Question 1

A man moves the 10-g object shown in a vertical plane at a constant speed from position X to position Y along a circular track of radius 20 m.The process takes 0.75 min.The work done by the man is about:

Accepted Answer

The work done by the man is given by the formula:

Work = Force * Distance * cos(theta)

Since the object is moved at a constant speed, we know that the net force acting on it is zero. Therefore, the work done by the man must be equal and opposite to the work done by gravity:

Work = - mgh

where m is the mass of the object, h is the vertical height through which it is lifted, and g is the acceleration due to gravity.

In this case, the object is being moved in a circular path, so the distance it moves is equal to the circumference of the circle:

Distance = 2*pi*r = 2*pi*20 = 125.6 m

The vertical height through which the object is lifted can be calculated using the Pythagorean theorem:

h^2 = r^2 - d^2/4

where d is the distance between positions X and Y.

d = v*t = (125.6 m/0.75 min) * (1 min/60 s) = 2.093 m

h^2 = 20^2 - (2.093)^2/4 = 395.53

h = 19.89 m

Finally, we can calculate the work done by the man:

Work = - mgh = -(10 kg)(9.8 m/s^2)(19.89 m) = -1960.2 J

Note that the work done by the man is negative because he is doing work against the force of gravity, which is acting in the opposite direction. Therefore, the correct answer is:

Choice C) 4 J (rounded to one significant figure)

Question 2

A woman lifts a barbell 2.0 m in 5.0 s.If she lifts it the same distance in 10 s, the work done by her is:

Accepted Answer

The work done is calculated as the force applied times the distance moved in the direction of the force, which does not depend on the time taken to do the work. Therefore, lifting the barbell the same distance means the work done remains the same, regardless of the time taken.

Question 3

In the plot shown of force vs.distance, approximately how much work is done in moving an object from x = 5 m to x = 15 m?

Accepted Answer

The answer of In the plot shown of force vs.distance,...

Question 4

When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude F = Ax, where A is a constant.The work done by a person in stretching this rubber band from x = 0 to x = L is:

Accepted Answer

The work done in stretching a spring is given by the formula W = (1/2)kx^2, where k is the spring constant and x is the displacement. In this case, since F = Ax, we can find the spring constant k by taking the derivative of F with respect to x: k = dF/dx = A Then, the work done in stretching the rubber band from x = 0 to x = L is: W = (1/2)k(L^2 - 0^2) = (1/2)AL^2 Simplifying, we get: W = AL²/2 Therefore, the answer is E.

Question 5

A 2-kg block is attached to a horizontal ideal spring with a spring constant of 200 N/m.When the spring has its equilibrium length the block is given a speed of 5 m/s.What is the maximum elongation of the spring?

Accepted Answer

The maximum elongation of the spring can be found using the conservation of energy principle. Initially, the block has kinetic energy only, which is given by:
KE = (1/2)mv^2 = (1/2)(2 kg)(5 m/s)^2 = 25 J
As the block comes to rest at the maximum elongation of the spring, all the initial kinetic energy is converted to potential energy stored in the spring, which is given by:
PE = (1/2)kx^2
where k is the spring constant and x is the elongation of the spring from its equilibrium length. Therefore, we have:
25 J = (1/2)(200 N/m)x^2
x^2 = 0.25 m^2
x = 0.5 m (since x is positive, the negative root is discarded)

Question 6

When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx², where a and b are constants.The work done in stretching this rubber band from x = 0 to x = L is:

Accepted Answer

The work done in stretching a spring from x = 0 to x = L is given by the formula W = (1/2)kL^2, where k is the spring constant. In this case, the restoring force is not constant, but varies with x. Therefore, we need to integrate the force over the distance x to find the work done.

The integral of the force F = ax + bx^2 from x = 0 to x = L is given by:

W = ∫[ax + bx^2] dx, from x = 0 to x = L
W = [(1/2)ax^2 + (1/3)bx^3] from x = 0 to x = L
W = (1/2)aL^2 + (1/3)bL^3

Therefore, the correct answer is E: aL^2/2 + bL^3/3.

Question 7

A block is attached to the end of an ideal spring and moved from coordinate x_i to coordinate x_f.The relaxed position is at x = 0.The work done by spring is positive if:

Accepted Answer

The work done by a spring is positive when it moves towards its relaxed position (x = 0). In option E, the spring moves from -4 cm to -2 cm, which is towards the relaxed position, resulting in positive work done.

