Q: Which of the following best describes the work done by a force $$\vec{F}$$ acting on an object that moves through a displacement $$\vec{s} at an $$angle $$\theta$$ between them?

$$W = F \cdot s \cdot \cos\theta$$

Q: A runner completes a 5 km run at 10 km/h, using energy at a rate of 700 W. How much energy does the runner use?

$$E = 700 \times 0.5 \times 3600$$

Q: A spring with $$k = 4691 \ \mathrm{N} \mathrm{m}^{-1} is $$stretched by $$0.09 m. $$What is the magnitude of the force required?

$$F = 4691 \times 0.09 = 422.19 \ \mathrm{N}$$

Question 1

Which of the following best describes the work done by a force $$\vec{F}$$ acting on an object that moves through a displacement $$\vec{s} at an $$angle $$	heta$$ between them?

Accepted Answer

$$W = F \cdot s \cdot \cos	heta$$

Question 2

A block of mass $$m is $$accelerated from velocity $$v_1 to$$ $$v_2 by a $$constant force $$F$$ over a displacement $$s. $$What is the work done by the force?

Accepted Answer

$$W = \frac{1}{2}m(v_2$^2 - v_1$^2)$$

Question 3

Which statement about the work-energy theorem is correct?

Accepted Answer

The work done by the net force on an object is equal to the change in its kinetic energy.

Question 4

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

Accepted Answer

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

Question 5

If a force $$F(x)$$ varies with position $$x$$, what is the general expression for the work done moving an object from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$W = \int_{x_1$}^{x_2$} F(x) dx$$

Question 6

A person pushes a child on a swing with a force perpendicular to the direction of motion. What is the work done by this force?

Accepted Answer

The work is zero because the force is perpendicular to the displacement.

Question 7

Which of the following is true for conservative forces?

Accepted Answer

The work done by a conservative force is independent of the path and depends only on the initial and final positions.

Question 8

A runner completes a 5 km run at 10 km/h, using energy at a rate of 700 W. How much energy does the runner use?

Accepted Answer

$$E = 700 	imes 0.5 	imes 3600$$

Question 9

Which equation correctly relates instantaneous power to force and velocity?

Accepted Answer

$$P = F \cdot v$$

Question 10

A block moves along a curved path under a varying force $$\vec{F}. $$What is the total work done by the force?

Accepted Answer

$$W = \int_{A}^{B} F \cdot ds$$

Question 11

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

Accepted Answer

Joule ($$J)$$

Question 12

A spring with $$k = 4691 \ \mathrm{N} \mathrm{m}^{-1} is $$stretched by $$0.09 m. $$What is the magnitude of the force required?

Accepted Answer

$$F = 4691 	imes 0.09 = 422.19 \ \mathrm{N}$$

Question 13

Which of the following best describes the relationship between work and kinetic energy?

Accepted Answer

Work done by the net force is equal to the change in kinetic energy.

Question 14

If the force applied to an object is not constant, how can the total work done be calculated?

Accepted Answer

By integrating the force over the displacement.

Question 15

A cyclist moves along a path where the force required to pedal varies with position. Which mathematical tool is necessary to calculate the total work done?

Accepted Answer

Integration

Question 16

Which of the following is true about the sign of work done by a force?

Accepted Answer

Work is positive if the force has a component in the direction of displacement.

Question 17

A person pushes a box along the floor with a force at an angle $$	heta to $$the horizontal. Which component of the force does work?

Accepted Answer

The horizontal component

Question 18

Which of the following is the correct expression for the instantaneous power delivered by a force $$F$$ moving an object at velocity $$v$$?

Accepted Answer

$$P = F \cdot v$$

Question 19

A spring is compressed by $$x$$ from its equilibrium position. What is the elastic potential energy stored in the spring?

Accepted Answer

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

DR2- Work and Kinetic energy

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