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: If 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?

$$W_{net} = (100 \text{ N} - 50 \text{ N}) \times 40 \text{ m} = 2000 \text{ J}$$

Q: A force varies as $$F(x) = 2x N$$, where $$x is in $$meters. How much work is done by this force as an object moves from $$x = 0 m to$$ $$x = 3 m$$?

$$W = \$$int_0$$^3 2x \, dx = 9 \text{ J}$$

Q: A spring with $$k = 360 \text{ N/m} is $$compressed by $$0.11 \text{ m}. $$What is the work done to compress the spring?

$$W = \frac{1}{2} \times 360 \times (0.11)^2$ = 2.178 \text{ J}$$

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

$$W = \int_{0.010}^{0.050} 2x \, dx = 0.0016 \text{ J}$$

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 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

$$W_{net} = (100 	ext{ N} - 50 	ext{ N}) 	imes 40 	ext{ m} = 2000 	ext{ J}$$

Question 4

Which force does NOT do work on a box being pulled horizontally across a floor?

Accepted Answer

The normal force perpendicular to the displacement

Question 5

A piano is moved 9 m down a 25° incline and kept from accelerating by a person pushing up the ramp. 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 6

Which statement about work and energy is correct?

Accepted Answer

Work is a scalar quantity, and energy is also a scalar quantity.

Question 7

A force varies as $$F(x) = 2x N$$, where $$x is in $$meters. How much work is done by this force as an object moves from $$x = 0 m to$$ $$x = 3 m$$?

Accepted Answer

$$W = \$$int_0$$^3 2x \, dx = 9 	ext{ J}$$

Question 8

According to Hooke's Law, what is the restoring force $$F of a $$spring displaced by $$\Delta x$$ from its equilibrium position?

Accepted Answer

$$F = -k \Delta x$$

Question 9

How much work is required to compress a spring with spring constant $$k$$ from its equilibrium position by a distance $$x$$?

Accepted Answer

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

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

Which of the following is the correct expression for the work-energy theorem?

Accepted Answer

$$W = \Delta KE = \frac{1}{2}mv_f^2$ - \frac{1}{2}mv_i^2$

Question 12

A spring with $$k = 360 	ext{ N/m} is $$compressed by $$0.11 	ext{ m}. $$What is the work done to compress the spring?

Accepted Answer

$$W = \frac{1}{2} 	imes 360 	imes (0.11)^2$ = 2.178 	ext{ J}$$

Question 13

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

Accepted Answer

Zero work

Question 14

A force $$F$$ acts on an object at an angle $$	heta to $$the direction of displacement $$\Delta x. $$For which value of $$	heta is $$the work done by the force maximized?

Accepted Answer

$$	heta = 0^\circ$$

Question 15

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

Accepted Answer

$$W = \int_{0.010}^{0.050} 2x \, dx = 0.0016 	ext{ J}$$

Question 16

Which of the following statements about frictional force is correct?

Accepted Answer

Frictional force does negative work when opposing motion.

Question 17

A spring is compressed from $$x = 0 to$$ $$x = 0.07 	ext{ m}$$ with $$k = 360 	ext{ N/m}. $$What is the kinetic energy of a 1.85 kg object released from the spring at $$x = 0.07 	ext{ m}$$?

Accepted Answer

$$KE = \frac{1}{2} 	imes 360 	imes (0.07)^2$ = 0.882 	ext{ J}$$

Question 18

Which of the following is the SI unit of work and energy?

Accepted Answer

Joule ($$	ext{J})$$

Work and Energy: Chapter 7 Study Notes

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