resistance, Rp. We then substitute this into the series circuits to get the total equivalent resistance, Req. Using Ohm's Law, we can calculate the equivalent current, Ieq.
Explanation:To solve this, we first need to determine the equivalent resistance of the whole circuit. As it is a combination of parallel and series circuits, we have to start by replacing the resistors in parallel. Using the formula for resistors in parallel, 1/R = 1/R2 + 1/R3, the parallel combination of R2 and R3 can be replaced by one resistor with resistance Rp = 1/ ((1/R2) + (1/R3)). This gives Rp = 13.333Ω. Now we have a simple series circuit with R1, Rp, and R4. The equivalent resistance of the whole circuit is then Req = R1 + Rp + R4 = 15.0Ω + 13.333Ω + 25.0Ω = 53.333Ω.
In part B, we apply Ohm's Law: I = E/R to get the equivalent current through the circuit. Using our values for E (12V) and Req (53.333Ω), we find Ieq = 0.225A.
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Related Questions
When its coil rotates at a frequency of 240 Hz, a certain generator has a peak emf of 73 V. (a) What is the peak emf of the generator when its coil rotates at a frequency of 44 Hz? (b) Determine the frequency of the coil's rotation when the peak emf of the generator is 180 V.
Answers
Answer: (a) peak emf = 13.38V
(b) frequency = 591.78Hz
Explanation: Please see the attachments below
What force (in N) is exerted on the water in an MHD drive utilizing a 25.0 cm diameter tube, if 125 A current is passed across the tube that is perpendicular to a 1.95 T magnetic field? (The relatively small size of this force indicates the need for very large currents and magnetic fields to make practical MHD drives.) N
Answers
Final answer:
The force exerted on the water in the MHD drive utilizing a 25.0 cm diameter tube, with a 125 A current and a 1.95 T magnetic field, is 60.94 N.
Explanation:
To find the force exerted on the water in the MHD drive, we can use the formula for the magnetic force:
F = ILB
Where F is the force, I is the current, L is the length of the wire (in this case, the 25.0-cm diameter tube), and B is the magnetic field strength.
Plugging in the given values, we have:
F = (125 A)(0.25 m)(1.95 T)
Solving for F, we get:
F = 60.94 N
Therefore, the force exerted on the water in the MHD drive is 60.94 N.
Final answer:
The force exerted on the water in an MHD drive utilizing a 25.0 cm diameter tube, with a 125 A current and a 1.95 T magnetic field, is approximately 118.13 N.
Explanation:
The force exerted on the water in an MHD drive can be calculated using the formula:
Force (N) = Current (A) * Magnetic Field (T) * Area (m²)
Given that the diameter of the tube is 25.0 cm and the current is 125 A, we can calculate the area as follows:
Area = π * (radius)²
Area = π * (0.125 m)²
Substituting the values into the formula:
Force = 125 A * 1.95 T * (π * (0.125 m)²)
Force ≈ 118.13 N
Therefore, the force exerted on the water in the MHD drive is approximately 118.13 N.
Compute VO when Vin = 0.5 V, in two different ways: a) using the equation VO = G (V+-V-) with G = 106; and b) using the Golden Rules. In both cases you can assume that the currents into the input terminals of the op-amp are negligible.
Answers
Final answer:
To compute Vout with Vin = 0.5 V: a) Using the equation VO = G (V+-V-) with G = 10⁶ would theoretically give 500,000 V, but this is practically limited by the op-amp's supply voltage. b) Using the Golden Rules, assuming an ideal op-amp, Vout would be equal to Vin, thus Vout = 0.5 V.
Explanation:
To compute Vout when Vin = 0.5 V, we can use two different methods:
a) Using the equation VO = G (V+-V-) with G = 10⁶, we assume that for an ideal operational amplifier (op-amp), the voltage at the non-inverting input (V+) is equal to the voltage at the inverting input (V-). Since the question suggests that V- is at circuit common and therefore is 0 V, we have VO = G * (V+ - V-). Substituting values gives VO = 10⁶ * (0.5 V - 0 V) = 500,000 V. However, because real op-amps cannot output such high voltages, Vout would typically be limited by the supply voltage of the op-amp.
b) Using the Golden Rules of op-amps, which state that no current flows into the input terminals of an op-amp and the voltage at the inverting terminal is equal to the voltage at the non-inverting terminal, we can infer that because Vin = 0.5 V is applied to the non-inverting terminal and no current flows into the op-amp, then the voltage difference across the inputs is zero. Thus, Vout must also be 0.5 V to maintain this condition. Therefore, Vout = Vin = 0.5 V under the ideal op-amp approximation.
Determine an appropriate size for a square cross-section solid steel shaft to transmit 260 hp at a speed of 550 rev/min if the maximum allowable shear stress is 15 kpsi.
Answers
Answer:46.05 mm
Explanation:
Given
[tex]Power=260\ hp\approx 260\times 746=193.96\ KW[/tex]
speed [tex]N=550\ rev/min[/tex]
allowable shear stress [tex](\tau )_{max}=15\ kpsi\approx 103.421\ MPa[/tex]
Power is given by
[tex]P=\frac{2\pi NT}{60}[/tex]
[tex]193.96=\frac{2\pi 550\times T}{60}[/tex]
[tex]T=3367.6\ N-m[/tex]
From Torsion Formula
[tex]\frac{T}{J}=\frac{\tau }{r}-----1[/tex]
where J=Polar section modulus
T=Torque
[tex]\tau [/tex]=shear stress
For square cross section
[tex]r=\frac{a}{2}[/tex]
where a=side of square
[tex]J=\frac{a^4}{6}[/tex]
Substituting the values in equation 1
[tex]\frac{3376.6}{\frac{a^4}{6}}=\frac{103.421\times 10^6}{\frac{a}{2}}[/tex]
[tex]a=0.04605\ m[/tex]
[tex]a=46.05\ mm[/tex]
A square cross-section solid steel shaft of approximately 5 inches on each side can transmit 260 hp at 550 rev/min without exceeding a maximum allowable shear stress of 15 kpsi.
Explanation:The size of the steel shaft can be calculated by using the power-transmitting capacity of a shaft equation, which states:
P = (16πNT) / (60 * 33000), where P is power in hp, N is rotational speed in rev/min, and T is torque in lb-ft.
We also know that the shear stress (τ) is given by the equation: τ = (16T) / (πd^3), where d is the diameter in inches.
To find the correct torque, we start by rearranging the power equation for T: T = (P * 60 * 33000) / (16πN).
Substituting in the given power and rotational speed, we find that the torque is approximately 13400 lb-ft.
