Physics 2010 Practice Exam 2 – Step-by-Step Study Guidance

Q1. A hockey puck slides across a frictionless ice surface at constant velocity. Which statement is correct?

Background

Topic: Newton's First Law of Motion (Inertia)

This question tests your understanding of forces and motion, specifically what happens to an object moving at constant velocity on a frictionless surface.

Key Terms:

• Net Force: The vector sum of all forces acting on an object.

• Constant Velocity: Motion with unchanging speed and direction.

• Newton's First Law: An object in motion stays in motion at constant velocity unless acted on by a net external force.

Step-by-Step Guidance

1. Recall that if an object moves at constant velocity, its acceleration is zero.

2. According to Newton's First Law, zero acceleration means the net force on the object must also be zero.

3. Consider what would happen if there were a net force: the puck would accelerate, which contradicts the given information.

Try solving on your own before revealing the answer!

Q2. An astronaut has a mass of 80 kg on Earth. She travels to the Moon, where gravity is about 1/6 that of Earth. What happens to her mass and weight?

Background

Topic: Mass vs. Weight

This question tests your understanding of the difference between mass (an intrinsic property) and weight (the force due to gravity).

Key Terms and Formulas:

• Mass (m): The amount of matter in an object (measured in kg), does not change with location.

• Weight (W): The force of gravity on an object: $W = m g$

• g: Acceleration due to gravity (9.8 m/s2 on Earth, about 1/6 of that on the Moon).

Step-by-Step Guidance

1. Recognize that mass is constant regardless of location (Earth or Moon).

2. Weight depends on the local gravitational acceleration: $W_{\text{moon}} = m \times g_{\text{moon}}$

3. Since $g_{\text{moon}} = \frac{1}{6} g_{\text{Earth}}$, the astronaut's weight on the Moon will be less than on Earth.

Try solving on your own before revealing the answer!

Q3. A child moves from the edge toward the center of a rotating merry-go-round. What happens to her tangential speed and angular velocity?

Background

Topic: Rotational Motion – Tangential Speed and Angular Velocity

This question tests your understanding of the relationship between tangential speed, angular velocity, and radius in rotational motion.

Key Terms and Formulas:

• Tangential Speed (v): $v = \omega r$

• Angular Velocity (\omega): The rate of rotation (rad/s).

• r: Distance from the axis of rotation.

Step-by-Step Guidance

1. As the child moves toward the center, the radius $r$ decreases.

2. If the merry-go-round is rotating at constant angular velocity $\omega$, then $v$ decreases because $v = \omega r$.

3. If angular momentum is conserved and no external torque acts, $\omega$ may change depending on the system setup.

Try solving on your own before revealing the answer!

Q4. Which quantity is measured in radians per second squared (rad/s²)?

Background

Topic: Units in Rotational Motion

This question tests your ability to identify the correct physical quantity based on its units.

Key Terms:

• Angular Velocity (\omega): Measured in rad/s.

• Angular Acceleration (\alpha): Measured in rad/s².

• Angular Displacement (\theta): Measured in radians (rad).

• Tangential Velocity (v): Measured in m/s.

Step-by-Step Guidance

1. Recall the units for each rotational quantity listed above.

2. Match the unit rad/s² to the correct physical quantity.

Try solving on your own before revealing the answer!

Q5. A spinning top completes one revolution every 0.200 seconds. What is its angular frequency in radians per second?

Background

Topic: Angular Frequency

This question tests your ability to convert between period and angular frequency.

Key Formula:

• Period (T): Time for one revolution (in seconds).

• Angular Frequency (\omega): $\omega = \frac{2\pi}{T}$

Step-by-Step Guidance

1. Identify the period: $T = 0.200$ s.

2. Use the formula $\omega = \frac{2\pi}{T}$ to set up the calculation.

3. Plug in the value for $T$ and simplify the expression, but do not calculate the final value yet.

Try solving on your own before revealing the answer!

Q6. A uniform ladder leans against a smooth wall with its base on the ground. The system is in static equilibrium. Which conditions must be satisfied?

Background

Topic: Static Equilibrium

This question tests your understanding of the requirements for an object to be in static equilibrium.

Key Terms:

• Net Force: The sum of all forces acting on the object.

• Net Torque: The sum of all torques (moments) about any axis.

Step-by-Step Guidance

1. Recall the two conditions for static equilibrium:

   • The net force must be zero: $\sum \vec{F} = 0$

   • The net torque must be zero: $\sum \tau = 0$

2. Apply these conditions to the ladder scenario.

Try solving on your own before revealing the answer!

Q7. Two cylinders have the same mass. Cylinder A is solid; Cylinder B is hollow with the same outer radius. Which requires more torque to reach the same angular acceleration?

Background

Topic: Rotational Dynamics – Moment of Inertia

This question tests your understanding of how mass distribution affects rotational inertia and the torque needed for angular acceleration.

Key Terms and Formulas:

• Torque (\tau): $\tau = I \alpha$

• Moment of Inertia (I): For a solid cylinder: $I_{\text{solid}} = \frac{1}{2} M R^2$; for a hollow cylinder: $I_{\text{hollow}} = M R^2$

• Angular Acceleration (\alpha): The rate of change of angular velocity.

