Q: A 5.0 kg cannonball is fired straight up at 35 m/s. What is its speed after rising 45 m? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{35^2$ - 2 \times 9.8 \times 45}$$

Q: A 70 kg skier is gliding at 2.0 m/s when he starts down a very slippery 50-m-long, 10° slope. What is his speed at the bottom? (Ignore friction and air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{(2.0)^2$ + 2 \times 9.8 \times 50 \times \sin(10^\circ)}$$

Q: A 1500 kg car is towed, starting from rest, and the tension force in the tow rope is constant at 5000 N as the car travels from $$x = 0 m to$$ $$x = 200 m. $$What is the car's speed after being pulled 200 m?

$$v = \sqrt{2 \times 5000 \times 200 / 1500}$$

Question 1

A hydroelectric power plant converts the gravitational potential energy of water in a reservoir into electrical energy. If the mass flow rate of water through the turbine is $$m kg/s$$, the height difference between the reservoir and the turbine is $$h$$, and $$g is $$the acceleration due to gravity, what is the maximum possible power output (ignoring losses)?

Accepted Answer

$$P = mg h$$

Question 2

Which of the following best describes the work done by a force $$\vec{F}$$ acting at an angle $$	heta to $$the displacement $$d\vec{r}$$ along a path from point A to point B?

Accepted Answer

$$W = \int_A^B \vec{F} \cdot d\vec{r}$$

Question 3

A 5.0 kg cannonball is fired straight up at 35 m/s. What is its speed after rising 45 m? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{35^2$ - 2 	imes 9.8 	imes 45}$$

Question 4

Two equal-mass pucks on frictionless ice are pushed toward each other by two equal but opposite forces. Let the system be both pucks. Is the total work done on the system positive, negative, or zero?

Accepted Answer

Zero, because the forces are internal to the system.

Question 5

A crane uses a single cable to lower a steel girder with constant speed. The cable tension does work $$W_T$$ and gravity does work $$W_G. $$Which statement is true?

Accepted Answer

$$W_T is $$negative and $$W_G is $$positive.

Question 6

A 70 kg skier is gliding at 2.0 m/s when he starts down a very slippery 50-m-long, 10° slope. What is his speed at the bottom? (Ignore friction and air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{(2.0)^2$ + 2 	imes 9.8 	imes 50 	imes \sin(10^\circ)}$$

Question 7

Which of the following statements about work is correct?

Accepted Answer

A force perpendicular to the displacement does no work.

Question 8

A 1500 kg car is towed, starting from rest, and the tension force in the tow rope is constant at 5000 N as the car travels from $$x = 0 m to$$ $$x = 200 m. $$What is the car's speed after being pulled 200 m?

Accepted Answer

$$v = \sqrt{2 	imes 5000 	imes 200 / 1500}$$

Question 9

A spring with constant $$k = 50\ \mathrm{N/m} is $$attached to a 2.0 kg block. The coefficient of static friction is 0.60. The spring is stretched by a motorized toy train moving at 5.0 cm/s. When does the block slip?

Accepted Answer

When $$k \Delta x = \mu_s m g$$

Question 10

What is the work done by a spring with constant $$k$$ when it moves from an initial displacement $$\Delta x_i to a $$final displacement $$\Delta x_f$$?

Accepted Answer

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

Question 11

Which of the following is true about conservative forces?

Accepted Answer

The work done by a conservative force over a closed path is zero.

Question 12

A 1500 kg car has a front profile that is 1.6 m wide by 1.4 m high. The car's drag coefficient is 0.50, and its coefficient of rolling friction is 0.02. What power must a tow-truck engine provide to tow this car on a level road at a steady 25 m/s if the drive train efficiency is 90%? ($$\rho = 1.2\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$P = \frac{1}{0.9} \left[ (0.02)(1500)(9.8) + \frac{1}{2}(0.5)(1.2)(1.6 	imes 1.4)(25^2$) ight] 	imes 25$$

Question 13

Which of the following statements about dissipative forces is correct?

Accepted Answer

Dissipative forces convert mechanical energy into thermal energy.

Question 14

The power delivered by a force $$F$$ moving an object at constant velocity $$v is $$given by:

Accepted Answer

$$P = Fv$$

Question 15

A box is pulled across a rough surface at constant speed. Which of the following is true about the work done by friction?

Accepted Answer

The work done by friction is negative and equal in magnitude to the work done by the pulling force.

Question 16

Which of the following is NOT a valid reason for zero work being done by a force?

Accepted Answer

The force is parallel to the displacement.

Question 17

If a force $$\vec{F}$$ acts on a particle and the particle moves along a path such that $$\vec{F} is $$always perpendicular to the displacement $$d\vec{r}$$, what is the total work done by $$\vec{F}$$?

Accepted Answer

Zero, because $$\vec{F} \cdot d\vec{r} = 0 at $$all points.

Physics I: Mechanics – Energy and Work Study Guidance

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