We then substitute this value and the allowable shear stress into the shear stress equation, solving for d to get d ≈ 5 inches.
So, a square cross-section solid steel shaft about 5 inches on each side should be able to transmit the given power at the stated speed without exceeding the maximum allowable shear stress.
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A dockworker applies a constant horizontal force of 90.0Nto a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves a distance 12.0min a time of 5.20s.If the worker stops pushing after 5.20s, how far does the block move in the next 5.30s
Answers
Answer:
Distance traveled in the next 5.30 seconds is 24.454 meters.
Explanation:
Considering the block moves with a constant acceleration when the force is applied, the average speed would be half of the speed at the end of 5.20 seconds of acceleration.
This means:
Average Speed = Total distance / Time
Average Speed = 12 / 5.20 = 2.307 m/s
Speed at end of 5.20 seconds = 2 * Average Speed
Speed at end of 5.20 seconds = 2 * 2.307
Speed at end of 5.20 seconds = 4.614 m/s
Now that we have the speed at which the block is traveling, and there is no friction to reduce or change the speed, we can solve for the distance covered in the next 5.30 seconds in the following way:
Distance traveled in the next 5.30 seconds:
Distance = Speed * Time
Distance = 4.614 * 5.30
Distance = 24.454 meters
A massless beam supports two weights as shown.
Find W such that the supporting force at
A is zero (static equilibrium). Force is 471 L' is L/3 and L'' is 9. Answer in nearest whole number.
Answers
Taking moments about B
N x L'' = W x L'
Here the moment is = force x perpendicular distance between the axis of rotation and the point of applied force .
Here L' = L/3 and L'' = 9
Thus from figure
471 x 9 = W x [tex]\frac{L}{3}[/tex]
But L'' = [tex]\frac{1}{2}[/tex]( L - [tex]\frac{L}{3}[/tex] ) = [tex]\frac{L}{3}[/tex] = 9
Thus W = 471 N
The value of the weight ( W ) is ; 471 N
Determine the weight ( W) valueFirst step : take moments about B
N * L" = W * L'
Where : L' = L/3, L" = 9
From the figure
471 * 9 = W * [tex]\frac{L}{3}[/tex]
also:
L" = 1/2 ( L - L/3 ) = L/3 = 9
Hence ; W = 471 N
Hence we can conclude that The value of the weight ( W ) is ; 471 N
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To apply the law of conservation of energy to an object launched upward in Earth's gravitational field.
In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy.
In this problem, you will apply the law of conservation of energy to different objects launched from Earth. The energy transformations that take place involve the object's kinetic energy K=(1/2)mv^2 and its gravitational potential energy U=mgh. The law of conservation of energy for such cases implies that the sum of the object's kinetic energy and potential energy does not change with time. This idea can be expressed by the equation
K_{\rm i}+U_{\rm i}=K_{\rm f}+U_{\rm f}\;\;\;\;,
where "i" denotes the "initial" moment and "f" denotes the "final" moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem.
Using conservation of energy, find the maximum height h_max to which the object will rise
Answers
Answer:
The maximum height is [tex]h_{max} = \frac{v^2}{2g}[/tex]
Explanation:
From the question we are given that
[tex]K_{\rm i}+U_{\rm i}=K_{\rm f}+U_{\rm f}\;\;\;\;,[/tex]
and [tex]K=(1/2)mv^2[/tex]
while [tex]U=mgh[/tex]
Now at the minimum height the kinetic energy is maximum and the potential energy is 0
[tex]K_i \ is \ max[/tex]
[tex]U_i = 0[/tex]
At maximum height [tex]h_{max}[/tex]
The kinetic energy is 0 and kinetic energy is
Hence the above equation
[tex]K_i = U_f[/tex]
[tex]\frac{1}{2}mv^2 = mgh_{max}[/tex]
Making [tex]h_{max}[/tex] the subject of the formula we have
[tex]h_{max} = \frac{v^2}{2g}[/tex]
As an object moves from point A to point B only two forces act onit: one force is nonconservative and does -30 J of work, the otherforce is conservative and does +50 J of work. Between A andB,
a. the kineticenergy of object increases, mechanical energydecreases.
b. the kineticenergy of object decreases, mechanical energydecreases.
c. the kineticenergy of object decreases, mechanical energyincreases.
d. the kineticenergy of object increases, mechanical energyincreases.
e. None of theabove.
Answers
To solve this problem we will apply the principles of energy conservation. On the one hand we have that the work done by the non-conservative force is equivalent to -30J while the work done by the conservative force is 50J.
This leads to the direct conclusion that the resulting energy is 20J.
The conservative force is linked to the movement caused by the sum of the two energies, therefore there is an increase in kinetic energy. The decrease in the mechanical energy of the system is directly due to the loss given by the non-conservative force, therefore there is a decrease in mechanical energy.
Therefore the correct answer is A. Kintetic energy increases and mechanical energy decreases.
Based on the given question, we can infer that a. the kinetic energy of object increases, mechanical energy decreases.
What is Kinetic Energy?This refers to the form of energy which makes use of the motion of an object to move.
Hence, we can see that based on the principles of energy conservation, we can see that the work done by the non-conservative force is equivalent to -30J while the work done by the conservative force is 50J.
With this in mind, we can see that the resulting energy is 20J.
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There are two important isotopes of uranium, 235U
and 238U; these isotopes are nearly identical chemically
but have different atomic masses. Only 235U is very
useful in nuclear reactors. Separating the isotopes is called
uranium enrichment (and is often in the news as of this
writing, because of concerns that some countries are
enriching uranium with the goal of making nuclear
weapons.) One of the techniques for enrichment, gas
diffusion, is based on the different molecular speeds of
uranium hexafluoride gas, UF6 . (a) The molar masses of
235U and 238UF6 are 349.0 g/mol and 352.0 g/mol,
respectively. What is the ratio of their typical speeds vrms ?
(b) At what temperature would their typical speeds differ by
1.00 m/s? (c) Do your answers in this problem imply that
this technique may be difficult?
Answers
Answer:
a) (vᵣₘₛ₁/vᵣₘₛ₂) = 1.00429
where vᵣₘₛ₁ represents the vᵣₘₛ for 235-UF6 and vᵣₘₛ₂ represents the vᵣₘₛ for 238-UF6.
b) T = 767.34 K
c) The answers point to a difficult seperation technique, as the two compounds of the different isotopes have very close rms speeds and to create a difference of only 1 m/s In their rms speeds would require a high temperature of up to 767.34 K.
Explanation:
The vᵣₘₛ for an atom or molecule is given by
vᵣₘₛ = √(3RT/M)
where R = molar gas constant = J/mol.K
T = absolute temperature in Kelvin
M = Molar mass of the molecules.
