The mass of the North American continent is calculated by multiplying the volume of the continent by the density of the rock it is made of. The volume is determined based on the given dimensions, converted to meters. Multiplying the resulting volume by the rock's density provides the estimated mass of 1.59712e21 kilograms.
Explanation:In order to find the mass of a continent, we need to multiply the volume of the continent by the density of the rock that it's made of. First, we need to convert the dimensions of the North American continent into meters from kilometers since the density is in kg/m³. That's 4700km x 1000m/km =4.7e6m for length & width, and 25km x 1000m/km = 2.5e4m for depth. Thus, the volume of the continent becomes 4.7e6m x 4.7e6m x 2.5e4m = 5.54e17m³.
Now, we multiply by the rock's density, which is 2880 kg/m³. So, mass = volume * density = 5.54e17 m³ x 2880 kg/m³ = 1.59712e21 kg. So, the theoretical mass of the North American continent is approximately 1.59712e21 kilograms considering its simplified shape as a slab of rock.
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car leaves a stop sign and exhibits a constant acceleration of 0.300 m/s2 parallel to the roadway. The car passes over a rise in the roadway such that the top of the rise is shaped like an arc of a circle of radius 500 m. Now the car is at the top of the rise, its velocity vector is horizontal and has a magnitude of 6.00 m/s. What are the magnitude and direction of the total acceleration vector for the car at this instant
Answer:
0.308 m/s2 at an angle of 13.5° below the horizontal
Explanation:
The parallel acceleration to the roadway is the tangential acceleration on the rise.
The normal acceleration is the centripetal acceleration due to the arc. This is given by
[tex]a_N = \dfrac{v^2}{r} = \dfrac{36^2}{500}=0.072[/tex]
The tangential acceleration, from the question, is
[tex]a_T = 0.300[/tex]
The magnitude of the total acceleration is the resultant of the two accelerations. Because these are perpendicular to each other, the resultant is given by
[tex]a^2 =a_T^2 + a_N^2 = 0.300^2 + 0.072^2[/tex]
[tex]a = 0.308[/tex]
The angle the resultant makes with the horizontal is given by
[tex]\tan\theta=\dfrac{a_N}{a_T}=\dfrac{0.072}{0.300}=0.2400[/tex]
[tex]\theta=13.5[/tex]
Note that this angle is measured from the horizontal downwards because the centripetal acceleration is directed towards the centre of the arc
A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.2 m/s. The car is a distance d away. The bear is 29 m behind the tourist and running at 6.0 m/s. The tourist reaches the car safely. What is the maximum possible value for d
Explanation:
It is known that the relation between speed and distance is as follows.
velocity = [tex]\frac{distance}{time}[/tex]
As it is given that velocity is 6 m/s and distance traveled by the bear is (d + 29). Therefore, time taken by the bear is calculated as follows.
[tex]t_{bear} = \frac{(d + 29)}{6 m/s}[/tex] ............. (1)
As the tourist is running in a car at a velocity of 4.2 m/s. Hence, time taken by the tourist is as follows.
[tex]t_{tourist} = \frac{d}{4.2}[/tex] ............. (2)
Now, equation both equations (1) and (2) equal to each other we will calculate the value of d as follows.
[tex]t_{bear} = t_{tourist}[/tex]
[tex]\frac{(d + 29)}{6 m/s}[/tex] = [tex]\frac{d}{4.2}[/tex]
4.2d + 121.8 = 6d
d = [tex]\frac{121.8}{1.8}[/tex]
= 67.66
Thus, we can conclude that the maximum possible value for d is 67.66.
The current supplied by a battery as a function of time is I(t) = (0.88 A) e^(-t*6 hr). What is the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead?
a. 3.7 x 10^18
b. 5.3 x 10^23
c. 4.4 x 10^22
d. 1.6 x 10^19
e. 1.2 x 10^23
Answer:
e. 1.2 x 10²³
Explanation:
According to the problem, The current equation is given by:
[tex]I(t)=0.88e^{-t/6\times3600s}[/tex]
Here time is in seconds.
Consider at t=0 s the current starts to flow due to battery and the current stops when the time t tends to infinite.
The relation between current and number of charge carriers is:
[tex]q=\int\limits {I} \, dt[/tex]
Here the limits of integration is from 0 to infinite. So,
[tex]q=\int\limits {0.88e^{-t/6\times3600s}}\, dt[/tex]
[tex]q=0.88\times(-6\times3600)(0-1)[/tex]
q = 1.90 x 10⁴ C
Consider N be the total number of charge carriers. So,
q = N e
Here e is electronic charge and its value is 1.69 x 10⁻¹⁹ C.
N = q/e
Substitute the suitable values in the above equation.
[tex]N= \frac{1.9\times10^{4} }{1.69\times10^{-19}}[/tex]
N = 1.2 x 10²³
A simple circuit consists only of of a 1.0-μF capacitor and a 15-mH coil in series. At what frequency does the inductive reactance equal the capacitive reactance? 67 Hz 0.77 kHz 15 kHz 1.3 kHz
Answer:
The frequency is 1.3 kHz.
