Q: A 10 kg box is pushed across a horizontal floor by a constant force of 50 N over a distance of 4 m. What is the work done by the force? Use $$W = F_x \Delta x.$$

$$W = 50 \times 4 = 200\ \mathrm{J}$$

Q: A person pulls a sled with a force of 180 N at an angle of 40° above the horizontal for 5.0 m. What is the work done by the person? Use $$W = F \Delta x \cos \theta.$$

$$W = 180 \times 5.0 \times \cos 40^\circ = 690\ \mathrm{J}$$

Q: Which of the following is the correct scalar product (dot product) formula for work done by a force $$\vec{F}$$ over displacement $$\Delta \vec{r}$$?

$$W = \vec{F} \cdot \Delta \vec{r} = F \Delta r \cos \theta$$

Q: A 3000-kg truck is lifted vertically upward by a crane with a force of 31 kN over a distance of 2.0 m. What is the work done by the crane?

$$W = 31,000 \times 2.0 = 62,000\ \mathrm{J}$$

Q: A 700-kg crate is pushed up a 30° incline by a horizontal force of 5600 N for 3.0 m. What is the work done by the force $$P$$?

$$W = 5600 \times 3.0 = 16,800\ \mathrm{J}$$

Question 1

Which of the following best describes the concept of a 'system' in physics as it relates to energy transfer?

Accepted Answer

A system is a portion of the universe chosen for analysis, separated by a boundary, where energy can flow in and out as mechanical, heat, or electromagnetic energy.

Question 2

A 10 kg box is pushed across a horizontal floor by a constant force of 50 N over a distance of 4 m. What is the work done by the force? Use $$W = F_x \Delta x.$$

Accepted Answer

$$W = 50 	imes 4 = 200\ \mathrm{J}$$

Question 3

Which scenario results in zero work being done by a force on an object?

Accepted Answer

The force is perpendicular to the displacement of the object.

Question 4

A person pulls a sled with a force of 180 N at an angle of 40° above the horizontal for 5.0 m. What is the work done by the person? Use $$W = F \Delta x \cos 	heta.$$

Accepted Answer

$$W = 180 	imes 5.0 	imes \cos 40^\circ = 690\ \mathrm{J}$$

Question 5

Which of the following is the correct scalar product (dot product) formula for work done by a force $$\vec{F}$$ over displacement $$\Delta \vec{r}$$?

Accepted Answer

$$W = \vec{F} \cdot \Delta \vec{r} = F \Delta r \cos 	heta$$

Question 6

A 3000-kg truck is lifted vertically upward by a crane with a force of 31 kN over a distance of 2.0 m. What is the work done by the crane?

Accepted Answer

$$W = 31,000 	imes 2.0 = 62,000\ \mathrm{J}$$

Question 7

A 700-kg crate is pushed up a 30° incline by a horizontal force of 5600 N for 3.0 m. What is the work done by the force $$P$$?

Accepted Answer

$$W = 5600 	imes 3.0 = 16,800\ \mathrm{J}$$

Question 8

The kinetic energy of an object of mass $$m$$ moving at speed $$v is $$given by:

Accepted Answer

$$K = \frac{1}{2}mv^2$

Question 9

According to the work-energy theorem, the net work done on an object is equal to:

Accepted Answer

The change in the object's kinetic energy: $$W_{net} = \Delta K$$

Question 10

If $$W_{net} \u003c 0$$ for a particle, what happens to the particle's motion?

Accepted Answer

The particle slows down.

Question 11

Two objects, one of mass $$m$$ and the other of mass $$2m$$, are dropped from the same height. When they hit the ground, how do their kinetic energies compare?

Accepted Answer

The heavier one will have twice the kinetic energy of the lighter one.

Question 12

A 4.0-kg object is moving at 2.0 m/s, and a 1.0-kg object is moving at 4.0 m/s. Both are stopped by the same constant braking force. Which travels farther before stopping?

Accepted Answer

Both objects travel the same distance.

Question 13

The work done by a variable force $$F(x) as an $$object moves from $$x_1 to$$ $$x_2 is $$given by:

Accepted Answer

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

Question 14

A spring with force constant $$k$$ exerts a force $$F_{spring} = -kx. $$What is the work done by the spring as it moves from $$x_i to$$ $$x_f$$?

Accepted Answer

$$W = -\frac{1}{2}k(x_f^2$ - x_i^2$)$$

Question 15

A 4.0-kg block on a frictionless table is attached to a spring ($$k=400\ \mathrm{N/m}) $$and is compressed 5.0 cm. What is the speed of the block at equilibrium ($$x=0$$)?

Accepted Answer

$$v = \sqrt{\frac{kx^2$}{m}} = \sqrt{\frac{400 	imes (0.05)^2$}{4.0}} = 0.5\ \mathrm{m/s}$$

Question 16

The average power delivered by a force that does work $$\Delta W in $$time $$\Delta t is$$:

Accepted Answer

$$\overline{P} = \frac{\Delta W}{\Delta t}$$

Question 17

A cyclist (total mass 75 kg) rides at a steady 4.4 m/s against an 8.2 N air resistance. What power must the cyclist supply?

Accepted Answer

$$P = Fv = 8.2 	imes 4.4 = 36.08\ \mathrm{W}$$

Work, Kinetic Energy, and Power: Physics with Calculus Study Notes

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