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 suspended from it. What mass should be attached to the spring so that its 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{mg}{\Delta x}$

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 and the Doppler effect applies.)

Accepted Answer

Question 4

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

Accepted Answer

Vertically upward

Question 5

A charged particle is released from rest at the top plate of a parallel plate capacitor with $$E = 1.0 	imes 10^4$ N/C and plate separation d = 0.01$ m. If the particle is an electron, how much time is required for it to reach the lower plate? (Assume m_e = 9.11$$ 	imes $$10^{-31} kg$$, $$e = 1.60 	imes 10$$^{-19}$$ C)

Accepted Answer

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

Question 6

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

Accepted Answer

The vector sum of the forces from $$q_1$$ and $$q_2$$ using $$F = k \frac{|q_1$ q_3$|}{r^2$}$$ and $$F = k \frac{|q_2$ q_3$|}{r^2$}$$

Question 7

A spring with unknown spring constant $$k$$ stretches $$0.018 m $$under a $$2.8 kg $$mass. What is the value of $$k$$? (Assume $$g = 9.8 m/s$^2)$$

Accepted Answer

$$k = \frac{mg}{\Delta x}$$

Question 8

If the frequency of vibration of a mass-spring system is $$f = 3 Hz$$, what is the angular frequency $$\omega$$?

Accepted Answer

$$\omega = 2\pi f$$

Question 9

A lithium nucleus has a charge of $$+3e. $$What is the magnitude of the electrostatic force on an electron orbiting at radius $$r$$?

Accepted Answer

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

Question 10

A car emits a sound of frequency $$f_0$$ while moving away from a stationary observer. The observer hears a frequency $$f = 0.86 f_0$. What is the correct Doppler effect equation to use for calculating the car's speed?

Accepted Answer

$$f = f_0$ \left( \frac{v_{sound}}{v_{sound} + v_{car}} \right)$$

Question 11

A parallel plate capacitor has plates separated by $$d = 0.01 m $$and connected to a $$100 V $$battery. What is the relationship between the electric field $$E$$ and the voltage $$V$$?

Accepted Answer

$$E = \frac{V}{d}$$

Question 12

If an electron is released from rest in a uniform electric field $$E$$, what is its acceleration?

Accepted Answer

$$a = \frac{eE}{m_e}$$

Question 13

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

Accepted Answer

Frequency decreases by a factor of $$\sqrt{2}$$

Question 14

Three charges are placed at the corners of a rectangle. To find the net force on one charge, which principle should be used?

Accepted Answer

Superposition principle: sum the vector forces from each charge

Question 15

A spring stretches $$0.018 m $$under a $$2.8 kg $$mass. If you want the system to oscillate at $$3 Hz$$, what mass should you use? (Assume $$g = 9.8 m/s$^2)$$

Accepted Answer

Question 16

If a car moves toward you and you hear a frequency higher than the emitted frequency, which Doppler effect equation applies?

Accepted Answer

$$f = f_0$ \left( \frac{v_{sound}}{v_{sound} - v_{car}} \right)$$

Question 17

A parallel plate capacitor has a uniform electric field $$E. If $$the plates are $$d$$ apart and the voltage is $$V$$, what is the correct formula for $$E$$?

Accepted Answer

$$E = \frac{V}{d}$$

Question 18

If a spring stretches $$0.018 m $$under a $$2.8 kg $$mass, what is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k \Delta x^2$,\ where\ k = \frac{mg}{\Delta x}$

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