Q: At a stock car race, you hear a frequency that is $$0.86$$ times the frequency emitted by a moving car. If the speed of sound is $$343 m/s$$, what is the speed of the car? (Assume the car is moving away from you)

$$v = (1 - 0.86) \times 343 / 0.86 = 55.8 m/s$$

Q: If the electric field between two plates is $$E = 1.0 \times 10^4$ N/C and the plates are 1$ cm apart, what is the potential difference between the plates?

$$V = E \cdot d = 1.0 \times 10^4$ \times 0.01 = 100 V$$

Question 1

An electron orbits a lithium nucleus (with charge $$+3e) at a $$radius of $$1.76 	imes 10$$^{-11}$$ m. What is the acceleration of the electron due to the electrostatic force? (Assume e = 1.60$$ 	imes $$10^{-19} C$$, $$m_e = 9.11 	imes 10$$^{-31}$$ kg, k = 8.99$$ 	imes $$10^9 N$$·m$$^2/C$^2)$$

Accepted Answer

$$a = \frac{k \cdot 3e^2$}{m_e r^2$}$$

Question 2

A spring stretches by $$0.018 m $$when a $$2.8 kg $$mass is attached. What mass should be attached so that the frequency of vibration is $$3 Hz$$? (Assume $$g = 9.8 m/s$^2)$$

Accepted Answer

$$m = \frac{k}{(2\pi f)^2$}$$,\ where\ k = \frac{F}{x} = \frac{2.8 	imes 9.8}{0.018}$

Question 3

At a stock car race, you hear a frequency that is $$0.86$$ times the frequency emitted by a moving car. If the speed of sound is $$343 m/s$$, what is the speed of the car? (Assume the car is moving away from you)

Accepted Answer

$$v = (1 - 0.86) 	imes 343 / 0.86 = 55.8 m/s$$

Question 4

Two parallel plates are $$1 cm $$apart and connected to a $$100 V $$battery. The electric field between the plates is $$E = 1.0 	imes 10^4$ N/C. If the lower plate is positive, what is the direction of the electric field?

Accepted Answer

Vertically upward

Question 5

A proton is released from rest at the upper plate of the parallel plate setup described above. How much time is required for it to reach the lower plate? (Assume $$d = 0.01 m$$, $$E = 1.0 	imes 10^4$ N/C, m_p = 1.67$$ 	imes $$10^{-27} kg$$, $$e = 1.60 	imes 10$$^{-19}$$ C)

Accepted Answer

$$t = \sqrt{\frac{2d}{a}}$$,\ where\ a = \frac{eE}{m_p}$

Question 6

Three charged particles are placed at the corners of a $$5 cm x$$ $$10 cm $$rectangle: $$q_1 = -50$ nC, q_2$ = +50 nC$$, $$q_3 = +30$ nC. What is the net force on q_3$ due to the other two charges?

Accepted Answer

The vector sum of $$F_{13}$$ and $$F_{23}$$, where $$F_{ij} = k \frac{|q_i q_j|}{r_{ij}^2}$$

Question 7

If the spring in question 2 is used in a car suspension system, what would happen to the frequency of vibration if the mass of the car increases?

Accepted Answer

The frequency decreases, since $$f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$$

Question 8

A lithium atom is ionized so that only one electron orbits the nucleus. If the radius of the orbit is halved, what happens to the acceleration of the electron?

Accepted Answer

The acceleration increases by a factor of 4, since $$a \propto \frac{1}{r^2$}$$

Question 9

A car emits a sound at frequency $$f_0. If it $$moves toward a stationary observer at speed $$v$$, what is the observed frequency $$f$$? (Speed of sound $$c)$$

Accepted Answer

$$f = f_0$ \frac{c + v}{c}$$

Question 10

A $$2.8 kg $$mass stretches a spring by $$0.018 m. If $$the spring is compressed by $$0.018 m $$and released, what is the maximum speed of the mass as it passes through equilibrium?

Accepted Answer

$$v_{max} = x_{max} \sqrt{\frac{k}{m}}$$

Question 11

If the electric field between two plates is $$E = 1.0 	imes 10^4$ N/C and the plates are 1$ cm apart, what is the potential difference between the plates?

Accepted Answer

$$V = E \cdot d = 1.0 	imes 10^4$ 	imes 0.01 = 100 V$$

Question 12

A charged particle moves in a uniform electric field between two plates. If the field is doubled, what happens to the acceleration of the particle?

Accepted Answer

The acceleration doubles, since $$a = \frac{qE}{m}$$

Question 13

If the frequency detected from a moving car is less than the emitted frequency, what can you infer about the car's motion relative to the observer?

Accepted Answer

The car is moving away from the observer

Question 14

A spring-mass system oscillates with frequency $$f. If $$the spring constant $$k is $$quadrupled, what happens to the frequency?

Accepted Answer

The frequency doubles, since $$f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$$

Question 15

Three charges are placed at the corners of a rectangle. If the distance between $$q_1$$ and $$q_3 is $$doubled, what happens to the force between them?

Accepted Answer

The force is reduced to one-fourth, since $$F \propto \frac{1}{r^2$}$$

Question 16

A lithium nucleus has three protons. If an electron orbits at a certain radius, what is the magnitude of the electrostatic force acting on the electron?

Accepted Answer

$$F = k \frac{3e^2$}{r^2$}$$

Question 17

A $$2.8 kg $$mass stretches a spring by $$0.018 m. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{mg}{x} = \frac{2.8 	imes 9.8}{0.018}$$

Question 18

A proton is released from rest in a uniform electric field. What is its final speed after traveling a distance $$d$$?

Accepted Answer

$$v = \sqrt{2ad}$$,\ where\ a = \frac{eE}{m_p}$

Step-by-Step Physics Exam Practice Guidance (University Physics II)

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