₁₂
Let the vᵣₘₛ of 235-UF6 be vᵣₘₛ₁
And its molar mass = M₁ = 349.0 g/mol
vᵣₘₛ₁ = √(3RT/M₁)
√(3RT) = vᵣₘₛ₁ × √M₁
For the 238-UF6
Let its vᵣₘₛ be vᵣₘₛ₂
And its molar mass = M₂ = 352.0 g/mol
√(3RT) = vᵣₘₛ₂ × √M₂
Since √(3RT) = √(3RT)
vᵣₘₛ₁ × √M₁ = vᵣₘₛ₂ × √M₂
(vᵣₘₛ₁/vᵣₘₛ₂) = (√M₂/√M₁) = [√(352)/√(349)]
(vᵣₘₛ₁/vᵣₘₛ₂) = 1.00429
b) Recall
vᵣₘₛ₁ = √(3RT/M₁)
vᵣₘₛ₂ = √(3RT/M₂)
(vᵣₘₛ₁ - vᵣₘₛ₂) = 1 m/s
[√(3RT/M₁)] - [√(3RT/M₂)] = 1
R = 8.314 J/mol.K, M₁ = 349.0 g/mol = 0.349 kg/mol, M₂ = 352.0 g/mol = 0.352 kg/mol, T = ?
√T [√(3 × 8.314/0.349) - √(3 × 8.314/0.352) = 1
√T (8.4538 - 8.4177) = 1
√T = 1/0.0361
√T = 27.7
T = 27.7²
T = 767.34 K
c) The answers point to a difficult seperation technique, as the two compounds of the different isotopes have very close rms speeds and to create a difference of only 1 m/s In their rms speeds would require a high temperature of up to 767.34 K.
In an insulated container, liquid water is mixed with ice. What can you conclude about the phases present in the container when equilibrium is established?
a. There would be ice only.
b. There would be liquid water only.
c. There would be both ice and liquid water.
d. There is no way of knowing the phase composition without more information.
Answers
Answer:
d. There is no way of knowing the phase composition without more information.
Explanation:
There is no way to ascertain the phases present in the container when equilibrium is established because we are not furnished with enough information.
The most important information needed to have a deeper understanding and provide solution is temperature. Liquid water and ice can both exist at the same temperature. So we cannot conclude based on the information at hand.Consider a laser pointer that emits red light with wavelength 650 nm. This light is used for a photoelectric effect experiment where the anode in the evacuated glass tube is made up of a material that has work function equal to 1 eV. 1. What is the energy of an individual photon that comes out of the laser pointer?
Answers
Answer:
The energy of an individual photon that comes out of the laser pointer is 1.91 eV
Explanation:
The energy of a photon can be obtained using the expression below
E = hc/λ
where E is the energy;
h is the Planck's constant = 6.626 x 10-34 Js;
c is the speed of light = 3.00 x [tex]10^{8}[/tex] m/s (speed of light);
λ is the wavelength = 650 nm =650 x [tex]10^{-9}[/tex] m.
E = (6.626 x 10-34 Js) x (3.00 x [tex]10^{8}[/tex] m/s) /650 x [tex]10^{-9}[/tex] m
E = 3.058 x [tex]10^{-19}[/tex] J
1 joule = 6.242 x [tex]10^{18}[/tex] eV
3.058 x [tex]10^{-19}[/tex] J = 3.058 x [tex]10^{-19}[/tex] J x 6.242 x [tex]10^{18}[/tex] eV = 1.91 eV
Therefore the energy of an individual photon that comes out of the laser pointer is 1.91 eV
You give a crate a push to set it in motion. After the push is over, the crate skids to a stop on a rough, level floor. Describe the energy changes after the push (with the crate as the system).
Answers
Answer: potential to kinetic and then potential energies
Explanation:
Answer:
KE₁ = PE₂
Explanation:
From the principle of conservation of energy we know that
KE₁ + PE₁ = KE₂ + PE₂
where KE is the kinetic energy and PE is potential energy
KE = ½mv²
PE = mgd
Initially, you gave a push to crate and it started moving with some velocity
KE₁ = ½mv₁²
Initially, the potential energy is zero since it didnt cover any distance
PE₁ = mgd₁ = 0
At the final state, the crate stopped and its finally velocity become zero, therefore, the kinetic energy is zero.
KE₂ = ½mv₂² = 0
At the final state, the crate covered some distance and the final potential energy is
PE₂ = mgd₂
Therefore, the energy relation becomes
KE₁ + PE₁ = KE₂ + PE₂
KE₁ + 0 = 0 + PE₂
KE₁ = PE₂
Hence, the initial kinetic energy of the system is converted to final potential energy of the system.
4.77 Augment the rectifier circuit of Problem 4.70 with a capacitor chosen to provide a peak-to-peak ripple voltage of (i) 10% of the peak output and (ii) 1% of the peak output. In each case: (a) What average output voltage results? (b) What fraction of the cycle does the diode conduct? (c) What is the average diode current? (d) What is the peak diode current?
Answers
To augment the rectifier circuit with a capacitor, connect it in parallel with the load resistor. Calculate the capacitor value to achieve the desired ripple voltage. Determine the average output voltage, fraction of cycle during diode conduction, average diode current, and peak diode current using the ripple voltage and peak output voltage.
Explanation:To augment the rectifier circuit with a capacitor, we need to connect the capacitor in parallel with the load resistor. The peak-to-peak ripple voltage depends on the value of the capacitor. To calculate the average output voltage, we need to consider the ripple voltage and the peak output voltage. The fraction of the cycle during which the diode conducts, average diode current, and peak diode current can also be determined using the ripple voltage and peak output voltage.
(a) To achieve a peak-to-peak ripple voltage of 10% of the peak output, we can calculate the capacitor value using the equation Vr = (1/2πfc) * (Id / Ic) * Vp, where Vr is the ripple voltage, Id is the diode current, Ic is the capacitor current, Vp is the peak output voltage, f is the frequency, and c is the capacitor value. With the calculated capacitor value, we can find the average output voltage.
(b) The fraction of the cycle during which the diode conducts can be calculated by dividing the time during which the diode conducts by the total time of the cycle.
(c) The average diode current can be calculated by dividing the total charge passing through the diode by the total time period of the cycle.
(d) The peak diode current can be calculated by multiplying the average current by the diode conduction time.
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A pitcher claims he can throw a 0.145-kg baseball with as much momentum as a 3.00-g bullet moving with a speed of 1.50 3 103 m/s. (a) What must the baseball’s speed be if the pitcher’s claim is valid? (b) Which has greater kinetic energy, the ball or the bullet?