Explanation:
Given that,
Capacitance of the capacitor, [tex]C=1\ \mu F=10^{-6}\ C[/tex]
Inductance of the inductor, [tex]L=15\ mH=15\times 10^{-3}\ H[/tex]
We need to find the frequency when the inductive reactance equal the capacitive reactance such that :
[tex]X_c=X_L[/tex]
[tex]2\pi fL=\dfrac{1}{2\pi fC}[/tex]
[tex]f=\dfrac{1}{2\pi \sqrt{LC} }[/tex]
[tex]f=\dfrac{1}{2\pi \sqrt{15\times 10^{-3}\times 10^{-6}} }[/tex]
f = 1299.49 Hz
[tex]f=1.29\times 10^3\ Hz[/tex]
or
[tex]f=1.3\ kHz[/tex]
So, the frequency is 1.3 kHz. Therefore, the correct option is (d).
Three identical 4.0-kg cubes are placed on a horizontal frictionless surface in contact with one another. The cubes are lined up from left to right and a force is applied to the left side of the left cube causing all three cubes to accelerate to the right at 4.0 m/s2 . What is the magnitude of the force exerted on the right cube by the middle cube in this case
Final answer:
The magnitude of the force exerted on the right cube by the middle cube, when three identical cubes accelerate together on a frictionless surface, is calculated using Newton's second law (F = ma) and is found to be 16.0 Newtons.
Explanation:
The student's question pertains to Newton's second law of motion and the concept of force and acceleration. The problem involves three identical cubes on a frictionless surface accelerating due to a force applied to the first cube. To find the magnitude of the force exerted on the right cube by the middle cube, we use the formula F = ma, where F is the force, m is the mass, and a is the acceleration.
Since the cubes are identical and accelerate together, each 4.0-kg cube has an acceleration of 4.0 m/s². Therefore, the force exerted by one cube on another can be found by multiplying one cube's mass by the given acceleration:
F = m × aF = 4.0 kg × 4.0 m/s²F = 16.0 NThe force exerted on the right cube by the middle cube is 16.0 Newtons.
( 8c5p79) A certain force gives mass m1 an acceleration of 13.5 m/s2 and mass m2 an acceleration of 3.5 m/s2. What acceleration would the force give to an object with a mass of (m2-m1)
Answer:
[tex]4.725 m/s^{2}[/tex]
Explanation:
We know that from Newton's second law of motion, F=ma hence making acceleration the subject then [tex]a=\frac {F}{m}[/tex] where a is acceleration, F is force and m is mass
Also making mass the subject of the formula [tex]m=\frac {F}{a}[/tex]
For [tex]m1= \frac {F}{13.5}[/tex] and [tex]m2=\frac {F}{3.5}[/tex] hence [tex]F=(m2-m1)a= (\frac {F}{3.5}-\frac {F}{13.5})a=0.2116402116\\\frac {1}{a}=0.2116402116\\a=4.725 m/s^{2}[/tex]
An oxygen molecule is adsorbed onto a small patch of the surface of a catalyst. It's known that the molecule is adsorbed on of possible sites for adsorption (see sketch at right). Calculate the entropy of this system. Round your answer to significant digits, and be sure it has the correct unit symbol.
The given question is incomplete. The complete question is as follows.
An oxygen molecule is adsorbed onto a small patch of the surface of a catalyst. It's known that the molecule is adsorbed on 1 of 36 possible sites for adsorption. Calculate the entropy of this system.
Explanation:
It is known that Boltzmann formula of entropy is as follows.
s = k ln W
where, k = Boltzmann constant
W = number of energetically equivalent possible microstates or configuration of the system
In the given case, W = 36. Now, we will put the given values into the above formula as follows.
s = k ln W
= [tex]1.38 \times 10^{-23} ln (36)[/tex]
= [tex]4.945 \times 10^{-23} J/K[/tex]
Thus, we can conclude that the entropy of this system is [tex]4.945 \times 10^{-23} J/K[/tex].
The entropy of the given system is [tex]4.954 \times 10^{-23 } \rm\; J/K[/tex] in which an oxygen molecule is absorbed in one of the 36 possible states.
From the Boltzmann formula of entropy,
[tex]s = k \times ln W[/tex]
Where,
[tex]k[/tex]= Boltzmann constant = [tex]1.38\times 10^{-23} \rm\; J/K[/tex]
[tex]W[/tex] = Number of energetically equivalent possible microstates of the system = 36
Put the values in the formula
[tex]s =1.38\times 10^{-23} \times ln (36)\\\\s = 4.954 \times 10^{-23 } \rm\; J/K[/tex]
Therefore, the entropy of the given system is [tex]4.954 \times 10^{-23 } \rm\; J/K[/tex]
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A circular loop of wire of radius 0.50 m is in a uniform magnetic field of 0.30 T. The current in the loop is 2.0 A. What is the magnetic torque when the plane of the loop is parallel to the magnetic field?
Answer:
Torque = 0.47 Nm
Explanation:
Torque = BIAsin∅
Since the plane is parallel to the magnetic field, ∅ = 90⁰
sin 90 = 1
Magnetic field, B = 0.30 T
current, I = 2.0 A
Radius, R = 0.50 m
A = πR²
A = π(0.5)² = 0.785 m²
Torque = 0.3 * 2 * 0.785
Torque = 0.47 Nm
Answer:
The magnetic torque when the plane of the loop is parallel to the magnetic field is zero.
