Q: A box is pushed across the floor by a force $$\vec{F} at an $$angle $$\theta to $$the direction of displacement $$\Delta x. $$Which equation correctly calculates the work done by the force?

$$W = F \cdot \Delta x \cdot \cos(\theta)$$

Q: A 50 kg crate is pulled 40 m along a horizontal floor by a constant force of 100 N, while a frictional force of 50 N opposes the motion. What is the net work done on the crate?

$$W_{net} = (100\,\text{N} - 50\,\text{N}) \times 40\,\text{m}$$

Q: A force of 5 N is applied to a box for 2 m, then increased to 10 N for another 2 m. What is the total work done on the box?

$$W = (5 \times 2) + (10 \times 2)$$

Q: If a spring with $$k = 360\,\text{N/m} is $$compressed by $$x = 0.11\,\text{m}$$, what is the work required to compress it?

$$W = \frac{1}{2} \times 360 \times (0.11)^2$

Question 1

Which of the following best describes the physical definition of work in physics?

Accepted Answer

Work is the product of force and displacement in the direction of the force.

Question 2

A box is pushed across the floor by a force $$\vec{F} at an $$angle $$	heta to $$the direction of displacement $$\Delta x. $$Which equation correctly calculates the work done by the force?

Accepted Answer

$$W = F \cdot \Delta x \cdot \cos(	heta)$$

Question 3

If a force is applied perpendicular to the direction of displacement, what is the work done by that force?

Accepted Answer

No work is done.

Question 4

A 50 kg crate is pulled 40 m along a horizontal floor by a constant force of 100 N, while a frictional force of 50 N opposes the motion. What is the net work done on the crate?

Accepted Answer

$$W_{net} = (100\,	ext{N} - 50\,	ext{N}) 	imes 40\,	ext{m}$$

Question 5

Which of the following statements about work is correct?

Accepted Answer

Work is a scalar quantity and can be positive or negative.

Question 6

A piano is moved 9 m down a 25° incline and is kept from accelerating by a person exerting a force up the incline. What is the work done by the person if the force is applied directly opposite to the displacement?

Accepted Answer

$$W = F \cdot d \cdot \cos(180°)$$

Question 7

When a force varies with position, how is the total work done calculated?

Accepted Answer

By integrating the force over the displacement: $$W = \int F(x)\,dx$$

Question 8

A spring with spring constant $$k is $$stretched by a distance $$x$$ from its equilibrium position. What is the work required to stretch the spring?

Accepted Answer

$$W = \frac{1}{2}kx^2$

Question 9

Which law describes the restoring force of a spring?

Accepted Answer

Hooke's Law: $$F = -kx$$

Question 10

A 1000 kg car traveling at 15 m/s can brake to a stop in 20 m. If another car of the same mass is traveling at 30 m/s, what is its stopping distance assuming the same braking force?

Accepted Answer

80 m

Question 11

The work-energy theorem states:

Accepted Answer

The net work done on an object is equal to its change in kinetic energy: $$W_{net} = \Delta KE$$

Question 12

A force of 5 N is applied to a box for 2 m, then increased to 10 N for another 2 m. What is the total work done on the box?

Accepted Answer

$$W = (5 	imes 2) + (10 	imes 2)$$

Question 13

If a spring with $$k = 360\,	ext{N/m} is $$compressed by $$x = 0.11\,	ext{m}$$, what is the work required to compress it?

Accepted Answer

$$W = \frac{1}{2} 	imes 360 	imes (0.11)^2$

Question 14

Which of the following is true about the direction of force and work?

Accepted Answer

Work is negative when force opposes displacement.

Question 15

A video camera arm moves from $$x_i = 0.010\,	ext{m} to$$ $$x_f = 0.050\,	ext{m}$$ under a force $$F(x) = 2x + 3. $$What is the total work done by the force?

Accepted Answer

$$W = \int_{0.010}^{0.050} (2x + 3) dx$$

Question 16

Which of the following is the correct SI unit for work?

Accepted Answer

Joule ($$	ext{J})$$

Question 17

If the net work done on an object is zero, what can be said about its kinetic energy?

Accepted Answer

Its kinetic energy remains unchanged.

Question 18

A force acts on an object at an angle $$	heta to $$the direction of displacement. When is the work done by the force maximized?

Accepted Answer

When $$	heta = 0°$$

Question 19

Which of the following best explains why friction does negative work on a moving object?

Accepted Answer

Friction acts opposite to the direction of displacement.

Work and Energy: Mathematical Framework and Applications

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