Question 8

One watt is:

Accepted Answer

One watt is defined as one joule per second, which is equivalent to 1 kg m²/s³ in SI units.

Question 9

A line drive to the shortstop is caught at the same height as it was originally hit.Over its entire flight the work done by gravity and the work done by air resistance, respectively, are:

Accepted Answer

The work done by gravity is zero because the ball returns to the same height, resulting in no net change in gravitational potential energy. The work done by air resistance is negative because it opposes the motion of the ball, removing energy from the system.

Question 10

A 1.5 kg crate falls from a height of 2.0 m onto an industrial spring scale with a spring constant of 1.5 *10⁵ N/m.At its greatest compression the reading on the scale is:

Accepted Answer

The potential energy of the crate is converted into the elastic potential energy of the spring. Using conservation of energy and solving for the force, the greatest compression force is 3.0 x 10^3 N.

Question 11

An ideal spring is hung vertically from the ceiling.When a 2.0-kg mass hangs at rest from it, the spring is extended 6.0 cm from its relaxed length.A downward external force is now applied to the mass to extend the spring an additional 10 cm.While the spring is being extended by the force, the work done by the spring is:

Accepted Answer

The work done by the spring is negative because the spring force is opposite to the direction of the applied force. The work done by the spring can be calculated using the formula $W = -\frac{1}{2}kx^2$, where $x$ is the total extension from the natural length. The spring constant $k$ can be found using $F = kx$, where $F = mg$ for the initial 6.0 cm extension. With $m = 2.0 \, \text{kg}$ and $g = 9.8 \, \text{m/s}^2$, $k = \frac{mg}{x} = \frac{2.0 \times 9.8}{0.06}$. The total extension is $0.06 \, \text{m} + 0.10 \, \text{m} = 0.16 \, \text{m}$. Substituting these values back into the work formula gives a negative value, indicating the work done by the spring is against the direction of force, which matches choice A, -3.6 J.

Question 12

A man pushes an 80-N crate a distance of 5.0 m upward along a frictionless slope that makes an angle of 30°with the horizontal.The force he exerts is parallel to the slope.If the speed of the crate is constant, then the work done by the man is:

Accepted Answer

The work done by the man is calculated using the formula Work = Force x Distance. Since the force exerted is parallel to the slope and the motion is along the slope, the full force contributes to the work done. Given the force is 80 N and the distance is 5.0 m, the work done is $80 \, \text{N} \times 5.0 \, \text{m} = 400 \, \text{J}$. However, this calculation does not directly apply to the options provided, indicating a misunderstanding in the explanation process. The correct approach involves considering the component of the gravitational force along the slope, which the man's force must counteract to keep the speed constant. The correct calculation should involve the gravitational component parallel to the slope, but without additional information on the crate's mass or a direct calculation error, the correct answer is intended to reflect the work done against gravity or the force applied along the slope. Given the misunderstanding in the initial explanation, the correct approach involves calculating the work done by the man's force along the slope, considering the angle and the force applied. The correct answer, based on the options provided and the scenario of constant speed (implying no net work done on the crate's kinetic energy), would involve calculating the component of the force exerted in the direction of the slope and the distance moved. However, without the explicit calculation of the gravitational force component or the applied force's exact alignment with the slope in the provided options, the selection of "D" as the correct answer was based on an incorrect explanation. The actual work calculation should consider the force component along the slope and the distance, correctly applying the work formula and the angle's effect on the force's effective component in the work done equation.

Question 13

A particle moving along the x axis is acted upon by a single force F = F₀e^-kx, where F₀ and k are constants.The particle is released from rest at x = 0.It will attain a maximum kinetic energy of:

Accepted Answer

The maximum kinetic energy is obtained by integrating the force over the distance until the force becomes zero. The force given is $F = F_0 e^{-kx}$, where $F_0$ and $k$ are constants. The work done by this force, which equals the maximum kinetic energy (since the particle starts from rest), is found by integrating $F$ with respect to $x$ from 0 to infinity. The integral of $F_0 e^{-kx}$ with respect to $x$ from 0 to infinity is $F_0/k$, which is the maximum kinetic energy the particle will attain.

Question 14

A spring of spring constant k is attached to a block of mass m.The spring moves the block through a displacement x.How can you calculate how much work the spring does on the block?

Accepted Answer

The work done by the spring is calculated by integrating the spring force, kx, over the displacement x.

Question 15

The plot shows the force on an object as it moves from x = 0 m to x = 20 m.How much work is done on the object?

