Q: A gas undergoes a process shown as a straight line on a PV diagram, where pressure decreases linearly from 600 kPa to 200 kPa as volume increases from 1.0 L to 4.0 L. What is the work done by the gas during this process?

$$W = \frac{1}{2} (600{\text{ kPa}} + 200{\text{ kPa}}) \times (4.0{\text{ L}} - 1.0{\text{ L}})$$

Q: A force vs. displacement graph is a triangle with base 4 m and height 10 N. How much work is done?

$$W = \frac{1}{2} \times 4 \times 10$$

Q: A cyclist applies a torque of 10 Nm to a bicycle wheel of mass 2.5 kg and radius 0.25 m. Treat the wheel as a solid disk. What is the angular acceleration?

$$\alpha = \frac{\tau}{I}$$, where $$I = \frac{1}{2}mr^2$

Q: A beam is supported by a hinge at one end and a cable at the other. A 400 N load hangs 3 m from the center. Find the force in the cable.

Sum torques about the hinge: $$\sum \tau = 0$$

Question 1

A gas undergoes a process shown as a straight line on a PV diagram, where pressure decreases linearly from 600 kPa to 200 kPa as volume increases from 1.0 L to 4.0 L. What is the work done by the gas during this process?

Accepted Answer

$$W = \frac{1}{2} (600{	ext{ kPa}} + 200{	ext{ kPa}}) 	imes (4.0{	ext{ L}} - 1.0{	ext{ L}})$$

Question 2

A 15 kg backpack is carried up a ramp and then back down to the starting point. What is the net work done by gravity on the backpack?

Accepted Answer

The net work is zero because the displacement is zero.

Question 3

A ball of mass 0.2 kg moves in a horizontal circle of radius 0.5 m at 2.0 m/s, attached to a spring. What is the tension in the spring?

Accepted Answer

$$T = \frac{mv^2$}{r}$$

Question 4

Water flows through a pipe of cross-sectional area $$0.02\ 	ext{m}^2 at a $$speed of $$3\ 	ext{m/s}. $$What is the volume of water passing in 10 seconds?

Accepted Answer

$$Q = Av 	imes t$$

Question 5

Two masses, $$m_1 = 2$$\ 	ext{kg}$$ and m_2$ = 6\ 	ext{kg}$$, are connected by a light rope over a frictionless pulley. What is the acceleration of the system?

Accepted Answer

$$a = \frac{(m_2$ - m_1$)g}{m_1$ + m_2$}$$

Question 6

A force vs. displacement graph is a triangle with base 4 m and height 10 N. How much work is done?

Accepted Answer

$$W = \frac{1}{2} 	imes 4 	imes 10$$

Question 7

A 0.5 kg ball is thrown straight up at 20 m/s. How long until it reaches maximum height? (Assume $$g = 10\ 	ext{m/s}^2)$$

Accepted Answer

$$t = \frac{v}{g}$$

Question 8

A 2.0 kg iron block at 400°C is placed into 500 g of water at 20°C. Final temperature is 50°C. Does the water boil? (Specific heat of iron is $$c_{Fe} = 0.45\ 	ext{J/g}^\circ	ext{C}$$, water $$c_{w} = 4.18\ 	ext{J/g}^\circ	ext{C})$$

Accepted Answer

No, because the final temperature is below 100°C.

Question 9

A force is applied 2.0 m from a pivot at an angle of 30°. What is the torque?

Accepted Answer

$$	au = rF\sin	heta$$

Question 10

A cyclist applies a torque of 10 Nm to a bicycle wheel of mass 2.5 kg and radius 0.25 m. Treat the wheel as a solid disk. What is the angular acceleration?

Accepted Answer

$$\alpha = \frac{	au}{I}$$, where $$I = \frac{1}{2}mr^2$

Question 11

A 0.5 kg object is attached to a spring and oscillates with maximum displacement 0.5 m. What is the displacement at $$t = T/2$$?

Accepted Answer

$$x = 0$$

Question 12

A 4 kg block slides towards a 2 kg block at 6 m/s and hits it elastically. The 2 kg block is initially at rest. What is the velocity of the 2 kg block after the collision?

Accepted Answer

$$v = \frac{2m_2}{m_1$ + m_2$}v_{1i}$$

Question 13

A refrigerator removes 400 J of heat from inside and exhausts 600 J to the room. How much work does it consume?

Accepted Answer

$$W = Q_{out} - Q_{in}$$

Question 14

A cart of mass $$m$$ enters a vertical loop of radius $$R. $$What is the minimum speed at the top to stay in contact with the track?

Accepted Answer

$$v = \sqrt{gR}$$

Question 15

A 100 g sample of water at 20°C is heated until it becomes steam at 100°C. What is the total heat added? (Assume $$c_{water} = 4.18\ 	ext{J/g}^\circ	ext{C}$$, $$L_v = 2260\ 	ext{J/g})$$

Accepted Answer

$$Q = mc\Delta T + mL_v$$

Question 16

A diver plate of mass 12 kg breaks into three pieces. One piece of mass 2 kg moves east at 3 m/s, another of mass 10 kg moves north at 2 m/s. What is the velocity of the third piece?

Accepted Answer

Use conservation of momentum: $$\vec{p}_A + \vec{p}_B + \vec{p}_C = 0$$

Question 17

A beam is supported by a hinge at one end and a cable at the other. A 400 N load hangs 3 m from the center. Find the force in the cable.

Accepted Answer

Sum torques about the hinge: $$\sum 	au = 0$$

Question 18

A 0.5 kg object is thrown vertically upward with an initial speed of 10 m/s. What is the maximum height reached? (Assume $$g = 10\ 	ext{m/s}^2)$$

Accepted Answer

$$h = \frac{v^2$}{2g}$$

Comprehensive Study Notes for Introductory College Physics

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