To find the magnitude and direction of the resultant vector, use the Pythagorean theorem and inverse tangent function respectively.
Explanation:To find the magnitude of the resultant vector, we can use the Pythagorean theorem. The resultant vector is the sum of the three force vectors: F1, F2, and F3. We can find the x and y components of each vector using trigonometry, and then add the components to find the x and y components of the resultant vector. Finally, we can use the Pythagorean theorem to find the magnitude of the resultant vector.
To find the direction of the resultant vector, we can use the inverse tangent function to find the angle between the positive x-axis and the resultant vector. Since the problem specifies that angles are measured counterclockwise from the positive x-axis, we need to make sure the angle is within the range of -180° to +180°. If the angle is greater than 180°, we subtract 360° to get the equivalent angle within the specified range.
The magnitude of the resultant vector is 95.2 N and the direction is -95.5°.
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A small box of mass m1 is sitting on a board of mass m2 and length L. The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is μs. The coefficient of kinetic friction between the board and the box is, as usual, less than μs.
Throughout the problem, use g for the magnitude of the acceleration due to gravity. In the hints, use Ff for the magnitude of the friction force between the board and the box.
uploaded image
Find Fmin, the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box (which will then fall off of the opposite end of the board).
Express your answer in terms of some or all of the variables mu_s, m_1, m_2, g, and L. Do not include F_f in your answer.
Answer: Fmin = (m₁ + m₂) μsg
Explanation:
To begin, we would first define the parameters given in the question.
Mass of the box = m₁
Mass of the board = m₂
We have a Frictionless surface given that Fr is acting as the frictional force between the box and the board.
from our definition of force, i.e. the the frictional force against friction experienced by the box, we have
Fr = m₁a ...................(1)
Also considering the force between the box and the board gives;
Fr = μsm₁g .................(2)
therefore equating both (1) and (2) we get
m₁a = μsm₁g
eliminating like terms we get
a = μsg
To solve for the minimum force Fmin that must be applied to the board in order to pull the board out from under the box, we have
Fmin = (m₁ + m₂) a ...........(3)
where a = μsg, substituting gives
Fmin = (m₁ + m₂) μsg
cheers i hope this helps
The constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box is [tex]\mu_{s} g({m_{1}+m_{2}})[/tex].
Given data:
The mass of small box is, [tex]m_{1}[/tex].
The mass of board is, [tex]m_{2}[/tex].
The length of board is, L.
The coefficient of static friction between the board and box is, [tex]\mu_{s}[/tex].
The linear force acting between the box and the board provides the necessary friction to box. Therefore,
[tex]F=F_{f}\\F=\mu_{s}m_{1}g\\m_{1} \times a = \mu_{s} \times m_{1}g\\a= \mu_{s} \times g[/tex]
a is the linear acceleration of board.
Then, the minimum force applied on the board is,
[tex]F_{min}=({m_{1}+m_{2}})a\\F_{min}=({m_{1}+m_{2}})(\mu_{s} \times g)\\F_{min}=\mu_{s} g({m_{1}+m_{2}})[/tex]
Thus, the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box is
[tex]\mu_{s} g({m_{1}+m_{2}})[/tex].
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When Raymond observes certain natural phenomena, he often forms ideas about their causes and effects. Suppose that Raymond surmises that leaves change color in autumn due to scarcity of sunlight. In order to test whether his idea is accurate, he must first construct a falsifiable that defines a clear relationship between two variables. Raymond's next step is to that would isolate and test the relationship between the two variables. This task can be pretty daunting because Raymond will need to identify and eliminate any variables that could confuse test results.
Answer:
The student needs to group variables into dimensionless quantities.
Explanation:
Large experiments take a lot of time to perform because the significant variables need to be separated from the non-significant variables. However, for large quantities of variables, it is necessary to focus on the key variables.
One technique to do that is to use the Buckingham Pi Theorem. The theorem states that the physical variables can be expressed in terms or independent fundamental physical quantities. In other words:
P = n- k
n = total number of quantities
k = independent physical quantities.
A place to start with will be to find dimensionless quantities involving the mass, length, time, and at times temperature. These units are given as M, L, T, and Θ
The grouping helps because it eliminates unwanted and unnecessary experiments.
Answer:
I just took the test, It's hypothesis then design an experiment, the last one i got wrong but its not dependent. hope that helped a little.
What possible source of errors would be in this experiment besides human error and why?
Explanation:
Besides human error, other sources of error include friction on the cart (we assumed there is no friction, but in reality, that's never the case), and instrument errors (imprecision in the spring scale).
Besides human error, experiments can also encounter sampling errors, nonsampling errors, uncertainty factors, and spontaneous errors. These can be caused by an inaccurate sampling process, equipment malfunctions, variability in samples, and limitations in the measuring device.
Explanation:Possible sources of error in an experiment, besides human error, could include sampling errors and non-sampling errors. Sampling errors occur when the sample utilized may not be large enough or not accurately representative of the larger population.
This can lead to inaccurate assumptions and conclusions. Non-sampling errors, on the other hand, are unrelated to the sampling process and could be a result of equipment or instrument malfunction (like a faulty counting device). An example for this would be an uncertainty in measurement induced by the fact that smallest division on a measurement ruler is 0.1 inches.
Further, variability in samples can also lead to errors called spontaneous errors. These can be due to natural phenomena such as exposure to ultraviolet or gamma radiation, or to intercalating agents. Lastly, uncertainty factors can contribute to errors as well. These factors include limitations of the measuring device, inaccuracies caused by the instrument itself (e.g., a paper cutting machine that causes one side of the paper to be longer than the other).
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John performs an experiment on an electric circuit. He increases the voltage from 25 volts to 50 volts while keeping the resistance constant. What will be the effect of John's changes on the current?