Answers
(a) The baseball's speed must be approximately 6.89 m/s.
(b) The bullet has greater kinetic energy.
Explanation:To determine the baseball's speed, we use the principle of conservation of momentum, which states that the total momentum of an isolated system remains constant. The momentum of the bullet before the pitch must equal the combined momentum of the baseball and the pitcher afterward. By equating the momenta and solving for the baseball's speed, we find it to be approximately 6.89 m/s.
Now, to compare the kinetic energies of the baseball and the bullet, we use the kinetic energy formula, which is proportional to the square of the velocity. Despite the baseball having a larger mass, the bullet's significantly higher velocity results in greater kinetic energy. This is due to the quadratic relationship between velocity and kinetic energy.
In conclusion, the baseball must travel at around 6.89 m/s to match the claimed momentum. However, the bullet still possesses greater kinetic energy due to its higher speed, highlighting the importance of velocity in determining kinetic energy.
a) The speed of the baseball must be [tex]\( {31.0 \, \text{m/s}} \)[/tex] to match the momentum of the bullet.
b) The bullet has significantly greater kinetic energy [tex](\(3375 \, \text{J}\))[/tex] compared to the baseball [tex](\(69.86 \, \text{J}\))[/tex].
To solve the problem, we will use the principles of momentum and kinetic energy.
Part (a): Speed of the Baseball
First, we need to calculate the momentum of the bullet and then find the speed at which the baseball must be thrown to have the same momentum.
1. Momentum of the Bullet:
- Mass of the bullet [tex](\(m_b\))[/tex]: [tex]\(3.00 \, \text{g} = 0.003 \, \text{kg}\)[/tex]
- Speed of the bullet [tex](\(v_b\))[/tex]: [tex]\(1.50 \times 10^3 \, \text{m/s}\)[/tex]
Momentum [tex](\(p\))[/tex] is given by:
[tex]\[ p = m_b \cdot v_b \][/tex]
[tex]\[ p = 0.003 \, \text{kg} \times 1.50 \times 10^3 \, \text{m/s} \][/tex]
[tex]\[ p = 4.50 \, \text{kg} \cdot \text{m/s} \][/tex]
2. Speed of the Baseball:
- Mass of the baseball [tex](\(m_{bb}\)): \(0.145 \, \text{kg}\)[/tex]
- Let the speed of the baseball be [tex]\(v_{bb}\).[/tex]
We want the baseball to have the same momentum as the bullet:
[tex]\[ p = m_{bb} \cdot v_{bb} \][/tex]
[tex]\[ 4.50 \, \text{kg} \cdot \text{m/s} = 0.145 \, \text{kg} \cdot v_{bb} \][/tex]
Solving for [tex]\(v_{bb}\):[/tex]
[tex]\[ v_{bb} = \frac{4.50 \, \text{kg} \cdot \text{m/s}}{0.145 \, \text{kg}} \][/tex]
[tex]\[ v_{bb} = 31.034 \, \text{m/s} \][/tex]
So, the baseball must be thrown with a speed of approximately [tex]\( \boxed{31.0 \, \text{m/s}} \).[/tex]
Part (b): Kinetic Energy Comparison
To compare the kinetic energies of the baseball and the bullet, we use the kinetic energy formula:
[tex]\[KE = \frac{1}{2} m v^2\][/tex]
1. Kinetic Energy of the Bullet:
- Mass [tex](\(m_b\)): \(0.003 \, \text{kg}\)[/tex]
- Speed [tex](\(v_b\)): \(1.50 \times 10^3 \, \text{m/s}\)[/tex]
[tex]\[ KE_b = \frac{1}{2} \cdot 0.003 \, \text{kg} \cdot (1.50 \times 10^3 \, \text{m/s})^2 \][/tex]
[tex]\[ KE_b = \frac{1}{2} \cdot 0.003 \, \text{kg} \cdot 2.25 \times 10^6 \, \text{m}^2/\text{s}^2 \][/tex]
[tex]\[ KE_b = 0.0015 \cdot 2.25 \times 10^6 \][/tex]
[tex]\[ KE_b = 3375 \, \text{J} \][/tex]
2. Kinetic Energy of the Baseball:
- Mass [tex](\(m_{bb}\)): \(0.145 \, \text{kg}\)[/tex]
- Speed [tex](\(v_{bb}\)): \(31.034 \, \text{m/s}\)[/tex]
[tex]\[ KE_{bb} = \frac{1}{2} \cdot 0.145 \, \text{kg} \cdot (31.034 \, \text{m/s})^2 \][/tex]
[tex]\[ KE_{bb} = \frac{1}{2} \cdot 0.145 \, \text{kg} \cdot 963.1 \, \text{m}^2/\text{s}^2 \][/tex]
[tex]\[ KE_{bb} = 0.0725 \cdot 963.1 \][/tex]
[tex]\[ KE_{bb} = 69.86 \, \text{J} \][/tex]
You are watching people practicing archery when you wonder how fast an arrow is shot from a bow. With a flash of insight you remember your physics and see how you can easily determine what you want to know by a simple measurement. You ask one of the archers to pull back her bow string as far as possible and shoot an arrow horizontally. The arrow strikes the ground 107 feet from the archer making an angle of 3 degrees below the horizontal. What is the initial speed of the arrow?
Answers
Answer:
[tex]u_x=55.208\ m.s^{-1}[/tex]
Explanation:
Given:
horizontal distance form the point of shooting where the arrow hits ground, [tex]s=107\ ft[/tex] [tex]=32.614\ m[/tex]
angle below the horizontal form the point of release of arrow where it hits ground, [tex]\theta=3^{\circ}[/tex]
So the height above the ground from where the arrow was shot:
[tex]\tan3^{\circ}=\frac{h}{107}[/tex]
[tex]h=5.6076\ ft=1.71\ m[/tex]
Since the arrow is shot horizontally so the initial vertical component of the velocity is zero ( [tex]u_y=0[/tex] ), we've the final vertical component of the velocity as:[tex]v_y=\sqrt{2g.h}[/tex]
[tex]v_y=\sqrt{2\times 9.8\times 1.71}[/tex]
[tex]v_y=5.789\ m.s^{-1}[/tex]
Using equation of motion:
[tex]v_y=u_y+g.t[/tex]
where:
t = time taken
[tex]5.789=0+9.8\times t[/tex]
[tex]t=0.591\ s[/tex]
Now the horizontal component of speed of the arrow (which remains constant throughout the motion by the Newton's first law of motion):[tex]u_x=\frac{s}{t}[/tex]
[tex]u_x=\frac{32.614}{0.591}[/tex]
[tex]u_x=55.208\ m.s^{-1}[/tex]
The 10-lb block has a speed of 4 ft>s when the force of F = (8t2) lb is applied. Determine the velocity of the block when it moves s = 30 ft. The coefficient of kinetic friction at the surface is ms = 0.2.