Explanation:
Given;
radius of wire, r = 0.50 m
strength of magnetic field, B = 0.3 T
current in the wire, I = 2.0 A
Dipole moment, μ = I x A
where;
A is the area of the circular loop = πr² = π(0.5)² = 0.7855 m²
Dipole moment, μ = 2A x 0.7855m² = 1.571 Am²
magnetic torque, τ = μBsinθ
when the plane of the loop is parallel to the magnetic field, θ = 0
τ = 1.571 Am² x 0.3sin0
τ = 0
Therefore, the magnetic torque when the plane of the loop is parallel to the magnetic field is zero.
Considering the form of the Gibb's Free Energy and the condition about it that some process be spontaneous, if some system has the following properties, what would be the result?
Answer:
A) Always Spontaneous.
B) Spontaneous at lower temperatures.
C) Spontaneous at higher temperatures.
D) Never Spontaneous.
Explanation:
The change in Gibb's free energy for a process, ΔG, is given by
ΔG = ΔH - TΔS
where ΔH is the change in enthalpy for the process
T = absolute temperature in Kelvin of the process
ΔS = change in enthalpy of the process.
And for a process to be spontaneous, its change in Gibb's free energy must be negative.
If it is positive, then the reaction isn't spontaneous.
So, we consider the conditions given one by one.
A) The enthalpy change is negative and the entropy change is positive.
ΔH = -ve, ΔS = +ve
ΔG = ΔH - TΔS = (negative number) - T(positive number) = (negative number - negative number) = negative number (since T isn't negative for these processes.)
Hence, the process with these conditions is always spontaneous.
B) The enthalpy change is negative and the entropy change is negative.
ΔH = negative, ΔS = negative
ΔG = ΔH - TΔS
For this relation, ΔG can only be positive if the numerical value of the ΔH (without the sign) is greater than TΔS.
This will happen mostly at low temperatures as low T, helps to reduce the numerical value of TΔS, thereby making ΔH (without the negative sign) the bigger number and subsequently makethe overall expression negative and the process, spontaneous.
C) The enthalpy change is positive and the entropy change is positive.
ΔH = positive, ΔS = positive.
ΔG = ΔH - TΔS
For this to be spontaneous,
TΔS > ΔH
And the one thing that favours this is high temperatures for the process.
At high temperatures, TΔS gives a much larger number which would drive the overall expression towards the negative sign, thereby making the process spontaneous.
D) The enthalpy change is positive and the entropy change is negative.
ΔH = positive, ΔS = negative.
ΔG = ΔH - TΔS
The signs on these state functions mean that the change in Gibb's free energy will always be positive for this set of conditions (since the temperature can't go as low as being negative).
A process with these conditions, is never spontaneous.
List the laws of thermodynamic and describe their relevance in the chemical reactions2. Define the standard reduction potential. Why aerobic grow generates the highest amount ofenergy (ATP).
Explanation:
Thermodynamic Laws -
The primary law, otherwise called the Law of Conservation of Energy, expresses that energy remains constant in the overall reaction, it is not created or destroyed. The second law of thermodynamics expresses that the entropy increases. after the completion of the reaction of any isolated system The third law of thermodynamics expresses that as the temperature reaches towards an absolute zero point the entropy of a system becomes constant.Standard Electronic potential -
The standard reduction potential may be defined as the tendency of a chemical species or the reactants to get into its reduced form after the overall reaction. It is estimated at volts. The more is the positive potential the more is the reduction of the chemical speciesAerobic grow is much more efficient at making ATP because of the presence of oxygen the cycles in the respiration are carried out at an efficient rate which forces the cell to undergo a much large amount of ATP production.
. An electron moving at 4.00×103m/s in a 1.25-T magnetic field experiences a magnetic force of 1.40×10−16N . What angle does the velocity of the electron make with the magnetic field? There are two answers.
Answer: 9.59° and 350.41°
Explanation: The formulae that relates the force F exerted on a moving charge q with velocity v in a magnetic field of strength B is given as
F =qvB sin x
Where x is the angle between the strength of magnetic field and velocity of the charge.
q = 1.609×10^-19 C
v = 4×10³ m/s
B = 1.25 T
F = 1.40×10^-16 N
By substituting the parameters, we have that
1.40×10^-16 = 1.609×10^-19 × 4×10³ × 1.25 × sinx
sin x = 1.40×10^-16/ 1.609×10^-19 × 4×10³ × 1.25
sin x = 1.40×10^-16 /8.045*10^(-16)
sin x = 0.1666
x = 9.59°
The value of sin x is positive in first and fourth quadrant.
Hence to get the second value of x, we move to the 4th quadrant of the trigonometric quadrant which is 360 - x
Hence = 360 - 9.59 = 350.41°
Final answer:
The angle between the velocity of the electron and the magnetic field is approximately 6.27° or 173.73°.
Explanation:
To find the angle between the velocity of the electron and the magnetic field, we can use the formula:
F = q(vsinθ)B
Where F is the magnetic force, q is the charge of the electron, v is the velocity of the electron, θ is the angle between the velocity and the magnetic field, and B is the magnetic field strength.
In this case, the magnetic force is given as 1.40 × 10^-16 N, the charge of an electron is 1.6 × 10^-19 C, the velocity of the electron is 4.00 × 10³ m/s, and the magnetic field strength is 1.25 T.
Plugging in these values, we can solve for θ:
1.40 × 10^-16 N = (1.6 × 10^-19 C)(4.00 × 10³ m/s)(sinθ)(1.25 T)
Solving for sinθ:
sinθ = (1.40 × 10^-16 N) / [(1.6 × 10^-19 C)(4.00 × 10³ m/s)(1.25 T)]
sinθ ≈ 0.109
Taking the inverse sine of 0.109, we find that θ ≈ 6.27° or θ ≈ 173.73°.