The current will double
Explanation:
The relationship between voltage and current in an electric circuit is given by the following equation (Ohm's law):
[tex]V=IR[/tex]
where
V is the voltage
I is the current
R is the resistance
making R the subject,
[tex]R=\frac{V}{I}[/tex]
Since in this experiment the resistance is kept constant, we can write:
[tex]\frac{V_1}{I_1}=\frac{V_2}{I_2}[/tex]
where
[tex]V_1=25 V[/tex] is the voltage in the 1st experiment
[tex]V_2=50 V[/tex] is the voltage in the 2nd experiment
[tex]I_1,I_2[/tex] are the currents in the 1st and 2nd experiment
We can re-arrange the equation as
[tex]\frac{I_2}{I_1}=\frac{V_2}{V_1}=\frac{50}{25}=2[/tex]
This means that the current will double in the 2nd experiment.
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Two manned satellites approaching one another at a relative speed of 0.150 m/s intend to dock. The first has a mass of 4.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite. (a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest. Incorrect: Your answer is incorrect. m/s (b) What is the loss of kinetic energy in this inelastic collision? Incorrect: Your answer is incorrect. J (c) Repeat both parts, in the frame of reference in which the second satellite was originally at rest. final velocity Incorrect: Your answer is incorrect. Check the sign of your answer for velocity in part (c). m/s loss of kinetic energy Correct: Your answer is correct. J
a) Final velocity after docking: +0.094 m/s
b) Kinetic energy loss: 31.6 J
c) Final velocity after docking: -0.056 m/s
d) Kinetic energy loss: 31.6 J
Explanation:
a)
Since the system of two satellites is an isolated system, the total momentum is conserved. So we can write:
[tex]p_i = p_f[/tex]
Or
[tex]m_1 u_1 + m_2 u_2 = (m_1 + m_2)v[/tex]
where, in the reference frame in which the first satellite was originally at rest, we have:
[tex]m_1 = 4.50\cdot 10^3 kg[/tex] is the mass of the 1st satellite
[tex]m_2 = 7.50\cdot 10^3 kg[/tex] is the mass of the 2nd satellite
[tex]u_1 = 0[/tex] is the initial velocity of the 1st satellite
[tex]u_2 = +0.150 m/s[/tex] is the initial velocity of the 2nd satellite
v is their final velocity after docking
Solving for v,
[tex]v=\frac{m_2 u_2}{m_1 +m_2}=\frac{(7.50\cdot 10^3)(0.150)}{4.50\cdot 10^3 + 7.50\cdot 10^3}=0.0938 m/s[/tex]
b)
The initial kinetic energy of the system is just the kinetic energy of the 2nd satellite:
[tex]K_i = \frac{1}{2}m_2 u_2^2 = \frac{1}{2}(7.50\cdot 10^3)(0.150)^2=84.4 J[/tex]
The final kinetic energy of the two combined satellites is:
[tex]K_f = \frac{1}{2}(m_1 +m_2)v^2=\frac{1}{2}(4.50\cdot 10^3+7.50\cdot 10^3)(0.0938)^2=52.8 J[/tex]
Threfore, the loss in kinetic energy during the collision is:
[tex]\Delta K = K_f - K_i = 52.8 - 84.4=-31.6 J[/tex]
c)
In this case, we are in the reference frame in which the second satellite is at rest. So, we have
[tex]u_2 = 0[/tex] (initial velocity of satellite 2 is zero)
[tex]u_1 = -0.150 m/s[/tex] (initial velocity of a satellite 1)
Therefore, by applying the equation of conservation of momentum,
[tex]m_1 u_1 + m_2 u_2 = (m_1 + m_2)v[/tex]
And solving for v,
[tex]v=\frac{m_1 u_1}{m_1 +m_2}=\frac{(4.50\cdot 10^3)(-0.150)}{4.50\cdot 10^3 + 7.50\cdot 10^3}=-0.0563 m/s[/tex]
d)
The initial kinetic energy of the system is just the kinetic energy of satellite 1, since satellite 2 is at rest:
[tex]K_i = \frac{1}{2}m_1 u_1^2 = \frac{1}{2}(4.50\cdot 10^3)(-0.150)^2=50.6 J[/tex]
The final kinetic energy of the system is the kinetic energy of the two combined satellites after docking:
[tex]K_f = \frac{1}{2}(m_1 + m_2)v^2=\frac{1}{2}(4.50\cdot 10^3+ 7.50\cdot 10^3)(-0.0563)^2=19.0 J[/tex]
Therefore, the kinetic energy lost in the collision is
[tex]\Delta K = K_f - K_i = 19.0 -50.6 = -31.6 J[/tex]
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A 2,000 kg car starts from rest and coasts down from the top of a 5.00 m long driveway that is sloped at an angel of 20o with the horizontal. If an average friction force of 4,000 N impedes the motion of the car, find the speed of the car at the bottom of the driveway.
Answer:
The speed at the bottom of the driveway is3.67m/s.
Explanation:
Height,h= 5sin20°= 1.71m
Potential energy PE=mgh= 2000×9.8×1.71
PE= 33516J
KE= PE- Fk ×d
0.5mv^2= 33516 - (4000×5)
0.5×2000v^2= 33516 - 20000
1000v^2= 13516
v^2= 13516/1000
v =sqrt 13.516
v =3.67m/s
What sentence(s) is/are true when we talk about equipotential lines?
a. Electric potential is the same along an equipotential line
b. Work is necessary to move a charged particle along these lines.
c. They are always perpendicular to electric field lines
d. They are always parallel to electric field lines
Answer:
a. True
Explanation:
Equipotential lines are the imaginary lines in the space where actually the electric potential is same at each and every point.