Answers
v=6ft/sec
To determine the velocity of the block when it moves a distance of 30 ft, we can use the equations of motion and consider the force applied and the friction acting on the block. First, let's find the acceleration of the block using the force applied. Next, we need to consider the frictional force acting on the block. Finally, we can calculate the net force and use the equation of motion to determine the velocity of the block.
Explanation:To determine the velocity of the block when it moves a distance of 30 ft, we can use the equations of motion and consider the force applied and the friction acting on the block.
First, let's find the acceleration of the block using the force applied. The force applied is given by F = 8t^2 lb, where t is the time in seconds. So, at t = 0, the force is F = 0 lb, and at t = 1, the force is F = 8 lb.
We can now use the equations of motion to find the acceleration. Since the mass of the block is not given, we can assume it to be 10 lb (as mentioned in the question). From the second law of motion, F = ma, where F is the net force, m is the mass, and a is the acceleration. Therefore, 8 = 10a. Solving for a, we get a = 0.8 ft/s^2.
Next, we need to consider the frictional force acting on the block. The coefficient of kinetic friction is given as μs = 0.2. The frictional force, Ff, can be calculated using Ff = μs * N, where N is the normal force. The normal force is equal to the weight of the block, N = mg, where g is the acceleration due to gravity, approximately 32 ft/s^2. So, N = 10 * 32 = 320 lb. Substituting the values, we get Ff = 0.2 * 320 = 64 lb.
Now, we can calculate the net force acting on the block. The net force, Fn, is given as Fn = F - Ff, where F is the force applied. Substituting the values, Fn = 8t^2 - 64 lb.
Finally, we can use the equation of motion, v^2 = u^2 + 2as, to determine the velocity of the block when it moves a distance of 30 ft. Here, v is the final velocity, u is the initial velocity (which is 0 ft/s because the block starts from rest), a is the acceleration, and s is the distance traveled. Substituting the values, v^2 = 0 + 2 * 0.8 * 30. Solving for v, we find
v = 6 ft/s.
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As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. When you push the platform, you compress the springs. You do an amount of work of 79.0 J when you compress the springs a distance of 0.190 m from their uncompressed length.(a) What magnitude of force must you apply to hold the platform in this position?
Answers
Explanation:
The given data is as follows.
Work done by the force, (W) = 79.0 J
Compression in length (x) = 0.190 m
So, formula for parallel combination of springs equivalent is as follows.
[tex]k_{eq} = K_{1} + K_{2}[/tex]
= 2k
Hence, work done is as follows.
W = [tex]\frac{1}{2}k_{eq} \times x^{2}[/tex]
[tex]k_{eq} = \frac{2W}{x^{2}}[/tex]
= [tex]\frac{2 \times 79}{(0.19)^{2}}[/tex]
= [tex]\frac{158}{0.0361}[/tex]
= 4376.73 N/m
Hence, magnitude of force required to hold the platform is as follows.
F = [tex]k_{eq}x[/tex]
= [tex]4376.73 N/m \times 0.19 m[/tex]
= 831.58 N
Thus, we can conclude that magnitude of force you must apply to hold the platform in this position is 831.58 N.
P7.16 A thin flat plate 55 by 110 cm is immersed in a 6-m/s stream of SAE 10 oil at 20C. Compute the total friction drag if the stream is parallel to (a) the long side and (b) the short side.
Answers
Answer:
a
The total friction drag for the long side of the plate is 107 N
b
The total friction drag for the long side of the plate is 151.4 N
Explanation:
The first question is to obtain the friction drag when the fluid i parallel to the long side of the plate
The block representation of the this problem is shown on the first uploaded image
Where the U is the initial velocity = 6 m/s
So the equation we will be working with is
[tex]F = \frac{1}{2} \rho C_fAU^2[/tex]
Where [tex]\rho[/tex] is the density of SAE 10W = [tex]870\ kg/m^3[/tex] This is obtained from the table of density at 20° C
[tex]C_f[/tex] is the friction drag coefficient
This coefficient is dependent on the Reynolds number if the Reynolds number is less than [tex]5*10^5[/tex] then the flow is of laminar type and
[tex]C_f[/tex] = [tex]\frac{1.328}{\sqrt{Re} }[/tex]
But if the Reynolds number is greater than [tex]5*10^5[/tex] the flow would be of Turbulent type and
[tex]C_f = \frac{0.074}{Re_E^{0.2}}[/tex]
Where Re is the Reynolds number
To obtain the Reynolds number
[tex]Re = \frac{\rho UL}{\mu}[/tex]
where L is the length of the long side = 110 cm = 1.1 m
and [tex]\mu[/tex] is the Dynamic viscosity of SAE 10W oil [tex]= 1.04*10^{-1} kg /m.s[/tex]
This is gotten from the table of Dynamic viscosity of oil
So
[tex]Re = \frac{870 *6*1.1}{1.04*10^{-1}}[/tex]
[tex]= 55211.54[/tex]
Since 55211.54 < [tex]5.0*10^5[/tex]
Hence
[tex]C_f = \frac{1.328}{\sqrt{55211.54} }[/tex]
[tex]= 0.00565[/tex]
[tex]A[/tex] is the area of the plate = [tex]\frac{ (110cm)(55cm)}{10000}[/tex] =[tex]0.55m^2[/tex]
Since the area is immersed totally it should be multiplied by 2 i.e the bottom face and the top face are both immersed in the fluid
[tex]F = \frac{1}{2} \rho C_f(2A)U^2[/tex]
[tex]F =\frac{1}{2} *870 *0.00565*(2*0.55)*6^2[/tex]
[tex]F = 107N[/tex]
Considering the short side
To obtain the Reynolds number
[tex]Re = \frac{\rho U b}{\mu}[/tex]
Here b is the short side
[tex]Re =\frac{870*6*0,55}{1.04*10^{-1}}[/tex]
[tex]=27606[/tex]
Since the value obtained is not greater than [tex]5*10^5[/tex] then the flow is laminar
And
[tex]C_f = \frac{1.328}{\sqrt{Re} }[/tex]
[tex]= \frac{1.328}{\sqrt{27606} }[/tex]
[tex]= 0.00799[/tex]
The next thing to do is to obtain the total friction drag
[tex]F = \frac{1}{2} \rho C_f(2A)U^2[/tex]
Substituting values
[tex]F = \frac{1}{2} * 870 * 0.00799 * 2( 0.55) * 6^2[/tex]
[tex]= 151.4 N[/tex]
Final answer:
To calculate the total friction drag on the plate immersed in the given fluid stream, use the drag force formula. Compute the drag for both the long and short sides by multiplying the relevant dimensions with the velocity and viscosity.
