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

Q1. A single electron orbits a lithium nucleus (3 protons, +3e) at a radius of $1.76 \times 10^{-11}$ m. Determine the acceleration of the electron.

Background

Topic: Electrostatics & Circular Motion

This question tests your understanding of the forces acting on an electron in a circular orbit around a nucleus, specifically the centripetal acceleration due to electrostatic attraction.

Key Terms and Formulas

• Coulomb's Law: $F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2}$

• Centripetal acceleration: $a = \frac{v^2}{r}$

• Newton's Second Law for circular motion: $F = m a$

• For an electron orbiting a nucleus: The electrostatic force provides the centripetal force.

Step-by-Step Guidance

1. Identify the charges involved: The lithium nucleus has charge $+3e$ and the electron has charge $-e$.

2. Write the expression for the electrostatic force between the nucleus and the electron: $F = \frac{1}{4\pi\epsilon_0} \frac{(3e)(e)}{r^2}$

3. Set this force equal to the centripetal force required for circular motion: $F = m_e a$

4. Express acceleration in terms of the known quantities: $a = \frac{F}{m_e}$

5. Substitute the values for $e$, $r$, $\epsilon_0$, and $m_e$ into the formula, but stop before plugging in the numbers.

Try solving on your own before revealing the answer!

Q2. A spring stretches by 0.018 m when a 2.8 kg object is suspended from its end. How much mass should be attached to this spring so that its frequency of vibration is 3 Hz?

Background

Topic: Simple Harmonic Motion (SHM)

This question tests your ability to relate the spring constant to the mass and frequency of a vibrating spring-mass system.

Key Terms and Formulas

• Hooke's Law: $F = kx$

• Spring constant: $k$

• Frequency of SHM: $f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$

• Weight: $F = mg$

Step-by-Step Guidance

1. Use Hooke's Law to find the spring constant: $k = \frac{mg}{x}$, where $m = 2.8$ kg and $x = 0.018$ m.

2. Write the formula for the frequency of a mass-spring system: $f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$

3. Rearrange the frequency formula to solve for mass $m$ given $f$ and $k$.

4. Substitute the value of $k$ from step 1 and the desired frequency $f = 3$ Hz into the rearranged formula.

5. Set up the equation for $m$ but stop before calculating the final value.

Try solving on your own before revealing the answer!

Q3. At a stock car race, you hear a frequency that is 0.86 times as small as the frequency emitted by a moving car. The speed of sound is 343 m/s. What is the speed of the car?

Background

Topic: Doppler Effect

This question tests your understanding of how the observed frequency changes due to the motion of a sound source relative to an observer.

Key Terms and Formulas

• Doppler Effect for a moving source: $f' = f \left( \frac{v}{v + v_s} \right)$

• $f'$ = observed frequency

• $f$ = emitted frequency

• $v$ = speed of sound

• $v_s$ = speed of the source (car)

Step-by-Step Guidance

1. Set up the ratio: $f' = 0.86 f$

2. Write the Doppler formula for a source moving away: $f' = f \left( \frac{v}{v + v_s} \right)$

3. Set $0.86 f = f \left( \frac{v}{v + v_s} \right)$ and cancel $f$ from both sides.

4. Solve for $v_s$ in terms of $v$ and the ratio.

5. Substitute $v = 343$ m/s and the ratio $0.86$ into your equation, but stop before calculating $v_s$.

Try solving on your own before revealing the answer!

Q4. The terminals of a 100 V battery are connected to two parallel, horizontal plates 1 cm apart. The resulting charge produces a uniform electric field $E = 1.0 \times 10^4$ N/C. Suppose the lower plate has a positive charge, so the electric field is vertically upward. How much time is required for it to reach the lower plate?

Background

Topic: Electric Fields & Motion of Charged Particles

This question tests your understanding of how a charged particle moves in a uniform electric field between parallel plates.

Key Terms and Formulas

• Electric field: $E = \frac{V}{d}$

• Force on a charge: $F = qE$

• Acceleration: $a = \frac{F}{m} = \frac{qE}{m}$

• Distance traveled: $d = \frac{1}{2} a t^2$ (assuming initial velocity is zero)

Step-by-Step Guidance

1. Identify the distance between plates: $d = 0.01$ m.

2. Write the formula for acceleration: $a = \frac{qE}{m}$

3. Use the kinematic equation for distance: $d = \frac{1}{2} a t^2$

4. Rearrange to solve for time $t$ in terms of $d$ and $a$.

5. Set up the equation for $t$ but stop before plugging in the values.

Try solving on your own before revealing the answer!

Q5. Three charged particles with $q_1 = -50$ nC, $q_2 = +50$ nC, and $q_3 = +30$ nC are placed on the corners of a 5 cm x 10 cm rectangle. What is the net force on charge $q_3$ due to the other two charges?

Background

Topic: Electrostatics & Vector Addition

This question tests your ability to calculate the net force on a charge due to other point charges using Coulomb's Law and vector addition.

Key Terms and Formulas

• Coulomb's Law: $F = \frac{1}{4\pi\epsilon_0} \frac{|q_1 q_2|}{r^2}$

• Vector addition: Forces must be added as vectors, considering direction.

• Convert cm to m: $1$cm$= 0.01$ m

Step-by-Step Guidance

1. Identify the positions of the charges on the rectangle and calculate the distances between $q_3$ and the other charges.

2. Calculate the force between $q_3$ and $q_1$ using Coulomb's Law.

3. Calculate the force between $q_3$ and $q_2$ using Coulomb's Law.

4. Determine the direction of each force (attractive or repulsive) and resolve them into components if necessary.

5. Set up the vector addition for the net force but stop before calculating the final magnitude and direction.

Try solving on your own before revealing the answer!