The sound intensity at a distance of 16 m from a noisy generator is measured to be 0.25 W/m2. What is the sound intensity at a distance of 28 m from the generator?
Answer:
0.1111 W/m²
Explanation:
If all other parameters are constant, sound intensity is inversely proportional to the square of the distance of the sound. That is,
I ∝ (1/r²)
I = k/r²
Since k can be the constant of proportionality. k = Ir²
We can write this relation as
I₁ × r₁² = I₂ × r₂²
I₁ = 0.25 W/m²
r₁ = 16 m
I₂ = ?
r₂ = 24 m
0.25 × 16² = I₂ × 24²
I₂ = (0.25 × 16²)/24²
I₂ = 0.1111 W/m²
The sound intensity at a distance of 28 m from the generator will be "0.1111 W/m²".
Distance and Sound intensityAccording to the question,
Distance, r₁ = 16 m
r₂ = 28 m
Sound intensity, I₁ = 0.25 W/m²
We know the relation,
→ I ∝ ([tex]\frac{1}{r^2}[/tex])
or,
I ∝ [tex]\frac{k}{r^2}[/tex]
Now,
→ I₁ × r₁² = I₂ × r₂²
By substituting the values,
0.25 × (16)² = I₂ × (24)²
I₂ = [tex]\frac{0.25\timers (16)^2}{(24)^2}[/tex]
= 0.1111 W/m²
Thus the above answer is correct.
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a bag of ice cubes absorbs 149,000 J of heat, which causes its temperature to increase by 5.23 degrees celsius. what is the mass of the ice in the bag?
Ice=c=2000J/(kg*c) (unit=kg)
Answer:
14.3kg
Explanation:
Given parameters:
Quantity of heat = 149000J
Change in temperature = 5.23°C
specific heat of the ice = 2000J/kg°C
Unknown:
Mass of the ice in the bag = ?
Solution:
The heat capacity of a substance is given as:
H = m c Ф
H is the heat capacity
m is the mass
c is the specific heat
Ф is the temperature change;
since m is the unknown, we make it the subject of the expression;
m = H/ mФ
m = [tex]\frac{149000}{2000 x 5.23}[/tex] = 14.3kg
Answer: 14.2447
Explanation:
A rock is thrown upward from a bridge into a river below. The function f(t)=−16t2+44t+138 determines the height of the rock above the surface of the water (in feet) in terms of the number of seconds t since the rock was thrown. g
Answer:
a) 138 ft
b) 4.62 s
c) 1.375 s
d) 168.25 ft
Explanation:
The height of a rock (thrown from the top of a bridge) above the level of water surface as it varies with time when thrown is given in the question as
h = f(t) = -16t² + 44t + 138
with t in seconds, and h in feet
a) The bridge's height above the water.
At t=0 s, the rock is at the level of the Bridge's height.
At t = 0,
h = 0 + 0 + 138 = 138 ft
b) How many seconds after being thrown does the rock hit the water?
The rock hits the water surface when h = 0 ft. Solving,
h = f(t) = -16t² + 44t + 138 = 0
-16t² + 44t + 138 = 0
Solving this quadratic equation,
t = 4.62 s or t = -1.87 s
Since time cannot be negative,
t = 4.62 s
c) How many seconds after being thrown does the rock reach its maximum height above the water?
At maximum height or at the maximum of any function, the derivative of that function with respect to the independent variable is equal to 0.
At maximum height,
(dh/dt) = f'(t) = (df/dt) = 0
h = f(t) = -16t² + 44t + 138
(dh/dt) = (df/dt) = -32t + 44 = 0
32t = 44
t = (44/32)
t = 1.375 s
d) What is the rock's maximum height above the water?
The maximum height occurs at t = 1.375 s,
Substituting this for t in the height equation,
h = f(t) = -16t² + 44t + 138
At t = 1.375 s, h = maximum height = H
H = f(1.375) = -16(1.375²) + 44(1.375) + 138
H = 168.25 ft
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The spring of constant k = 170 N/m is attached to both the support and the 1.5-kg cylinder, which slides freely on the horizontal guide. If a constant 14-N force is applied to the cylinder at time t = 0 when the spring is undeformed and the system is at rest, determine the velocity of the cylinder when x = 65 mm. Also determine the maximum displacement of the cylinder.
Answer:
Velocity at 64 mm is 0.532 m/s
Maximum displacement = 0.082 m or 82 mm
Explanation:
The maximum displacement or amplitude is determined by the applied force from Hooke's law
[tex]F = kA[/tex]
[tex]A=\dfrac{F}{k}=\dfrac{14 \text{ N}}{170 \text{ N/m}}=0.082 \text{ m}[/tex]
The velocity at at any point, x, is given by
[tex]v=\sqrt{\dfrac{k}{m}(A^2 - x^2)}[/tex]
m is the mass of the load, here the cylinder.
In fact, the expression [tex]\sqrt{\dfrac{k}{m}}[/tex] represents the angular velocity, [tex]\omega[/tex].