Work is not required to move along such points of the equipotential line because the movement is always perpendicular to the electric field lines because these lines are always perpendicular to the electric field lines.
The electric potential for a point charge is given mathematically as:
[tex]V=\frac{1}{4\pi.\epsilon_0}\times \frac{Q}{r}[/tex]
where:
[tex]Q=[/tex] magnitude of the point charge
[tex]r=[/tex] radial distance form the charge
[tex]\epsilon_0=[/tex] permittivity of free space
Equipotential lines in physics are lines where the electric potential remains constant, perpendicular to electric field lines, and require no work to move a charge along them.
Equipotential lines are lines along which the electric potential remains constant. These lines are perpendicular to the electric field lines. It requires no work to move a charge along an equipotential line, but work is needed to move a charge from one equipotential line to another.
A tennis ball has a mass of 0.059 kg. A professional tennis player hits the ball hard enough to give it a speed of 41 m/s (about 92 miles per hour.) The ball moves toward the left, hits a wall and bounces straight back to the right with almost the same speed (41 m/s).
A) What is the average speed of the ball during the period from first contact with the wall to the moment the ball's speed is momentarily zero?
B) How much time elapses between first contact with the wall, and coming to a stop?
C) What is the magnitude of the average force exerted by the wall on the bal dring contact?
D) In contrast, what is the magnitude of the gravitational force of the Earth on the ball?
There is an omission of some sentences in the question which affects the answering of question B and C, so we will based the omission of the sentences on assumption in order to solve the question that falls under it.
NOTE: The omitted sentences are written in bold format
A tennis ball has a mass of 0.059 kg. A professional tennis player hits the ball hard enough to give it a speed of 41 m/s (about 92 miles per hour.) The ball moves toward the left, hits a wall and bounces straight back to the right with almost the same speed (41 m/s).
As indicated in the diagram below, high-speed photography shows that the ball is crushed about d = 2.0 cm at the instant when its speed is momentarily zero, before rebounding.
A) What is the average speed of the ball during the period from first contact with the wall to the moment the ball's speed is momentarily zero?
B) How much time elapses between first contact with the wall, and coming to a stop?
C) What is the magnitude of the average force exerted by the wall on the bal dring contact?
D) In contrast, what is the magnitude of the gravitational force of the Earth on the ball?
Answer:
a) [tex]V_{avg} = 20.5m/s[/tex]
b) 9.76 × 10⁻⁴s
c) 247.9 N
d) 5.8 N
Explanation:
Given that;
Initial speed [tex](V_i)[/tex] = 0
Final speed [tex](V_f)[/tex] = 41 m/s
Distance (d) = 0.002
mass (m) = 0.059 kg
g = 9.8 m/s²
a)
The average speed of the ball can be calculated as;
[tex]V_{avg} = \frac{V_i+V_f}{2}[/tex]
[tex]V_{avg} = \frac{0+41}{2}[/tex]
[tex]V_{avg} = 20.5m/s[/tex]
b)
The time elapsed can be calculated by using the second equation of motion which is given as:
[tex]S=(\frac{V_i+V_f}{2})t[/tex]
If we make time (t) the subject of the formula; we have:
[tex](V_i+V_f)t=2S[/tex]
[tex]t= (\frac{2S}{V_I+V_f})[/tex]
[tex]=\frac{2(0.02)}{41+0}[/tex]
[tex]=\frac{0.04}{41}[/tex]
= 0.000976
=9.76 × 10⁻⁴s
c)
the magnitude of the average force (F) exerted by the wall on the bal dring contact can be determined using;
Force (F) = mass × acceleration
where acceleration [tex](a)= \frac{Vo}{t}[/tex]
[tex]\frac{41}{0.00976}[/tex]
acceleration (a) = 4200.82 m/s²
F = m × a
= 0.059 × 4200.82
= 247.85
≅ 247.9 N
d)
the magnitude of the gravitational force of the Earth on the ball
Force (F) = mass (m) × gravity (g)
= 0.059kg × 9.8 m/s²
= 5.782 N
≅ 5.8 N
The average speed of the tennis ball during contact with the wall is zero, and without the time of contact, we cannot determine the time elapsed or the average force exerted by the wall. However, the gravitational force on the ball is 0.5782 N.
Explanation:The question relates to the change in momentum and the forces involved when a tennis ball bounces off a wall. Specifically, a tennis ball with a mass of 0.059 kg is hit at a speed of 41 m/s, bounces off a wall, and comes back at the same speed. To tackle the posed questions, it is essential to apply concepts from Newton's laws of motion and the conservation of momentum.
Part AThe average speed of the ball during contact is zero since the speed decreases uniformly from 41 m/s to zero.
Part BWithout the time of contact with the wall, this cannot be determined. Previous examples of collisions show time of contact can vary, so it must be provided to answer this part of the question.
Part CTo calculate the magnitude of the average force exerted by the wall on the ball, we would need the time of contact with the wall. Since it is not given, this cannot be calculated accurately.
Part DThe magnitude of the gravitational force of the Earth on the ball is calculated as the product of the mass of the ball and the acceleration due to gravity (9.8 m/s²), which is 0.059 kg * 9.8 m/s² = 0.5782 N.
A horse pulls on an object with a force of 300 newtons and does 12,000 joules of work. How far was the object moved?
1. 40
2. 0.03
3. 5 ×10↑5
4. 10 ×10↑4
Answer:
1.
Explanation:
because 12,000 divided by 300 is 40 so its 40m
In order to ensure that a cable is not affected by electromagnetic interference, how far away should the cable be from fluorescent lighting?
Answer:
the answer is at least 3 feet
Explanation:
In order to ensure that a cable is not affected by electromagnetic interference, it should be at least 3 feet away from fluorescent lighting.