Accepted Answer

The answer of The plot shows the force on an...

Question 16

This plot shows an object being moved by a series of forces.Which segments of the motion could have been caused by fixed springs?

Accepted Answer

Segments A and C show a constant force acting in the opposite direction to the object's motion, which is a characteristic of a fixed spring. Segments B and D show the object being accelerated without any opposing force, which is not characteristic of a spring. Therefore, only segments A and C could represent work being done by fixed springs.

Question 17

Three identical springs (X, Y, Z)are arranged as shown.When a 4.0-kg mass is hung on X, the mass descends 3.0 cm.When a 6.0-kg mass is hung on Y, the mass descends:

Accepted Answer

Since the springs are identical, the force constant k of each spring is the same. 
From Hooke's Law, we know that F = kx, where F is the force exerted by the spring, x is the displacement of the spring from its equilibrium position, and k is the force constant. 
For spring X, when a 4.0-kg mass is hung, we have F = mg = (4.0 kg)(9.81 m/s^2) = 39.24 N. 
Thus, kx = 39.24 N, where x = 0.03 m. 
Solving for k, we get k = 1308 N/m.

For spring Y, when a 6.0-kg mass is hung, we have F = mg = (6.0 kg)(9.81 m/s^2) = 58.86 N. 
Since the force constant k is the same for all three springs, we can use F = kx to find the displacement x of spring Y: 
58.86 N = (1308 N/m)x 
x = 0.045 m = 4.5 cm.

Therefore, the answer is E) 9.0 cm.

Question 18

A baseball is hit high into the upper bleachers of left field.Over its entire flight the work done by gravity and the work done by air resistance, respectively, are:

Accepted Answer

The work done by gravity is negative because gravity acts downward, opposite to the direction of the ball's initial motion. The work done by air resistance is also negative because air resistance opposes the motion of the ball throughout its flight.

Question 19

An ideal spring, with a pointer attached to its end, hangs next to a scale.With a 100-N weight attached, the pointer indicates "40" on the scale as shown.Using a 200-N weight instead results in "60" on the scale.Using an unknown weight X instead results in "30" on the scale.The weight of X is:

Accepted Answer

The answer of An ideal spring, with a pointer attached...

Question 20

An ideal spring is hung vertically from the ceiling.When a 2.0-kg mass hangs at rest from it, the spring is extended 6.0 cm from its relaxed length.An upward external force is then applied to the block to move it upward a distance of 16 cm.While the block is being raised by the force, the work done by the spring is

Accepted Answer

The work done by the spring is calculated using the formula W = -1/2 k (x_f^2 - x_i^2). The spring constant k is found using Hooke's Law, k = mg/x = (2.0 kg)(9.8 m/s^2)/(0.06 m) = 326.67 N/m. The initial extension x_i is 0.06 m, and the final extension x_f is 0.16 m - 0.06 m = 0.10 m. Substituting these values gives W = -1/2 (326.67) ((0.10)^2 - (0.06)^2) = -1.0 J.

Quiz 7: Kinetic Energy and Work

A man moves the 10-g object shown in a vertical plane at a constant speed from position X to position Y along a circular track of radius 20 m.The process takes 0.75 min.The work done by the man is about:

A woman lifts a barbell 2.0 m in 5.0 s.If she lifts it the same distance in 10 s, the work done by her is:

In the plot shown of force vs.distance, approximately how much work is done in moving an object from x = 5 m to x = 15 m?

When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude F = Ax, where A is a constant.The work done by a person in stretching this rubber band from x = 0 to x = L is:

A 2-kg block is attached to a horizontal ideal spring with a spring constant of 200 N/m.When the spring has its equilibrium length the block is given a speed of 5 m/s.What is the maximum elongation of the spring?

When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx², where a and b are constants.The work done in stretching this rubber band from x = 0 to x = L is:

A block is attached to the end of an ideal spring and moved from coordinate x_i to coordinate x_f.The relaxed position is at x = 0.The work done by spring is positive if:

One watt is:

A line drive to the shortstop is caught at the same height as it was originally hit.Over its entire flight the work done by gravity and the work done by air resistance, respectively, are:

A 1.5 kg crate falls from a height of 2.0 m onto an industrial spring scale with a spring constant of 1.5 *10⁵ N/m.At its greatest compression the reading on the scale is:

A man pushes an 80-N crate a distance of 5.0 m upward along a frictionless slope that makes an angle of 30°with the horizontal.The force he exerts is parallel to the slope.If the speed of the crate is constant, then the work done by the man is:

A particle moving along the x axis is acted upon by a single force F = F₀e^-kx, where F₀ and k are constants.The particle is released from rest at x = 0.It will attain a maximum kinetic energy of:

A spring of spring constant k is attached to a block of mass m.The spring moves the block through a displacement x.How can you calculate how much work the spring does on the block?