Substituting given values,
[tex]v=\sqrt{\dfrac{170}{1.5}(0.082^2 - 0.065^2)} = 0.532 \text{ m/s}[/tex]
In some amazing situations, people have survived falling large distances when the surface they land on is soft enough. During a traverse of Eiger's infamous Nordvand, mountaineer Carlos Ragone's rock anchor gave way and he plummeted 512 feet to land in snow. Amazingly, he suffered only a few bruises and a wrenched shoulder. Assuming that his impact left a hole in the snow 4.8 ft deep, estimate his average acceleration as he slowed to a stop (that is while he was impacting the snow). Pick a coordinate system where down is positive.
Answer:
-3413 ft/s2
Explanation:
We need to know the velocity with which he landed on the snow.
He 'dropped' from 512 feet. This is the displacement. His initial velocity is 0 and the acceleration of gravity is 32 ft/s2.
We use the equation of mition
[tex]v^2 = u^2 + 2as[/tex]
v and u are the initial and final velocities, a is the acceleration and s is the displacement. Putting the appropriate values
[tex]v^2 = 0^2 + 2\times32\times512[/tex]
[tex]v = \sqrt{2\times32\times512} = 128\sqrt{2}[/tex]
This is the final velocity of the fall and becomes the initial velocity as he goes into the snow.
In this second motion, his final velocity is 0 because he stops after a displacement of 4.8 ft. We use the same equation of motion but with different values. This time, [tex]u=128\sqrt{2}[/tex], v = 0 and s = 4.8 ft.
[tex]0^2 = (128\sqrt{2})^2 + 2a\times4.8[/tex]
[tex]a = -\dfrac{2\times128^2}{2\times4.8} = -3413[/tex]
Note that this is negative because it was a deceleration, that is, his velocity was decreasing.
A spaceship of proper length ? = 100 m travels in the positive x direction at a speed of 0.700 c0 relative to Earth. An identical spaceship travels in the negative x direction along a parallel course at the same speed relative to Earth. At t = 0, an observer on Earth measures a distance d = 58,000 km separating the two ships.
Part A
At what instant does this observer see the leading edges of the two ships pass each other?
Answer:
observer see the leading edges of the two ships pass each other at time 0.136 s
Explanation:
given data
spaceship length = 100 m
speed of 0.700 Co = [tex]0.700\times 3 \times 10^8[/tex] m/s
distance d = 58,000 km = 58000 × 10³ m
solution
as here distance will be half because both spaceship travel with same velocity
so they meet at half of distance
Distance Da = [tex]\frac{d}{2}[/tex] ............1
Distance Da = [tex]\frac{58000\times 10^3}{2}[/tex]
Distance Da = 29 ×[tex]10^{6}[/tex] m
and
time at which observer see leading edge of 2 spaceship pass
Δ time = [tex]\frac{Da}{v}[/tex] ..........2
Δ time = [tex]\frac{29 \times 10^6}{0.700\times 3 \times 10^8}[/tex]
Δ time = 0.136 s
Answer:
The time at which the observer see the leading edges of the two ships pass each other is 0.138 sec.
Explanation:
Given that,
Length = 100 m
Speed = 0.700 c
Distance = 58000 km
The distance should be halved because the spaceships both travel the same speed.
So they will meet at the middle of the distance
We need to calculate the distance
Using formula for distance
[tex]d'=\dfrac{d}{2}[/tex]
Put the value into the formula
[tex]d'=\dfrac{58000}{2}[/tex]
[tex]d'=29000\ km[/tex]
We need to calculate the time at which the observer see the leading edges of the two ships pass each other
Using formula of time
[tex]\Delta t=\dfrac{d}{V}[/tex]
Put the value into the formula
[tex]\Delta t=\dfrac{29\times10^{6}}{0.700\times3\times10^{8}}[/tex]
[tex]\Delta t=0.138\ sec[/tex]
Hence, The time at which the observer see the leading edges of the two ships pass each other is 0.138 sec.
A flat circular loop of wire of radius 0.50 m that is carrying a 2.0-A current is in a uniform magnetic field of 0.30 T. What is the magnitude of the magnetic torque on the loop when the plane of its area is perpendicular to the magnetic field
the magnitude of the magnetic torque on the loop when the plane of its area is perpendicular to the magnetic field is approximately [tex]\( 0.47 \, \text{N} \cdot \text{m} \)[/tex].
The magnetic torque [tex]\( \tau \)[/tex] on a current-carrying loop in a uniform magnetic field can be calculated using the formula:
[tex]\[ \tau = N \cdot I \cdot A \cdot B \cdot \sin(\theta) \][/tex]
Where:
- N is the number of turns in the loop (1 in this case, as there is a single loop),
- I is the current flowing through the loop (2.0 A),
- A is the area of the loop (πr² for a circular loop, where \( r \) is the radius),
- B is the magnetic field strength (0.30 T),
- [tex]\( \theta \)[/tex] is the angle between the normal to the loop's plane and the magnetic field (90° in this case, as the loop is perpendicular to the magnetic field).
Substituting the given values:
[tex]\[ \tau = (1) \cdot (2.0 \, \text{A}) \cdot (\pi \times (0.50 \, \text{m})^2) \cdot (0.30 \, \text{T}) \cdot \sin(90°) \][/tex]
[tex]\[ \tau = 2.0 \cdot \pi \cdot (0.50)^2 \cdot 0.30 \][/tex]
[tex]\[ \tau = 2.0 \cdot \pi \cdot 0.25 \cdot 0.30 \][/tex]
[tex]\[ \tau = 0.15 \cdot \pi \][/tex]
[tex]\[ \tau \approx 0.47 \, \text{N} \cdot \text{m} \][/tex]
So, the magnitude of the magnetic torque on the loop when the plane of its area is perpendicular to the magnetic field is approximately [tex]\( 0.47 \, \text{N} \cdot \text{m} \)[/tex].