Explanation:
The drag force per unit area on the plate is given by Fdrag = μSA, where μ is the viscosity of the fluid and A is the area of the plate. Here, the total friction drag can be calculated by multiplying the drag force per unit area by the total area of the plate.
For the long side: Total friction drag = μ(6)(0.55)(1.1)
For the short side: Total friction drag = μ(6)(0.11)(1.1)
The magnitude of the magnetic field that a long and extremely thin current-carrying wire produces at a distance of 3.0 µm from the center of the wire is 2.0 × 10-3 T. How much current is flowing through the wire?
Answers
Answer:
Current (I) = 3 x 10^-2 A
Explanation:
As we know, [tex]B = 4\pi 10^-7 *l/ 2\pi r[/tex]
By putting up the values needed from the data...
Current (I) = 2 x 3.14 x (3.0 x 10^-6) (2.0 x 10^-3) / 4 x 3.14 x 10^-7 = 3 x 10^-2 A
Answer: 0.03002A
Explanation: The formulae that relates the magnetic field strength B at a point (r) away from the center of a conductor carrying a current of value (I) is given below as
B = Uo×I/2πr
From our question, B =2.0×10^-3 T, r = 3.0×10^-6m
I =?, Uo = permeability of free space = 1.256×10^-6 mkg/s²A².
By substituting the parameters, we have that
2×10^-3 = 1.256×10^-6 × I/2π(3.0×10^-6)
2×10^-3 × 2π(3.0×10^-6) = 1.256×10^-6 × I
3.77×10^-8 = 1.256×10^-6 × I
I = 3.77×10^-8/ 1.256×10^-6
I = 3.002×10^-2 = 0.03002A
Determine the power required for a 1150-kg car to climb a 100-m-long uphill road with a slope of 308 (from horizontal) in 12 s (a) at a constant velocity, (b) from rest to a final velocity of 30 m/s, and (c) from 35 m/s to a final velocity of 5 m/s. Disregard friction, air drag, and rolling resistance.
Answers
Explanation:
Below is an attachment containing the solution.
Answer:
the question is incomplete, below is the complete question
"Determine the power required for a 1150-kg car to climb a 100-m-long uphill road with a slope of 30 (from horizontal) in 12 s (a) at a constant velocity, (b) from rest to a final velocity of 30 m/s, and (c) from 35 m/s to a final velocity of 5 m/s. Disregard friction, air drag, and rolling resistance."
a. [tex]47KW[/tex]
b. 90.1KW
c. -10.5KW
Explanation:
Data given
mass m=1150kg,
length,l=100m
angle, =30
time=12s
Note that the power is define as the rate change of the energy, note we consider the potiential and the
Hence
[tex]Power,P=\frac{energy}{time} \\P=\frac{mgh+1/2mv^{2}}{t}[/tex]
to determine the height, we draw the diagram of the hill as shown in the attached diagram
a. at constant speed, the kinetic energy is zero.Hence the power is calculated as
[tex]p=\frac{mgh}{t} \\p=\frac{1150*9.81*100sin30}{12}\\p=47*10^{3}W\\[/tex]
b.
for a change in velocity of 30m/s
we have the power to be
[tex]P=\frac{mgh}{t} +\frac{1/2mv^2}{t}\\ P=47Kw+\frac{ 0.5*1150*30^2}{12}\\ P=47kw +43.1kw\\P=90.1KW[/tex]
c. when i decelerate, we have the power to be
[tex]P=\frac{mgh}{t} +\frac{1/2mv^2}{t}\\ P=47Kw+\frac{ 0.5*1150*\\((5^2)-(35^2))}{12}\\ P=47kw -57.5kw\\P=-10.5KW[/tex]
You need to purchase a motor to supply 400 joules [J] in 10 seconds [s]. All of the motors you can choose from are 80% efficient. What is the minimum wattage [W] on the motor you need to choose
Answers
Answer:
32 W.
Explanation:
Power: This can be defined as the ratio of energy to time. The S.I unit of power is watt(W). The formula for power is given as,
P = W/t.................... Equation 1
Where P = power, W = work done, t = time.
Given: W = 400 J, t = 10 s.
Substitute into equation 1
P = 400/10
P = 40 W.
If the motors that is choose is 80% efficient,
P' = P(0.8)
Where P' = minimum power
P' = 40(0.8)
P' = 32 W.
A ball is rolling along at speed v without slipping on a horizontal surface when it comes to a hill that rises at a constant angle above the horizontal. In which case will it go higher up the hill: if the hill has enough friction to prevent slipping, or if the hill is perfectly smooth. Justify your answer with a conservation of energy statement
Answers
Final answer:
The ball will go higher up the hill if the hill has enough friction to prevent slipping.
Explanation:
The ball will go higher up the hill if the hill has enough friction to prevent slipping. This is because in the case where there is enough friction, the ball can convert some of its kinetic energy to rotational energy, allowing it to roll up the hill. The conservation of energy statement can be used to explain this:
When the ball rolls without slipping, its total mechanical energy is conserved.
As the ball rolls up the hill, its potential energy increases and its kinetic energy decreases.
In the case where there is enough friction, some of the kinetic energy is converted to rotational energy, allowing the ball to reach a higher height on the hill.
Therefore, the ball will go higher up the hill if the hill has enough friction to prevent slipping.
A block of mass m = 2.5 kg is attached to a spring with spring constant k = 940 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 29° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.11. In the initial position, where the spring is compressed by a distance of d = 0.13 m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational energy of the block as zero.
Required:
If the spring pushes the block up the incline, what distance, L in meters, will the block travel before coming to rest?
Answers
Final answer:
To find the distance L that the block will travel up the incline before stopping, we apply conservation of energy, accounting for the initial spring potential energy, the gravitational potential energy, and the work done against kinetic friction. By setting up the energy equation and substituting the given values, we can solve for L. Therefore, the value of L is approximately [tex]\( 0.25069 \)[/tex] m
Explanation:
To determine the distance L that the block will travel up the incline before coming to rest, we need to use the conservation of energy principle. The mechanical energy conserved will be the initial potential energy stored in the spring when compressed and the final kinetic energy of the block up the slope, taking into account the work done against friction.