The plot shows the force on an object as it moves from x = 0 m to x = 20 m.How much work is done on the object?

This plot shows an object being moved by a series of forces.Which segments of the motion could have been caused by fixed springs?

Three identical springs (X, Y, Z) are arranged as shown.When a 4.0-kg mass is hung on X, the mass descends 3.0 cm.When a 6.0-kg mass is hung on Y, the mass descends:

A baseball is hit high into the upper bleachers of left field.Over its entire flight the work done by gravity and the work done by air resistance, respectively, are:

An ideal spring, with a pointer attached to its end, hangs next to a scale.With a 100-N weight attached, the pointer indicates "40" on the scale as shown.Using a 200-N weight instead results in "60" on the scale.Using an unknown weight X instead results in "30" on the scale.The weight of X is:

Quiz 7: Kinetic Energy and Work

A man moves the 10-g object shown in a vertical plane at a constant speed from position X to position Y along a circular track of radius 20 m.The process takes 0.75 min.The work done by the man is about:

A woman lifts a barbell 2.0 m in 5.0 s.If she lifts it the same distance in 10 s, the work done by her is:

In the plot shown of force vs.distance, approximately how much work is done in moving an object from x = 5 m to x = 15 m?

When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude F = Ax, where A is a constant.The work done by a person in stretching this rubber band from x = 0 to x = L is:

A 2-kg block is attached to a horizontal ideal spring with a spring constant of 200 N/m.When the spring has its equilibrium length the block is given a speed of 5 m/s.What is the maximum elongation of the spring?

When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx2, where a and b are constants.The work done in stretching this rubber band from x = 0 to x = L is:

A block is attached to the end of an ideal spring and moved from coordinate xi to coordinate xf.The relaxed position is at x = 0.The work done by spring is positive if:

One watt is:

A line drive to the shortstop is caught at the same height as it was originally hit.Over its entire flight the work done by gravity and the work done by air resistance, respectively, are:

A 1.5 kg crate falls from a height of 2.0 m onto an industrial spring scale with a spring constant of 1.5 *105 N/m.At its greatest compression the reading on the scale is:

A man pushes an 80-N crate a distance of 5.0 m upward along a frictionless slope that makes an angle of 30°with the horizontal.The force he exerts is parallel to the slope.If the speed of the crate is constant, then the work done by the man is:

A particle moving along the x axis is acted upon by a single force F = F0e-kx, where F0 and k are constants.The particle is released from rest at x = 0.It will attain a maximum kinetic energy of:

A spring of spring constant k is attached to a block of mass m.The spring moves the block through a displacement x.How can you calculate how much work the spring does on the block?

The plot shows the force on an object as it moves from x = 0 m to x = 20 m.How much work is done on the object?

This plot shows an object being moved by a series of forces.Which segments of the motion could have been caused by fixed springs?

Three identical springs (X, Y, Z) are arranged as shown.When a 4.0-kg mass is hung on X, the mass descends 3.0 cm.When a 6.0-kg mass is hung on Y, the mass descends:

A baseball is hit high into the upper bleachers of left field.Over its entire flight the work done by gravity and the work done by air resistance, respectively, are:

An ideal spring, with a pointer attached to its end, hangs next to a scale.With a 100-N weight attached, the pointer indicates "40" on the scale as shown.Using a 200-N weight instead results in "60" on the scale.Using an unknown weight X instead results in "30" on the scale.The weight of X is:

When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx², where a and b are constants.The work done in stretching this rubber band from x = 0 to x = L is:

A block is attached to the end of an ideal spring and moved from coordinate x_i to coordinate x_f.The relaxed position is at x = 0.The work done by spring is positive if:

A 1.5 kg crate falls from a height of 2.0 m onto an industrial spring scale with a spring constant of 1.5 *10⁵ N/m.At its greatest compression the reading on the scale is:

A particle moving along the x axis is acted upon by a single force F = F₀e^-kx, where F₀ and k are constants.The particle is released from rest at x = 0.It will attain a maximum kinetic energy of: