Q: A ball of mass 1.5 kg is dropped from the top of a building with an initial speed of 10 m/s. It strikes the ground after 4.0 s. How high is the building? (Neglect air resistance.)

$$h = v_0$ t + \frac{1}{2} g t^2$ = 10 \times 4 + \frac{1}{2} \times 9.8 \times 16 = 40 + 78.4 = 118.4\ \mathrm{m}$$

Q: A 3.5 kg body accelerates from rest to a speed of 4.0 m/s in 4.0 s. What is the net force acting on the body?

$$F = m a = 3.5 \times \frac{4.0}{4.0} = 3.5\ \mathrm{N}$$

Q: A 2.0 m long wire forms a single vertical loop with a radius of 0.32 m. If a current of 5.0 A flows through the loop, what is the magnitude of the magnetic field at the center of the loop?

$$B = \frac{\mu_0$ I}{2 r} = \frac{4 \pi \times 10$$^{-7}$$ \times 5.0}{2 \times 0.32} \approx 9.8 \times 10$$^{-6}$$\ \mathrm{T}$$

Q: The volume coefficient of thermal expansion for gasoline is $$9.5 \times 10$$^{-4}$$\ ^\circ\mathrm{C}^{-1}. By $$how much does the volume of 2.5 L of gasoline change when the temperature rises from 10°C to 50°C?

$$\Delta V = V_0$ \beta \Delta T = 2.5 \times 9.5 \times 10$$^{-4}$$ \times 40 = 0.095\ \mathrm{L}$$

Q: 2.0 kg of water at 100°C condenses to water at 100°C. What is the change in entropy in the process?

$$\Delta S = \frac{Q}{T} = \frac{m L}{T} = \frac{2.0 \times 2.26 \times 10^6$}{373} \approx 12,130\ \mathrm{J/K}$$

Q: A wheel accelerates with a constant angular acceleration of $$2\ \mathrm{rad/s}^2. If $$the initial angular velocity is $$4\ \mathrm{rad/s}$$, what is the angle the wheel rotates through in $$4.0\ \mathrm{s}$$?

$$\theta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$ = 4 \times 4 + 0.5 \times 2 \times 16 = 16 + 16 = 32\ \mathrm{rad}$$

Question 1

A ball of mass 1.5 kg is dropped from the top of a building with an initial speed of 10 m/s. It strikes the ground after 4.0 s. How high is the building? (Neglect air resistance.)

Accepted Answer

$$h = v_0$ t + \frac{1}{2} g t^2$ = 10 	imes 4 + \frac{1}{2} 	imes 9.8 	imes 16 = 40 + 78.4 = 118.4\ \mathrm{m}$$

Question 2

A 3.5 kg body accelerates from rest to a speed of 4.0 m/s in 4.0 s. What is the net force acting on the body?

Accepted Answer

$$F = m a = 3.5 	imes \frac{4.0}{4.0} = 3.5\ \mathrm{N}$$

Question 3

A 2.0 m long wire forms a single vertical loop with a radius of 0.32 m. If a current of 5.0 A flows through the loop, what is the magnitude of the magnetic field at the center of the loop?

Accepted Answer

$$B = \frac{\mu_0$ I}{2 r} = \frac{4 \pi 	imes 10$$^{-7}$$ 	imes 5.0}{2 	imes 0.32} \approx 9.8 	imes 10$$^{-6}$$\ \mathrm{T}$$

Question 4

A human body temperature (98.6°F) in Celsius degrees is:

Accepted Answer

$$T_C = \frac{5}{9}(98.6 - 32) = 37\ ^\circ\mathrm{C}$$

Question 5

A sound wave departs from a stationary observer. The frequency heard by the observer is:

Accepted Answer

$$f' = f \left( \frac{v}{v + v_s} \right)$$

Question 6

The volume coefficient of thermal expansion for gasoline is $$9.5 	imes 10$$^{-4}$$\ ^\circ\mathrm{C}^{-1}. By $$how much does the volume of 2.5 L of gasoline change when the temperature rises from 10°C to 50°C?

Accepted Answer

$$\Delta V = V_0$ \beta \Delta T = 2.5 	imes 9.5 	imes 10$$^{-4}$$ 	imes 40 = 0.095\ \mathrm{L}$$

Question 7

A metal object floats in water with 30% of its volume above the waterline. What does the object weigh compared to the buoyant force?

Accepted Answer

The object's weight equals the buoyant force.

Question 8

2.0 kg of water at 100°C condenses to water at 100°C. What is the change in entropy in the process?

Accepted Answer

$$\Delta S = \frac{Q}{T} = \frac{m L}{T} = \frac{2.0 	imes 2.26 	imes 10^6$}{373} \approx 12,130\ \mathrm{J/K}$$

Question 9

An ideal gas occupies 200 cm³ at 30°C. At what temperature will it occupy 350 cm³ if the pressure remains constant?

Accepted Answer

$$T_2$$ = $$T_1$$ \frac{$$V_2$$}{$$V_1$$} = (30 + 273) \frac{350}{200} = 303 	imes 1.75 = 530.25\ \mathrm{K}$$

Question 10

A wheel accelerates with a constant angular acceleration of $$2\ \mathrm{rad/s}^2. If $$the initial angular velocity is $$4\ \mathrm{rad/s}$$, what is the angle the wheel rotates through in $$4.0\ \mathrm{s}$$?

Accepted Answer

$$	heta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$ = 4 	imes 4 + 0.5 	imes 2 	imes 16 = 16 + 16 = 32\ \mathrm{rad}$$

Question 11

A 4.0 kg object moves to the left with a speed of 10.0 m/s. It collides perfectly inelastically with a 6.0 kg object moving to the right at 8.0 m/s. What is the speed and direction of the combined object after the collision?

Accepted Answer

$$v = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{4.0 	imes (-10.0) + 6.0 	imes 8.0}{10.0} = \frac{-40 + 48}{10} = 0.8\ \mathrm{m/s}$$\ to\ the\ right

Question 12

An organ pipe open at both ends has a length of 0.85 m. If the velocity of sound in air is 340 m/s, what is the wavelength and frequency of the second harmonic?

Accepted Answer

Wavelength: $$\$$lambda_2$$ = \frac{L}{n/2} = \frac{0.85}{2/2} = 0.85\ \mathrm{m}$$; Frequency: $$f_2$$ = \frac{v}{\$$lambda_2$$} = \frac{340}{0.85} = 400\ \mathrm{Hz}$$

Question 13

A 0.25 kg piece of copper, initially at 100°C, is dropped into 0.40 kg of water contained in a 0.10 kg aluminum cup, with both water and aluminum initially at 20°C. What is the final temperature of the system? (Specific heat of copper: 387 J/kg·K, water: 4184 J/kg·K, aluminum: 900 J/kg·K)

Accepted Answer

Set $$Q_{lost} = Q_{gained}$$: $$0.25 	imes 387 	imes (100 - T_f) = 0.40 	imes 4184 	imes (T_f - 20) + 0.10 	imes 900 	imes (T_f - 20)$$; $$T_f \approx 23.6\ ^\circ\mathrm{C}$$

Question 14

Assuming that the build-up of fatty tissue on the wall of an artery decreases the radius by 50%, by how much would the pressure provided by the heart have to be increased to maintain a constant blood flow?

Accepted Answer

According to Poiseuille's Law, $$Q \propto r^4$, so pressure must increase by a factor of 2^4$ = 16.$$

Question 15

A piece of metal sinks in water but a piece of wood floats. This is due to which of the following physical properties?

Accepted Answer

Density

Question 16

A car engine converts 200 kJ of heat into 50 kJ of work. What is the efficiency of the engine?

Accepted Answer

$$\eta = \frac{W}{Q_{in}} = \frac{50}{200} = 0.25 = 25\%$$

Question 17

A 1.5 kg block slides down a frictionless incline of height 2.0 m. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 2.0} = \sqrt{39.2} \approx 6.26\ \mathrm{m/s}$$

Question 18

A 0.5 kg object is attached to a spring with a spring constant $$k = 200\ \mathrm{N/m}. $$What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}} = 2\pi \sqrt{\frac{0.5}{200}} = 2\pi \sqrt{0.0025} = 2\pi 	imes 0.05 \approx 0.314\ \mathrm{s}$$

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