Initially, the spring's potential energy (Us) is given by Us = 1/2 k d^2, where k is the spring constant and d is the compression distance. As the spring pushes the block up the incline, the block gains gravitational potential energy (Ug = mgh), does work against friction (Wf), and could have some residual kinetic energy (which is zero at the highest point).
The work done against friction can be found by Wf = μk N L, where μk is the coefficient of kinetic friction, N is the normal force (N=m*g*cos(θ)), and L is the distance traveled. Since we are considering the point where the block comes to rest, we set the total mechanical energy at this position equal to the initial energy.
Equating the initial and final energies we get: (1/2 k d^2) = mgh + μk m*g*cos(θ)L. We can now solve for L by plugging in the known values: m = 2.5 kg, k = 940 N/m, d = 0.13 m, μk = 0.11, g = 9.8 m/s^2, and θ = 29 degrees.
Substituting these values, we solve for L:
L = [(1/2) * 940 N/m * (0.13 m)^2 - 2.5 kg * 9.8 m/s^2 * sin(29 degrees)] / [2.5 kg * 9.8 m/s^2 * cos(29 degrees)* 0.11]
let's break it down step by step.
Given:
[tex]- Spring constant: \(k = 940 \, \text{N/m}\)\\- Displacement: \(x = 0.13 \, \text{m}\)\\- Mass: \(m = 2.5 \, \text{kg}\)\\- Gravitational acceleration: \(g = 9.8 \, \text{m/s}^2\)\\- Angle: \(\theta = 29^\circ\)\\- Length: \(l = 0.11 \, \text{m}\)[/tex]
Let's calculate it step by step:
1. Calculate the potential energy stored in the spring using the formula:
[tex]\[ U_{\text{spring}} = \frac{1}{2} k x^2 \][/tex]
Substitute the given values:
[tex]\[ U_{\text{spring}} = \frac{1}{2} \times 940 \, \text{N/m} \times (0.13 \, \text{m})^2 \]\[ U_{\text{spring}} = \frac{1}{2} \times 940 \times 0.0169 \, \text{N} \cdot \text{m}^2 \]\[ U_{\text{spring}} = 7.963 \, \text{J} \][/tex]
2. Calculate the gravitational potential energy using the formula:
[tex]\[ U_{\text{gravitational}} = mgh \]\\where \( h \) is the vertical height.\[ h = l \sin(\theta) \]\[ h = 0.11 \, \text{m} \times \sin(29^\circ) \]\[ h \approx 0.055 \, \text{m} \][/tex]
Substitute the values into the gravitational potential energy formula:
[tex]\[ U_{\text{gravitational}} = 2.5 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 0.055 \, \text{m} \]\[ U_{\text{gravitational}} = 1.3525 \, \text{J} \][/tex]
3. Now, plug these values into the given expression:
[tex]\[ L = \frac{(7.963 \, \text{J} - 1.3525 \, \text{J})}{(2.5 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times \cos(29^\circ) \times 0.11 \, \text{m})} \][/tex]
Let's evaluate the denominator first:
[tex]\[ 2.5 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times \cos(29^\circ) \times 0.11 \, \text{m} \]\[ = 2.5 \times 9.8 \times \cos(29^\circ) \times 0.11 \]\[ \approx 26.368 \][/tex]
Now, let's plug it back into the expression:
[tex]\[ L = \frac{(7.963 \, \text{J} - 1.3525 \, \text{J})}{26.368} \]\[ L = \frac{6.6105}{26.368} \]\[ L \approx 0.25069 \][/tex]
Therefore, the value of L is approximately [tex]\( 0.25069 \)[/tex] m.
A 1200-kg car, initially moving at 20 m/s, comes to a stop at a red light over a time of 3 s from the moment the driver hit the brakes. What is the impulse delivered to the car by the static friction force (assumed constant) between the road and the tires
Answers
Answer:
Explanation:
Mass of car (M)=1200kg
Initial velocity (u)=20m/s
Stop after time (t)=3sec.
Come to stop implies that the final velocity is zero, v=0m/s
Using newton second law of motion
F=m(v-u)/t
Ft=m(v-u)
Since impulse is Ft
I=Ft
Then, I=Ft=m(v-u)
I=m(v-u)
I=1200(0-20)
I=1200×-20
I=-24,000Ns
The impulse delivered to the car by static friction is -24,000Ns
The impulse delivered to the car by static friction is -24,000Ns
Calculation of the impulse:Since A 1200-kg car, initially moving at 20 m/s, comes to a stop at a red light over a time of 3 s from the moment the driver hit the brakes.
Now here we used second law of motion of newton.
F=m(v-u)/t
Ft=m(v-u)
Since impulse is Ft
So,
I=Ft
Now
, I=Ft=m(v-u)
So,
I=m(v-u)
I=1200(0-20)
I=1200×-20
I=-24,000Ns
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Place several E-Field Sensors at a few points on different equipotential lines, and look at the relationship between the electric field and the equipotential lines. Which statement is true?
1-At any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of higher voltages.
2-At any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of lower voltages.
3-At any point, the electric field is parallel to the equipotential line at that point.
Answers
Answer:
2.
Explanation:
If a charge is moved along a equipotential line, no work is done on the charge.If we remember that the work done by an external force, is just the product of the component of the force parallel to the displacement, if the force produces no work, this means that is perpendicular to the displacement.So, as the electric field is just the force per unit charge, and has the same direction as the force (for a positive charge), it must be perpendicular to any equipotential line.As the electric field (by convention) has the same direction as it would be taken by a positive test charge, and positive charges move from higher voltages to lower ones, the electric field is directed toward lines of lower voltages (like it happens between the plates of a capacitor).Suppose that a meter stick is balanced at its center. A 0.11 kg mass is then positioned at the 17-cm mark. At what cm mark must a 0.38 kg mass be placed to balance the 0.11 kg mass
Answers
Answer:
59.55 cm
Explanation:
Note: A meter stick has a length of 100 cm, and it is balanced at 50 cm.
From the principle of moment,
Sum of clockwise moment = sum of anti clockwise moment
Taking moment about the center
mg(50-x) = m'(y-50)g.................. Equation 1
Where m = first mass, m' = second mass, x = position of the first mass, y = position of the second mass, g = acceleration
make y the subject of the equation
y = (m(50-x)/m')+50.................... Equation 2
y = (0.11(50-17)/0.38)+50
y = (0.11(33)/0.38)+50
y = 9.55+50
y = 59.55 cm
In a cloud chamber experiment, a proton enters a uniform 0.280 T magnetic field directed perpendicular to its motion. You measure the proton's path on a photograph and find that it follows a circular arc of radius 6.12 cm. How fast was the proton moving?