This is because, cables can be adversely affected by electromagnetic interference - which is a disturbance that affects an electrical circuit due to either electromagnetic induction or radiation emitted from an external source - and insulation alone cannot provide adequate protection for these cables.
Therefore, the cables should be kept a few feet away from flourescent lighting in order to prevent this interference.
To minimize the EMI on a cable from fluorescent lighting, it should be kept at a distance of at least 2 feet or 0.6 meters. The distance can vary depending on the cable type, the electromagnetic field size and the data's sensitivity.
Explanation:To minimize the electromagnetic interference (EMI) effect on a cable from fluorescent lighting, it is recommended to maintain a distance of at least 2 feet or 0.6 meters. This is because the fluorescent light produces a magnetic field that can interact with the cable and cause electromagnetic interference. The above mentioned distance is considered a safe threshold, yet it can vary depending on the type of cable, the strength of the electromagnetic field produced by the light and the sensitivity of the data being transmitted.
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One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at a frequency 129 Hz. The other end passes over a pulley and supports a mass of 1.50 kg. The linear mass density of the rope is 0.0590 kg/m. What is the speed of a transverse wave on the rope? What is the wavelength? How would your answers to parts (a) and (b) be changed if the mass were increased to 2.80 kg?
Answer:
(a). The speed of transverse wave on the rope is 15.78 m/s.
(b). The wavelength is 0.122 m.
(c). The changed speed of transverse wave on the rope is 21.56 m/s.
The changed wavelength is 0.167 m.
Explanation:
Given that,
Frequency = 129 Hz
mass = 1.50 kg
Linear mass density of the rope = 0.0590 kg/m
(a). We need to calculate the speed of a transverse wave on the rope
Using formula of speed
[tex]v=\sqrt{\dfrac{T}{\mu}}[/tex]
Put the value into the formula
[tex]v=\sqrt{\dfrac{1.50\times9.8}{0.0590}}[/tex]
[tex]v=15.78\ m/s[/tex]
(b). We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda =\dfrac{v}{f}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{15.78}{129}[/tex]
[tex]\lambda=0.122\ m[/tex]
(c). If the mass were increased to 2.80 kg.
We need to calculate the speed of a transverse wave on the rope
Using formula of speed
[tex]v=\sqrt{\dfrac{T}{\mu}}[/tex]
Put the value into the formula
[tex]v=\sqrt{\dfrac{2.80\times9.8}{0.0590}}[/tex]
[tex]v=21.56\ m/s[/tex]
We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda =\dfrac{v}{f}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{21.56}{129}[/tex]
[tex]\lambda=0.167\ m[/tex]
Hence, (a). The speed of transverse wave on the rope is 15.78 m/s.
(b). The wavelength is 0.122 m.
(c). The changed speed of transverse wave on the rope is 21.56 m/s.
The changed wavelength is 0.167 m.
The speed of the transverse wave on the rope is 2.48 m/s and the wavelength is 0.019 m. If the mass were increased to 2.80 kg, the speed of the wave would stay the same but the wavelength would be different.
Explanation:To find the speed of a transverse wave on the rope, we can use the equation:
v = √(T/μ)
where v is the speed of the wave, T is the tension in the rope, and μ is the linear mass density of the rope. Plugging in the values given in the question, we get:
v = √(1.50 kg * 9.8 m/s^2 / 0.0590 kg/m) = 2.48 m/s
To find the wavelength of the wave, we can use the equation:
λ = v/f
where λ is the wavelength, v is the speed of the wave, and f is the frequency of the tuning fork. Plugging in the values given in the question, we get:
λ = 2.48 m/s / 129 Hz = 0.019 m
If the mass were increased to 2.80 kg, the speed of the wave on the rope would remain the same. However, the wavelength would be different because it is determined by the frequency of the tuning fork and the speed of the wave, not the mass of the hanging weight.
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You are an evolutionary biologist studying a population of bats in the rain forest in Brazil. Most of the population possesses moderate length wings, although some individuals have long wings and some individuals have short wings. Over the course of time, you notice that the frequency of moderate-length wings increases. You conclude that the most likely cause of this development is:
a. diversifying natural selection
b. stabilizing natural selection.
c. directional natural selection.
d. co-evolution.
Answer:
Option (B)
Explanation:
In the stabilizing natural selection, the extreme traits from both the ends are eliminated by natural selection and natural selection favors the intermediate trait. So over time individuals having the intermediate traits are selected over the individuals having extreme traits.
So here the population of the bat which possesses moderate wing length is selected over the individual with extreme traits like individuals with short wings and long wings. As a result, the population of moderate length wing bats increased.
Therefore the correct answer is (B)- stabilizing natural selection.
A car accelerates uniformly from rest to 20 m/sec in 5.6 sec along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if (a) the weight of the car is 9,000 N, and (b) the weight of the car is 14,000 N.
Answer:
(a) [tex]P=33000W[/tex]
(b) [tex]P=51000W[/tex]
Explanation:
The average power is defined as the amount of work done during a time interval:
[tex]P=\frac{W}{t}(1)[/tex]
According to work-energy theorem, the work done is equal to the change in kinetic energy. So, we have:
[tex]W=\Delta K\\W=K_f-K_0\\W=\frac{mv_f^2}{2}-\frac{mv_0^2}{2}\\(2)[/tex]
Recall that the weight is given by:
[tex]w=mg\\m=\frac{w}{g}(3)[/tex]
The car accelerates uniformly from rest ([tex]v_0=0[/tex]). Replacing (3) in (2), we have:
[tex]W=\frac{wv_f^2}{2g}[/tex]
(a) Finally, we replace this in (1):
[tex]P=\frac{wv_f^2}{2gt}\\P=\frac{9000N(20\frac{m}{s})^2}{2(9.8\frac{m}{s^2})(5.6s)}\\P=33000W[/tex]
(b)
[tex]P=\frac{14000N(20\frac{m}{s})^2}{2(9.8\frac{m}{s^2})(5.6s)}\\P=51000W[/tex]
(a) The average power required to accelerate the car of 9000 N is 32798.57 W.
(b) The average power required to accelerate the car of 14,000 N is 51020.40 W.
Given data:
The initial velocity of car is, u = 0 m/s. (Since car was initially at rest)
The final velocity of car is, v = 20 m/s.
The time interval is, t = 5.6 s.
The given problem is based on the concept of average power. The average power is defined as the amount of work done during a time interval. Then,
P = W/t
Here, W is the work done and its value is obtained from the work - energy theorem as,
[tex]W = \Delta KE\\\\W = \dfrac{1}{2}m(v^{2}-u^{2})[/tex]
Here, m is the mass.
(a)
For the weight of 9000 N, the mass of car is,
[tex]w = mg\\\\9000 = m \times 9.8\\\\m =918.36 \;\rm kg[/tex]
So, the Work is obtained as,
[tex]W =\dfrac{1}{2} \times 918.36 \times (20^{2}-0^{2})\\\\W =183672\;\rm J[/tex]
Then, the average power required to accelerate the car is,
P = W/t
P = 183672 / 5.6
P = 32798.57 W
Thus, we can conclude that the average power required to accelerate the car of 9000 N is 32798.57 W.
(b)
For the weight of 14,000 N, the mass of car is,
[tex]w = mg\\\\14,000 = m \times 9.8\\\\m =1428.57 \;\rm kg[/tex]
So, the Work is obtained as,
[tex]W =\dfrac{1}{2} \times 1428.57.36 \times (20^{2}-0^{2})\\\\W =285714.28\;\rm J[/tex]
Then, the average power required to accelerate the car is,
P = W/t
P = 285714.28 / 5.6
P = 51020.40 W
Thus, we can conclude that the average power required to accelerate the car of 14,000 N is 51020.40 W.
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Two climates that are at the same latitude may be different because of ____.
A) bodies of water
B) distance from the poles
C) earth’s magnetic field
D) soil type
Answer: Bodies of water
Explanation:
Large bodies of water, such as oceans, seas and large lakes, can affect the climate of an area
The child then walks towards the center of the merry-go-round and stops at a distance 0.455 m from the center. Now what is the angular velocity of the merry-go-round? Answer in units of rad/s.
Final answer:
The new angular velocity of the merry-go-round can be calculated using the conservation of angular momentum. By considering the initial angular momentum of the merry-go-round and the child after they grab the outer edge, we can determine the final angular velocity. The new angular velocity is approximately 0.414 rad/s.
Explanation:
To calculate the new angular velocity of the merry-go-round, we can use the conservation of angular momentum. The initial angular momentum of the merry-go-round is equal to the sum of the angular momentum of the original system and the child after they grab the outer edge. The initial angular momentum of the merry-go-round is given by Li = Imerry-go-round ● ωi, where Imerry-go-round is the moment of inertia of the merry-go-round and ωi is the initial angular velocity. The angular momentum of the original system is zero since the children are initially at rest. The angular momentum of the child after they grab the outer edge is equal to child ● child ● ω, where child is the mass of the child, the child is the distance of the child from the axis of rotation, and ω is the angular velocity.
Applying the principle of conservation of angular momentum, we have:
Li = (Imerry-go-round + child ● child) ● ωf
Solving for ωf, we get:
ωf = Li / (Imerry-go-round + child ● child)
Substituting the given values, we have:
ωf = (1000.0 kg.m² ● 6.0 rev/min) / (1000.0 kg.m² + 22.0 kg ● 0.455 m)
Converting rev/min to rad/s, we get:
ωf = (1000.0 kg.m² ● (6.0 rev/min ● 2π rad/rev) / (60 s/min)) / (1000.0 kg.m² + 22.0 kg ● 0.455 m)
Simplifying the expression, we find that the new angular velocity of the merry-go-round is approximately 0.414 rad/s.
An electron beam in an oscilloscope is deflected by the electric field produced by oppositely charged metal plates. If the electric field between the plates is 2.07 x 105 N/C directed downward, what is the force on each electron when it passes between the plates?
Answer:
Explanation:
Given
Electric Field Strength [tex]E_0=2.07\times 10^5\ N/C[/tex]
Charge on electron [tex]q=1.6\times 10^{-19}\ C[/tex]
Force on any charged particle in an Electric field is given by
[tex]Force=charge\ on\ electron\times Electric\ Field\ strength [/tex]
[tex]F=1.6\times 10^{-19}\times 2.07\times 10^5[/tex]
[tex]F=3.312\times 10^{-14}\ N[/tex]
as the electric field is pointing downward therefore force will be acting downward on a positively charged particle but opposite for an electron i.e. in upward direction
A jetliner, traveling northward, is landing with a speed of 70.9 m/s. Once the jet touches down, it has 727 m of runway in which to reduce its speed to 14.0 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing (take the direction of the plane's motion as positive).
Answer:
Magnitude the of the acceleration is 3.32[tex]m/s^2[/tex] and direction is south
Explanation:
[tex]v_{0} =70.9 m/s\\v=14 m/s\\S=727 m[/tex]
we know that
[tex]v^2 = v_{0}^2 +2aS[/tex]
by substituting the values we can get the required acceleration
[tex]v^2 = v_{0}^2 +2aS\\14^2 = 70.9^2 +2\times a\times 727\\a=3.32 m/s^2[/tex]
Magnitude the of the acceleration is 3.32[tex]m/s^2[/tex] and direction is south
What kind of line does Edward Hopper use in New York Movie to divide theatre space from lobby space?
Answer:
hard line, soft line
Explanation:
A springboard diver leaps upward from the springboard, rises dramatically to a peak height, and than drops impressively into the water below the board. Neglect any influences of air or the atmosphere. During this trip, the diver experiences ________.
Answer:
a constant downward net force.
Explanation:
The diver experiences a constant downward net force because while on his was up he decelerates until he gets to his maximum height when the acceleration is zero, during this phase force is not constant. While on his way down neglecting influences of air or atmosphere he falls with a constant downward net acceleration hence his net downward force will be constant.
A riverboat took 2 h to travel 24km down a river with the current and 3 h to make the return trip against the current. Find the speed of the boat in still water and the speed of the current.
Explanation:
Let the speed of river be r and speed of boat be b.
Distance traveled = 24 km
Time taken to travel 24 km with current = 2 hr
We have
Distance = Speed x Time
24 = (b + r) x 2
b + r = 12 --------------------eqn 1
Time taken to travel 24 km against current = 3 hr
We have
Distance = Speed x Time
24 = (b - r) x 3
b - r = 8 --------------------eqn 2
eqn 1 + eqn 2
2b = 20
b = 10 km/hr
Substituting in eqn 1
10 + r = 12
r = 2 km/hr
Speed of boat in still water = 10 km/hr
Speed of current of river = 2 km/hr
The speed of the boat in still water is 10 km/h and the speed of the current is 2 km/h. This is a solved by using a system of linear equations with speed of the boat and the current as variables.
Explanation:This problem is a case for a system of linear equations. Let's denote the speed of the boat in still water as b km/h and the speed of the current as c km/h. When the boat travels down the river, the boat and the current speeds are added, because they move in the same direction. When the boat travels up the river, the speeds are subtracted, because they move in opposite directions.
So we have the following equations:
b + c = 24km/2h = 12 km/h (down the river)b - c = 24km/3h = 8 km/h (up the river)The solution to this system of equations will give you the speed of the boat in still water and the speed of the current. Adding these two equations together, we get:
2b = 20 km/hTherefore, b = 10 km/h, which is the speed of the boat in still water. Substitute b = 10 km/h into the first equation to find the speed of the current, c = 12 km/h - 10 km/h = 2 km/h.
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A baseball is hit at an initial speed of 40 m/s at an angle of 60° above the horizontal and reaches a maximum height of h meters. What would be the maximum height reached if it were hit at 80 m/s? a.) 2h b.) 4h c.) 6h d.) 8h
Answer:
b.) 4h
Explanation:
A friend of yours is loudly singing a single note at 412 Hz while racing toward you at 25.8 m/s on a day when the speed of sound is 347 m/s . What frequency do you hear?
Answer:
5541Hz
Explanation:
If the frequency of a wave is directly proportional to the velocity we have;
F = kV where;
F is the frequency
K is the constant of proportionality
V is the velocity
Since f = kV
K = f/v
K = F1/V1 = F2/V2
Given f1 = 412Hz v1 = 25.8m/s f2 = ? V2 = 347m/s
Substituting in the formula we have;
412/25.8=f2/347
Cross multiplying
25.8f2 = 412×347
F2 = 412×347/25.8
F2 = 5541Hz
The frequency heard will be 5541Hz
A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 50 ft from the base of the pole?
To find the speed of the tip of the woman's shadow, we use related rates and the similarities of triangles. The rate at which the shadow tip moves is found by setting up a proportion based on similar triangles and differentiating with respect to time. The result is that the tip of the shadow moves at 10.67 ft/sec when the woman is 50 ft from the light pole.
The question is about a real-world application of related rates, which is a concept in calculus where one rate is determined based on another rate. In this scenario, we have a woman walking away from a light pole, and we need to find out how fast the tip of her shadow is moving. To solve it, we use the similarities of triangles created by the woman and the light pole with their respective shadows.
Let's let the height of the light pole be P (16 ft), the height of the woman be W (6 ft), the distance of the woman from the pole be w (50 ft), and the distance of the tip of her shadow from the pole be s. We will use the fact that the ratios P/s and W/(s-w) are equal because the triangles are similar. Setting up the proportions, after some algebra, we find that ds/dt (the rate at which the tip of the shadow moves) is a function of dw/dt (the rate at which the woman walks).
By differentiating both sides of the proportion with respect to time t, applying the chain rule, and plugging in the known values, we can solve for ds/dt as follows:
ds/dt = P/W * dw/dt * (s/w) = (16/6) * 4 * (50/50) = 64/6 = 10.67 ft/sec
The tip of her shadow is moving along the ground at a rate of [tex]\frac{1600}{61}\) ft/sec[/tex] when she is 50 ft from the base of the pole
To solve this problem, we can use similar triangles to relate the woman's height to the height of the street light and their respective shadows. Let [tex]\(x\)[/tex] be the distance from the woman to the pole, [tex]\(s\)[/tex] be the length of her shadow, and [tex]\(h = 16\)[/tex] ft be the height of the street light. The woman's height is [tex]\(w = 6\) ft.[/tex] At any given moment, the triangles formed by the woman and her shadow and the street light and the woman's shadow are similar. Therefore, we have the proportion:
[tex]\[\frac{h}{w} = \frac{h + s}{x}\][/tex]
We can solve for [tex]\(s\):[/tex]
[tex]\[h \cdot x = w \cdot (h + s)\][/tex]
[tex]\[h \cdot x = w \cdot h + w \cdot s\][/tex]
[tex]\[h \cdot x - w \cdot h = w \cdot s\][/tex]
[tex]\[s = \frac{h \cdot x - w \cdot h}{w}\][/tex]
Now, we want to find the rate at which [tex]\(s\)[/tex] is changing with respect to time, denoted as [tex]\(\frac{ds}{dt}\).[/tex] To do this, we differentiate the expression for [tex]\(s\)[/tex] with respect to time [tex]\(t\):[/tex]
[tex]\[\frac{ds}{dt} = \frac{d}{dt}\left(\frac{h \cdot x - w \cdot h}{w}\right)\][/tex]
[tex]\[\frac{ds}{dt} = \frac{h}{w} \cdot \frac{dx}{dt}\][/tex]
Given that [tex]\(h = 16\) ft, \(w = 6\) ft, and \(\frac{dx}{dt} = 4\) ft/sec,[/tex] we can substitute these values into the equation:
[tex]\[\frac{ds}{dt} = \frac{16}{6} \cdot 4\][/tex]
[tex]\[\frac{ds}{dt} = \frac{64}{6}\][/tex]
[tex]\[\frac{ds}{dt} = \frac{160}{15}\][/tex]
[tex]\[\frac{ds}{dt} = \frac{1600}{150}\][/tex]
[tex]\[\frac{ds}{dt} = \frac{1600}{61}\][/tex]
A roofing tile slides down a roof and falls off the roof edge 10 m above the ground at a speed of 6 m/s. The roof makes an angle of 30 degrees to the horizontal. How far from the exit point on the roof does the tile land?