Therefore, the correct answer choice is [tex]\(\boxed{\text{0.47 N*m}}\)[/tex].
The complete Question is given below:
A flat circular loop of wire of radius 0.50 m that is carrying a 2.0-A current is in a uniform magnetic field of 0.30 T. What is the magnitude of the magnetic torque on the loop when the plane of its area is perpendicular to the magnetic field?
Answer choices.
.41N*m
.00N*m
.47N*m
.58N*m
.52N*m
A solenoid of length 2.50 cm and radius 0.750 cm has 25 turns. If the wire of the solenoid has 1.85 amps of current, what is the magnitude of the magnetic field inside the solenoid
Answer:
13.875 T
Explanation:
Parameters given:
Length of solenoid, L = 2.5 cm = 0.025 m
Radius of solenoid, r = 0.75 cm = 0.0075 m
Number of turns, N = 25 turns
Current, I = 1.85 A
Magnetic field, B, is given as:
B = (N*r*I) /L
B = (25 * 0.0075 * 1.85)/0.025
B = 13.875 T
A string is stretched to a length of 212 cm and both ends are fixed. If the density of the string is 0.02 g/cm, and its tension is 357 N, what is the fundamental frequency? Course hero
The fundamental frequency of a string fixed at both ends is f₁ = c/2L, where 'c' is calculated from the tension and linear mass density of the string. Using the given tension and density, one can find the wave speed 'c' first, then substitute into the formula to get the fundamental frequency.
To calculate the fundamental frequency of a string fixed at both ends, you can use the formula for the fundamental frequency of a string, which is given by f1 = c/2L, where f1 is the fundamental frequency, c is the speed of the wave on the string, and L is the length of the string.
To find the speed of the wave on the string, we use the formula c = \/(T/μ), where c is the speed of the wave, T is the tension in the string, and μ is the linear mass density of the string. Substituting the given values, c = \/(357 N / (0.02 g/cm * 100 cm/m)) = \/(357 / 0.0002 kg/m), we can calculate c and then use the result to find f1.
The vertical normal stress increase caused by a point load of 10 kN acting on the ground surface at a point 1m vertically below its point of application is: (a) 0 (b) 4.775 kN (c) 5 kN (d) 10 kN
Answer:
(b) 4.775 kN
Explanation:
see the attached file
In a dentist's office, an X-ray of a tooth is taken using X-rays that have a frequency of 9.81 1018 Hz. What is the wavelength in vacuum of these X-rays?
Answer:
[tex]\lambda=3.056\times10^{-11}m[/tex]
Explanation:
The equation that involves frequency (f) and wavelength ([tex]\lambda[/tex]) of a wave is [tex]v=\lambda f[/tex], where v is the speed of the wave. X-rays are a type of electromagnetic wave, so in vacuum it moves at the speed of light c, which means that our wavelength will be:
[tex]\lambda=\frac{c}{f}=\frac{299792458m/s}{9.81\times10^{18}Hz}=3.056\times10^{-11}m[/tex]
To calculate the wavelength of an X-ray with a frequency of 9.81 x 1018 Hz, we substitute the given frequency into the formula λ = c/f. The wavelength of these X-rays is approximately 3.06 x 10-11 meters.
Explanation:In Physics, we can find the wavelength of an X-ray given its frequency using the formula: λ=c/f, where 'λ' is the wavelength, 'c' is the speed of light (approximately 3.0 x 108 m/s in a vacuum), and 'f' is the frequency. Here, the frequency of the X-rays is given as 9.81 x 1018 Hz.
Substituting the values into the formula, we have: λ = (3.0 x 108) / (9.81 x 1018) = ~3.06 x 10-11 meters. The result indicates that the wavelength of these X-rays is incredibly small, which is consistent with our understanding of X-rays as high energy radiation with very short wavelengths and high frequencies.
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Two bodies are falling with negligible air resistance, side byside, above a horizontal plane near Earth's surface. If one of thebodies is given an additional horizontal acceleration during itsdescent, it ........................
(a) strikes the plane at the same time as the other body
(b) has the vertical component of its velocity altered
(c) has the vertical component of its accelerationaltered
(d) follows a hyperbolic path
(e) follows a straight line path along the resultantacceleration vector
Answer:
(a) strikes the plane at the same time as the other body
Explanation:
Two bodies are falling with negligible air resistance, side by side, above a horizontal plane near Earth's surface. If one of the bodies is given an additional horizontal acceleration during its descent, it strikes the plane at the same time as the other body
Two cars are driving towards an intersection from perpendicular directions. The first car's velocity is 2 meters per second and the second car's velocity is 9 meters per second. At a certain instant, the first car is 8 meters from the intersection and the second car is 6 meters from the intersection. What is the rate of change of the distance between the cars at that instant (in meters per second)? Choose 1 answer:
a -10
b -7
© -8.4
Answer:
Explanation:.
Given that
First car velocity is 2m/s
Second car velocity is 9m/s.
At a certain time the first car is 8m from intersection
And at the same time second car is 6m from intersection.