Answers
Answer:
The proton was moving at a speed of 1.64 x 10⁶ m/s
Explanation:
Given;
strength of magnetic field, B = 0.280 T
circular radius, R = 6.12 cm
mass of proton, m = 1.67 x 10⁻²⁷ kg
charge of electron. q = 1.602 x 10⁻¹⁹ C
When the proton follows a circular arc, then magnetic force will be equal to the centripetal force.
Magnetic force, Fm = qvB
Centripetal force, Fr = mv²/R
Fm = Fr
qvB = mv²/R
[tex]qvB = \frac{Mv^2}{R} \\\\\frac{qBR}{M} = \frac{v^2}{v} \\\\v =\frac{qBR}{M} = \frac{1.602*10^{-19} *0.28*0.0612}{1.67*10^{-27}} =1.64 *10^6 \ m/s[/tex]
Therefore, the proton was moving at a speed of 1.64 x 10⁶ m/s
Given Information:
Magnetic field = B = 0.280 T
Radius = r = 6.12 cm = 0.0612 m
Required Information:
Speed of proton = v = ?
Answer:
Speed of proton = v = 1641.77x10³ m/s
Explanation:
Since the proton is moving in a circular path we can model it in terms of magnetic force and centripetal force.
The magnetic force is given by
F = qvB
The centripetal force is given by
F = mv²/r
equating the both equations yields,
mv²/r = qvB
mv = qBr
v = qBr/m
Where q = 1.6x10⁻¹⁹ C is the of the proton, m = 1.67x10⁻²⁷ kg is the mass of proton, B is the magnetic field and r is the radius o circular arc around which proton is moving.
v = 1.6x10⁻¹⁹*0.280*0.0612/1.67x10⁻²⁷
v = 1641772.45 m/s
v = 1641.77x10³ m/s
Therefore, the proton is moving at the speed of 1641.77x10³ m/s.
When the temperature of 2.35 m^3 of a liquid is increased by 48.5 degrees Celsius, it expands by 0.0920 m^3. What is its coefficient of volume expansion?
Answers
Answer:
a liquid is increased by 48.5 degrees Celsius, it expands by 0.0920 m^3. Explanation:
The coefficient of volume expansion is [tex]0.000810 \, \text{per} \, ^\circ\text{C}.[/tex]
The coefficient of volume expansion (\(\beta\)) can be calculated using the formula:
[tex]\[\Delta V = V_0 \beta \Delta T\][/tex]
where:
- [tex]\(\Delta V\)[/tex] is the change in volume,
- [tex]\(V_0\)[/tex] is the initial volume,
- [tex]\(\beta\)[/tex] is the coefficient of volume expansion,
- [tex]\(\Delta T\)[/tex] is the change in temperature.
We need to solve for [tex]\(\beta\):[/tex]
[tex]\[\beta = \frac{\Delta V}{V_0 \Delta T}\][/tex]
Substituting the given values:
[tex]\[\beta = \frac{0.0920 \, \text{m}^3}{2.35 \, \text{m}^3 \times 48.5 \, ^\circ\text{C}}\][/tex]
First, calculate the denominator:
[tex]\[2.35 \, \text{m}^3 \times 48.5 \, ^\circ\text{C} = 113.575 \, \text{m}^3 \cdot ^\circ\text{C}\][/tex]
Now, calculate [tex]\(\beta\)[/tex]:
[tex]\[\beta = \frac{0.0920 \, \text{m}^3}{113.575 \, \text{m}^3 \cdot ^\circ\text{C}}\][/tex]
[tex]\[\beta \approx 0.000810 \, \text{per} \, ^\circ\text{C}\][/tex]
Therefore, the coefficient of volume expansion is approximately [tex]\[\beta \approx 8.10 \times 10^{-4} \, ^\circ\text{C}^{-1}\][/tex].
A farmer uses a tractor to pull a 150 kg bale of hay up a 15∘ incline to the barn at a steady 5.0 km/h. The coefficient of kinetic friction between the bale and the ramp is 0.40.Part A What is the tractor's power output?
Answers
Answer:
the tractor's power output = 1318.47 watts
Explanation:
Weight of bale = (mg) = (150 kg * 9.81 m/s²) = 1471.5 newtons
Resolve that weight force into its components at right angles to the ramp and parallel to the slope.
Down the slope we have 1471.5sin(15°) = 380.85 N
At right angles to the ramp we have 1471.5cos(15°) = 1421.35 N
OK, now we need the relationship between the coefficient of friction (μ), the friction force (Ff) and the normal force (Fn) {The normal force is the force at right angles to the friction surface. In this case Fn is equal in magnitude to the component of weight force at right angles to the surface.}
Ff = μ * Fn = (0.40 * 1421.35) = 568.54 N
The bale is not accelerating, so the "pull force" up the incline = component of weight + friction force down
= (380 N + 568.54 N)
= 948.54N
We need the speed in m/s not km/h
5.0 km/h = 5000 m/h
= (5000/3600)
= 1.39 m/s
Power = (948.54 N * 1.39m/s)
= 1318.47 N.m/s
= 1318.47 watts
The power output of the tractor is 1318.47 W
Power:According to the question the weight of bale
mg = 150 × 9.81 = 1471.5 N
Resolving the weight we get:
The normal reaction perpendicular to the ramp is given by:
N = 1471.5cos(15°) = 1421.35 N
The force of friction is given by:
[tex]f = \mu N = 0.40 \times 1421.35\\\\f = 568.54 N[/tex]
The bale is not accelerating, so the force up the incline = component of weight + friction force down
F = mgsin(15°) + f
F = 380 N + 568.54 N
F = 948.54N
Now, the engine speed is:
v = 5.0 km/h = 5000 m/h
v = (5000/3600)
v = 1.39 m/s
The power is defined as the product of force and speed, so:
Power P = Fv
P = 948.54 × 1.39
P = 1318.47 W
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A horizontal board of length 6.1 m and mass 12.8 kg rests on two supports. The first support is at one end of the board. The second support is at a distance of 2.38 m from the other end of the board. What force does this second support exert on the board
Answers
Answer:102.84 N
Explanation:
Given
Mass of board [tex]m=12.8\ kg[/tex]
Length of board [tex]l=6.1\ m[/tex]
First support is at one end and second support is at a distance of 2.38 m from the other end
Suppose [tex]R_1[/tex] and [tex]R_2[/tex] are the reactions at the two support
Taking moment about the first end we can write
[tex]mg\times \dfrac{6.1}{2}-R_2(6.1-2.38)=0[/tex]
[tex]R_2=\dfrac{12.8\times 9.8 \times 3.05}{3.72}[/tex]
[tex]R_2=102.84\ N[/tex]