The roofing tile will land around 3.1 meters away from the roof edge. This is found by using equations of motion and breaking the problem into vertical and horizontal components.
Explanation:To solve this, we can break the problem down into two dimensions (horizontal and vertical) and use equations of motion. On the vertical, the roofing tile starts off 10 m above the ground, and falls under acceleration due to gravity. On the horizontal, the tile leaves the roof edge with a horizontal speed of 6 m/s * cos(30), and continues with this speed (since there's no horizontal acceleration).
The time it takes the tile to hit the ground can be found using the equation y = v(initial)*t - 0.5*g*t^2. Assuming upward is positive and taking the initial velocity on the vertical as 6 m/s * sin(30), y = -10 m, v(initial) = 3 m/s and g = 9.8 m/s^2, we can solve for t to get approximately 0.598 seconds.
The distance from the exit point on the roof can be found by multiplying the horizontal speed 5.2 m/s (6 m/s * cos(30)) by the time (0.598 sec) to get approximately 3.1 m.
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Calculate the efficiency of an engine with an input temperature of 755 K and exhaust temperature of 453 K.
Answer:
40%
Explanation:
The other person got it right up until making it opposite because its a percentage. The equation is correct but you'd just need to take the 60% answer and subtract it from 100% because 60% is equal to how much effiency the exhaust is taking away, thus making your answer 40%
Charles is having a lot of problems with errors in a very complicated spreadsheet that he inherited from a colleague, and he turns to another co-worker, Seymour, for tips on how to trace errors in the sheet. If Charles sees which of the following, Seymour explains, there is a mistyped function name in the sheet.
a.#FORM?
b.#NAME?
c.#####
d.#FNCT?
Answer:
b.#NAME?
Explanation:
Remember, in Spreadsheet programs like Ms Excel several types of errors can occur such as value error.
However, since Seymour explains that there is a mistyped function name in the sheet it is more likely to display on the affected cell as #NAME?.
For example the function =SUM is wrongly spelled =SOM.
Therefore it is important to make sure the function name is spelled correctly.
A closed Gaussian surface in the shape of a cube of edge length 1.9 m with one corner at x = 1 4.8 m, y = 1 3.9 m.
The cube lies in a region where the electric field vector is given by [tex]E = 3.4 \hat{i} + 4.4 y^2 \hat{j} + 3.0 \hat{k}[/tex] NC with y in meters.
What is the net charge contained by the cube?
Answer:
Net charge = 2.59nC
Explanation:
Gauss' Law states that the net electric flux is given by:
∮→E⋅→d/A = q enc/ϵ0
At this point, we have to solve the net electric flux through each side.
One corner is at (4.8, 3.9, 0).
The other corners are each 1.9m apart, so the other corners are at
(4.8, 5.8, 0), (6.7, 3.9, 0) and (6.7, 5.8, 0).
The other four corners are 1.9m away in the z-axis:
(4.8, 5.8, 2), (6.7, 3.9, 2) and (6.7, 5.8, 2).
Therefore, there are two planes (parallel to the x-z plane), one at
y = 3.9
and the other at
y = 5.8 which have a constant y-coordinate and are facing in the −^j and +^j respectively.
Area = 1.9m * 1.9m = 3.61m²
The flux through the first plane (area of 3.61m²) is given by:
E.A = (3.4i + 4.4 * 3.9²j + 3.0k) * (-3.61m²j) = -241.59564
The flux through the other plane is
E.A = (3.4i + 4.4 * 5.8²j + 3.0k)* (3.61m²j) = 534.33776
Now, for the other planes. There are no ^j components for the unit vectors for the area.
Therefore, even though they change in y-coordinate, those terms cancel out.
Therefore, for the planes with unit vector in the x-direction, we get:
E.A = (3.4i + 4.4y²j + 3.0k) * (1.9m * 1.9m) = ±12.274
And in the z-direction:
E.A = (3.4i + 4.4y²j + 3.0k) * (1.9m * 1.9m) = ±10.83
Now, when we sum all these fluxes together, the contribution from the x- and z-directions cancel out. Therefore, our net flux is:
-241.59564 + 534.33776 = 292.74212
Therefore, the enclosed charge is given by
q enc = ϵ0* (292.74212)
= 2.5856871136363E−9C
= 2.59E-9 nC--_- Approximated
= 2.59nC
Answer:
Q_enclosed = 1.576 nC
Explanation:
Given:
- The edge length of the cube L = 1.9 m
- One corner of the cube P_1 = ( 4.8 , 13.9 ) m
- The Electric Field vector is given by:
E = 3.4 i + 4.4*y^2 j + 3.0 k N/C
Find:
What is the net charge contained by the cube?