The rate of change of distance, i.e dx/dt, which is the speed of the car.
Using Pythagoras theorem, their distance apart is given as
Z²=X²+Y²
Z²=6²+8²
Z²=36+64
Z²=100
Z=√100
Z=10m
Let assume the direction,
Let assume the first car is moving in positive x direction, then
dx/dt=2m/s
And also second car will be moving in negative y direction
dy/dt=-9m/s
Now, to know dz/dt, let use the Pythagoras formulae above
x²+y²=z²
differentiate with respect to t
2dx/dt+2dy/dt=2dz/dt
Divide through by 2
dz/dt=dx/dt+dy/dt
dz/dt=2-9
dz/dt=-7m/s
The rate of change of distance between the two body is -7m/s
Option B is correct
Answer:
Rate of change of the distance between the cars = -7 m/s
Explanation:
Let the distance between the first car and the intersection be p = 8 meters
Let the distance between the second car and the intersection be q = 6 meters
velocity of the first car, dp/dt = -2 m/s
velocity of the second car, dq/dt = -9 m/s
We can get the distance between the two cars using pythagora's theorem
s² = p² + q²...................................(1)
s² = 8² + 6²
s = √(8² + 6²)
s = 10 m
Differentiating equation (1) through with respect to t
2s ds/dt = 2p dp/dt + 2q dq/dt
(2*10*ds/dt) = (2*8*(-2)) + (2*6*(-9))
20 ds/dt = -32 - 108
20 ds/dt = -140
ds/dt = -140/20
ds/dt = -7 m/s
(a) Given a 48.0-V battery and 24.0-Ω and 96.0-Ω resistors, find the current and power for each when connected in series. (b) Repeat when the resistances are in parallel.
Answer with Explanation:w
a.We are given that
Potential difference, V=48 V
[tex]R_1=24\Omega[/tex]
[tex]R_2=96\Omega[/tex]
Equivalent resistance when R1 and R2 are connected in series
[tex]R_{eq}=R_1+R_2[/tex]
Using the formula
[tex]R_{eq}=24+96=120\Omega[/tex]
We know that
[tex]I=\frac{V}{R_{eq}}=\frac{48}{120}=0.4 A[/tex]
In series combination, current passing through each resistor is same and potential difference across each resistor is different.
Power, P=[tex]I^2 R[/tex]
Using the formula
Power,[tex]P_1=I^2R_1=(0.4)^2\times 24=3.84 W[/tex]
Power, [tex]P_2=I^2 R_2=(0.4)^2(96)=15.36 W[/tex]
b.
In parallel combination, potential difference remains same across each resistor and current passing through each resistor is different..
Current,[tex]I=\frac{V}{R}[/tex]
Using the formula
[tex]I_1=\frac{V}{R_1}=\frac{48}{24}=2 A[/tex]
[tex]I_2=\frac{V}{R_2}=\frac{48}{96}=0.5 A[/tex]
[tex]P_1=\frac{V^2}{R_1}=\frac{(48)^2}{24}=96 W[/tex]
[tex]P_2=\frac{V^2}{R_2}=\frac{(48)^2}{96}=24 W[/tex]
When two resistors are in series, the current through each is the same and is calculated by dividing the total voltage by the total resistance. The power through each resistor is the current squared times the resistance of each resistor. When resistors are in parallel, the total resistance decreases and the power increases. The current remains the same.
Explanation:When the 24-ohm and 96-ohm resistors are connected in series, the total resistance can be calculated using the formula R = R1 + R2. Here, R1 is the resistance of the first resistor (24 ohms) and R2 is the resistance of the second resistor (96 ohms). R equals 120 ohms. The current, I, is calculated using Ohm's Law, I = V / R. Therefore, the current flowing through the circuit is I = 48.0 V / 120 Ω = 0.4 A. The power, P, through each resistor is calculated using the formula P = I^2 * R. Therefore, for the 24-ohm resistor, P is (0.4 A)^2 * 24 Ω = 3.84 W, and for the 96-ohm resistor, P is (0.4 A)^2 * 96 Ω = 15.36 W. When the resistors are connected in parallel, the total resistance is calculated using the formula 1/R = 1/R1 + 1/R2. The current through each resistor remains the same (0.4 A) and the power for each resistor can be calculated in the same way as described above.
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Before the experiment, the total momentum of the system is 2.5 kg m/s to the right and the kinetic energy is 5J. After the experiment, the total momentum of the system is 2.5 kg m/s to the right and the kinetic energy is 4J.
a)This describes an elastic collision (and it could NOT be inelastic).
b)This describes an inelastic collision (and it could NOT be elastic).
c)This is NEITHER an elastic collision nor an inelastic collision
d)This describes a collision that is EITHER elastic or inelastic, but more information is required to determine which.
Answer:
B
Explanation:
Newton's third law of motion states that to every action there is equal an opposite reaction. Momentum is always conserved provided there is no net force on the body. Considering the experiment: the momentum is conserved as expected but the kinetic energy is not conserved meaning that the collision is not elastic; some energy is converted into internal energy. When the collision is elastic the total kinetic energy before will equal total kinetic energy after and when the body stick together, they move with a common velocity and that described a perfectly inelastic collision. 5J ≠ 4J
Final answer:
The scenario describes an inelastic collision because while the momentum is conserved, the kinetic energy decreases from 5J to 4J, indicating that not all kinetic energy is conserved in the collision.
