Step-by-Step Guidance for University Physics II Exam Practice Problems

Q1. A single electron orbits a lithium nucleus (3 protons, +3e) at a radius of 1.76 × 10-11 m. Determine the acceleration of the electron.

Background

Topic: Circular Motion & Coulomb's Law

This question tests your understanding of the forces acting on an electron in a hydrogen-like atom and how to relate the electrostatic force to the centripetal acceleration.

Key Terms and Formulas

• Coulomb's Law: $F = k_e \frac{q_1 q_2}{r^2}$

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

• Newton's Second Law: $F = ma$

• For circular orbits, the electrostatic force provides the centripetal force: $k_e \frac{q_1 q_2}{r^2} = m_e \frac{v^2}{r}$

Step-by-Step Guidance

1. Identify the charges involved: the electron ($q_e = -e$) and the lithium nucleus ($q_{Li} = +3e$).

2. Write the expression for the electrostatic force between the electron and the nucleus using Coulomb's Law.

3. Set this force equal to the required centripetal force for circular motion.

4. Express the centripetal acceleration $a$ in terms of the known quantities ($k_e$, $e$, $r$, $m_e$).

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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) & Hooke's Law

This question tests your ability to relate the properties of a spring-mass system to its oscillation frequency, using Hooke's Law and the formula for the frequency of a mass-spring system.

Key Terms and Formulas

• Hooke's Law: $F = kx$

• Frequency of mass-spring system: $f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$

• Weight: $F = mg$

Step-by-Step Guidance

1. Use the given stretch and mass to find the spring constant $k$ using Hooke's Law.

2. Write the formula for the frequency of a mass-spring system and set $f = 3$ Hz.

3. Rearrange the frequency formula to solve for the required mass $m$ in terms of $k$ and $f$.

4. Substitute the value of $k$ you found into the equation for $m$.

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Q3. At a stock car race, you hear a frequency that is 0.86 times 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 the Doppler effect for sound, specifically when the source is moving away from the observer.

Key Terms and Formulas

• Doppler Effect (source moving away): $f' = f \frac{v}{v + v_s}$

• $f'$ = observed frequency, $f$ = emitted frequency, $v$ = speed of sound, $v_s$ = speed of source (car)

Step-by-Step Guidance

1. Set up the Doppler effect equation for a source moving away from a stationary observer.

2. Substitute the given ratio $f'/f = 0.86$ and $v = 343$ m/s into the equation.

3. Rearrange the equation to solve for the speed of the car $v_s$.

4. Isolate $v_s$ and prepare to substitute the numbers.

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Q4. The terminals of a 100 V battery are connected to two parallel, horizontal plates 1 cm apart. The resulting charge on the plates produces a uniform electric field $E = 1.0 \times 10^4$ N/C between the plates. 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: Motion of Charged Particles in Electric Fields

This question tests your understanding of how a charged particle moves under the influence of a uniform electric field, and how to relate the field, force, acceleration, and kinematics.

Key Terms and Formulas

• Electric field: $E = \frac{V}{d}$

• Force on a charge: $F = qE$

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

• Kinematic equation for constant acceleration: $d = \frac{1}{2} a t^2$ (assuming initial velocity is zero)

Step-by-Step Guidance

1. Identify the distance $d$ the particle travels (1 cm = 0.01 m) and the electric field $E$.

2. Write the expression for the force on the particle due to the electric field.

3. Express the acceleration $a$ in terms of $q$, $E$, and $m$.

4. Set up the kinematic equation relating $d$, $a$, and $t$ to solve for $t$.

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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: Electric Forces & Vector Addition

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

Key Terms and Formulas

• Coulomb's Law: $F = k_e \frac{|q_1 q_2|}{r^2}$

• Vector addition: Forces are vectors and must be added using components.

• Convert distances from cm to m for calculations.

Step-by-Step Guidance

1. Draw a diagram of the rectangle and label the positions of the charges.

2. Calculate the force on $q_3$ due to $q_1$ (magnitude and direction).

3. Calculate the force on $q_3$ due to $q_2$ (magnitude and direction).

4. Break each force into x and y components, then set up the vector addition to find the net force components.

Try solving on your own before revealing the answer!