Solution:
- The flux net Ф through faces parallel to y-z plane is:
net Ф_yz = E_x . A . cos (θ)
Where, E_x is the component of E with unit vector i.
θ is the angle between normal vector dA and E.
Hence,
net Ф_yz = 3.4 . 1.9^2 . cos (0) + 3.4 . 1.9^2 . cos (180)
net Ф_yz = 3.4 . 1.9^2 - 3.4 . 1.9^2 . cos (180)
net Ф_yz = 0.
- Similarly, The flux net Ф through faces parallel to x-y plane is:
net Ф_xy = E_z . A . cos (θ)
Where, E_z is the component of E with unit vector k.
net Ф_xy = 3 . 1.9^2 . cos (0) + 3 . 1.9^2 . cos (180)
net Ф_xy = 3 . 1.9^2 - 3 . 1.9^2 . cos (180)
net Ф_xy = 0
-The flux net Ф through faces parallel to x-z plane is:
net Ф_xz = E_y . A . cos (θ)
Where, E_y is the component of E with unit vector j.
net Ф_xz = 4.4y_1^2 * 1.9^2 . cos (0) + 4.4y_2^2. 1.9^2 . cos (180)
Where, The y coordinate for face 1 y_1 = 3.9 - 1.9 = 2, & face 2 y_2 = 3.9
net Ф_xz = - 4.4*2^2*1.9^2 . cos (0) - 4.4*3.9^2. 1.9^2 . cos (180)
net Ф_xz = -63.536 + 241.59564 = 178.0596 Nm^2/C
- From gauss Law we have:
Total net Ф_x,y,z = Q_enclosed / ∈_o
Where,
Q_enclosed is the charge contained in the cube
∈_o is the permittivity of free space = 8.85*10^-12
Hence,
Total net Ф_x,y,z = net Ф_xz + net Ф_yz + net Ф_xy
Total net Ф_x,y,z = 178.0596 + 0 + 0 = 178.0596 Nm^2/C
We have,
Q_enclosed = Total net Ф_x,y,z * ∈_o
Q_enclosed = 178.0596 * 8.85*10^-12
Q_enclosed = 1.576 nC
LPG is a useful fuel in rural locations without natural gas pipelines. A leak during the filling of a tank can be extremely dangerous because the vapor is denser than air and drifts to low elevations before dispersing, creating an explosion hazard. a.) What volume of vapor is created by a leak of 40 L of LPG? Model the liquidbefore leaking as propane with density pL=0.24g/cm^3. b) what is the mass density of pure propane vapor after depressurization to 293K and 1 bar? compare to the mass density of air at the same conditions.
Answer:
The aanswers to the question are
(a) 5.33 m³
(b) 1.83 kg/m³
Explanation:
Volume of leak = 40 L, density of propane = 0.24g/cm³
Mass of leak = Volume × Density = 40000 cm³×0.24 g/cm³ = 9600 gram
Molar mass of propane = 44.1 g/mol Number of moles = 9600/44.1 = 217.69 moles
at 1 atmosphare and 298.15 K we have
PV = nRT therefore V = nRT/P = (217.69×8.3145×298.15)/101325 = 5.33 m³
The volume of the vapour = 5.33 m³
(b) Density = mass/volume
Recalculating the above for T = 293 K we have V = 5.33×293÷298.15 = 5.23 m³
Therefore density of propane vapor = 9600/5.23 = 1834.22 g/m³ or 1.83 kg/m³
A 3.42 kg mass hanging vertically from a spring on the Earth (where g = 9.8 m/s2) undergoes simple oscillatory motion. If the spring constant is 12 N/m, find the period of oscillation of this setup on the moon, where g = 1.6 m/s2.
Answer:
Time period of oscillation on moon will be equal to 3.347 sec
Explanation:
We have given mass which is attached to the spring m = 3.42 kg
Spring constant K = 12 N/m
We have to find the period of oscillation
Period of oscillation is equal to [tex]T=2\pi \sqrt{\frac{m}{K}}[/tex], here m is mass and K is spring constant
So period of oscillation [tex]T=2\times 3.14\times \sqrt{\frac{3.42}{12}}[/tex]
[tex]T=2\times 3.14\times 0.533=3.347sec[/tex]
So time period of oscillation will be equal to 3.347 sec
As it is a spring mass system and from the relation we can see that time period is independent of g
So time period will be same on earth and moon
. A child has a toy tied to the end of a string and whirls the toy at constant speed in a horizontal circular path of radius R. The toy completes each revolution of its motion in a time period T. What is the magnitude of the acceleration of the toy? a. c. Zero d. 4T2R/T2 e. TR/T2
Explanation:
Formula for centripetal acceleration of an object is as follows.
a = [tex]\frac{v^{2}}{r}[/tex]
When an object is travelling in a circular path then it is difficult to measure its velocity.
Hence, for a circular object the formula for acceleration is as follows.
a = [tex]\frac{4 \pi^{2} r}{T^{2}}[/tex]
a = [tex]\frac{V^{2}}{r}[/tex], and V = [tex]\frac{d}{T} = \frac{2 \pi r}{T}[/tex]
a = [tex]\frac{(\frac{[2\pi r]}{T})^{2}}{r}[/tex]
= [tex]\frac{4 \pi^{2} r}{T^{2}}[/tex]
Thus, we can conclude that the magnitude of the acceleration of the toy is [tex]\frac{4 \pi^{2} r}{T^{2}}[/tex].