Explanation:
When examining collisions in physics, an elastic collision is one in which both momentum and kinetic energy are conserved, whereas an inelastic collision is one where momentum is conserved but kinetic energy is not. Given that in the scenario the total momentum of the system remains the same before and after the collision, that part of the conservation law is satisfied in both cases. However, since the kinetic energy of the system decreases from 5J to 4J, this means that some of the kinetic energy has been transformed into other forms of energy, like heat or sound, which typically happens during an inelastic collision.
Therefore, the correct answer is (b): This describes an inelastic collision (and it could NOT be elastic) since the total kinetic energy of the system is not the same before and after the collision. An elastic collision would have required that the kinetic energy also remain constant.
Before entering the cyclotron, the particles are accelerated by a potential difference V. Find the speed v with which the particles enter the cyclotron.
A typical cell membrane is 8.0 nm thick and has an electrical resistivity of 1.3 107 Ohms · m.
(a) If the potential difference between the inner and outer surfaces of a cell membrane is 80 mV, how much current flows through a square area of membrane 1.2 µm on a side?
_____________A
(b) Suppose the thickness of the membrane is doubled, but the resistivity and potential difference remain the same. Does the current increase or decrease or remain the same?
By what factor?
Explanation:
Below is an attachment containing the solution.
A block slides down a rough ramp (with friction) of height h . Its initial speed is zero. Its final speeds at the bottom of the ramp is v . Choose the system to be the block and the Earth.
While the block is descending, its kinetic energy:
a. Increases.
b. Decreases.
c. Remains constant.
Answer:
a. Increases
Explanation:
Conceptually, when a block of certain mass slides on the rough ramp kept on the earth which happens under the influence of gravity.The block is initially at rest but as the acceleration due to gravity acts on the block at the ramp. The ramp is rough so it applies kinetic friction on the moving block as the block slides down the slope.By the definition we know that the acceleration is the rate of change in velocity and here we have acceleration component in the direction of motion of the block.
Mathematically:
when the body is moving down:
[tex]v=u+gt[/tex]
where:
[tex]v=[/tex] final velocity of the block
[tex]u=[/tex] initial velocity of the block
[tex]g=[/tex] acceleration due to gravity
[tex]t=[/tex] time of observation during the instance of motion
From above it is clear that the velocity of the block will increase as the time passes during the motion.As we know that kinetic energy is given as:
[tex]KE=\frac{1}{2} \times m.v^2[/tex]
where:
[tex]m=[/tex] mass of the block which remains constant (macroscopically)
[tex]v=[/tex] velocity of the block (which increases here as the body descends)
A small current element carrying a current of I = 5.00 A is placed at the origin given by d → l = 4.00 m m ^ j Find the magnetic field, d → B , at the locations specified. Enter the correct magnitude and select the direction from the list. If the direction is negative, indicate this by entering the magnitude as a negative number. What is the magnitude and direction of d → B on the x ‑axis at x = 2.00 m ?
Answer:
dB = (-5 × 10⁻⁷k) T
Magnitude of dB = (-5 × 10⁻⁷) T; magnitude is actually (5 × 10⁻⁷) T in the mathematical sense of what magnitude is, but this question instructs to include the negative of the direction of dB is negative.
Direction is in the negative z-direction as evident from the sign on dB's vector notation.
Explanation:
From Biot Savart's relation, the magnetic field is given by
dB = (μ₀I/4πr³) (dL × r)
μ₀ = (4π × 10⁻⁷) H/m
I = 5.0 A
r = (2î) m
Magnitude of r = 2
dL = (4j)
(dL × r) is the vector product of both length of current carrying wire vector and the vector position of the point where magnetic field at that point is needed.
(dL × r) = (4j) × (2î)
|i j k|
|0 4 0|
|2 0 0|
(dL × r) = (0î + 0j - 8k) = (-8k)
(μ₀I/4πr³) = (4π × 10⁻⁷ × 5)/(4π×2³)
(μ₀I/4πr³) = (6.25 × 10⁻⁸)
dB = (μ₀I/4πr³) (dL × r) = (6.25 × 10⁻⁸) × (-8k)
dB = (-5 × 10⁻⁷k) T
Magnitude of dB = (-5 × 10⁻⁷) T; magnitude is actually (5 × 10⁻⁷) T in the mathematical sense of what magnitude is, but this question instructs to include the negative of the direction of dB is negative.
Direction is in the negative z-direction as evident from the sign on dB's vector notation.
Hope this Helps!!!
When the distance is 4 m, the magnetic field strength is 2.5 x 10⁻⁷ T.
When the distance is 2 m, the magnetic field strength is 5 x 10⁻⁷ T.
Magnitude of magnetic fieldThe magnitude of magnetic field at any distance from a wire is determined by applying Biot-Savart law,
[tex]B = \frac{\mu_o I}{2\pi r}[/tex]
Where;
r is the distance from the conductor
When the distance is 4 m, the magnetic field strength is calculated as;
[tex]B = \frac{(4\pi \times 10^{-7}) \times5 }{2\pi \times 4} \\\\B = 2.5 \times 10^{-7} \ T[/tex]
When the distance is 2 m, the magnetic field strength is calculated as;
[tex]B = \frac{(4\pi \times 10^{-7} \times 5}{2\pi \times 2} \\\\B = 5 \times 10^{-7} \ T[/tex]
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