Step-by-Step Guidance

1. Recall that for the same mass and radius, the hollow cylinder has a larger moment of inertia than the solid one.

2. Since $\tau = I \alpha$, more torque is needed for a larger $I$ to achieve the same $\alpha$.

3. Compare the moments of inertia for both cylinders to determine which requires more torque.

Try solving on your own before revealing the answer!

Q8. A 15.0 kg box is pushed along a warehouse floor and released with an initial speed of 3.50 m/s. A constant friction force of 18.0 N acts on the box. How far does the box travel before coming to rest? (Use the work-energy theorem.)

Background

Topic: Work-Energy Theorem

This question tests your ability to apply the work-energy theorem to a situation involving friction and kinetic energy.

Key Formula:

• Work-Energy Theorem: $W_{\text{net}} = \Delta K$

• Kinetic Energy (K): $K = \frac{1}{2} m v^2$

• Work by Friction: $W_{\text{friction}} = -f d$ (where $f$ is the friction force and $d$ is the distance traveled)

Step-by-Step Guidance

1. Calculate the initial kinetic energy: $K_i = \frac{1}{2} m v^2$

2. Set the final kinetic energy to zero (since the box comes to rest).

3. Apply the work-energy theorem: $W_{\text{friction}} = K_f - K_i$

4. Substitute $W_{\text{friction}} = -f d$ and solve for $d$.

Try solving on your own before revealing the answer!

Q9. A probe is sent to a distant moon with mass $m_{\text{moon}} = 7.35 \times 10^{22}$ kg and radius $r_{\text{moon}} = 1.74 \times 10^6$ m. If a rock on Earth weighs 49.0 N, what does it weigh on the surface of this moon?

Background

Topic: Universal Gravitation and Weight

This question tests your ability to calculate weight on another celestial body using Newton's law of gravitation.

Key Formula:

• Weight on a planet/moon: $W = m g$

• Gravitational acceleration: $g = \frac{G M}{R^2}$

• Universal gravitational constant: $G = 6.674 \times 10^{-11}$ N·m²/kg²

Step-by-Step Guidance

1. Find the mass of the rock using its weight on Earth: $m = \frac{W_{\text{Earth}}}{g_{\text{Earth}}}$

2. Calculate the gravitational acceleration on the moon: $g_{\text{moon}} = \frac{G m_{\text{moon}}}{r_{\text{moon}}^2}$

3. Calculate the rock's weight on the moon: $W_{\text{moon}} = m \times g_{\text{moon}}$

Try solving on your own before revealing the answer!

Q10. A mechanic must tighten a bolt to a torque of 85.0 N·m using a 45.0 cm wrench, pulling at an angle of 55.0° with respect to the handle. What force must she apply?

Background

Topic: Torque and Lever Arm

This question tests your ability to relate torque, force, lever arm, and the angle of application.

Key Formula:

• Torque: $\tau = r F \sin \theta$

• r: Length of the wrench (in meters).

• F: Force applied.

• \theta: Angle between force and lever arm.

Step-by-Step Guidance

1. Convert the wrench length to meters: $r = 0.450$ m.

2. Set up the torque equation: $85.0 = 0.450 \times F \times \sin(55.0^\circ)$

3. Rearrange to solve for $F$.

Try solving on your own before revealing the answer!

Q11. A motorcycle rounds a flat, unbanked curve of radius 60.0 m. The coefficient of static friction is 0.70. What is the maximum speed to avoid sliding? (g = 9.80 m/s²)

Background

Topic: Circular Motion and Friction

This question tests your understanding of the role of friction in providing the centripetal force for circular motion.

Key Formula:

• Centripetal force: $F_c = \frac{m v^2}{r}$

• Maximum friction force: $F_{\text{friction}} = \mu_s m g$

Step-by-Step Guidance

1. Set the maximum friction force equal to the required centripetal force: $\mu_s m g = \frac{m v^2}{r}$

2. Notice that mass cancels out, so $v$ does not depend on $m$.

3. Solve for $v$ in terms of $\mu_s$, $g$, and $r$.

Try solving on your own before revealing the answer!

Q12. A uniform 3.0 m plank of mass 20.0 kg is supported at each end by a scale. A 70.0 kg student stands 1.0 m from the left end. What does each scale read in Newtons?

Background

Topic: Static Equilibrium and Torque

This question tests your ability to analyze forces and torques in a system in equilibrium.

Key Steps and Formulas:

• Total weight: $W_{\text{plank}} = m_{\text{plank}} g$

• Student's weight: $W_{\text{student}} = m_{\text{student}} g$

• Sum of upward forces equals total downward force.

• Take torques about one end to solve for one scale reading.

Step-by-Step Guidance

1. Draw a free-body diagram showing the forces: two upward scale forces, the plank's weight at its center, and the student's weight at 1.0 m from the left end.

2. Write the equation for the sum of vertical forces: $F_L + F_R = W_{\text{plank}} + W_{\text{student}}$

3. Take torques about the left end to solve for the right scale force $F_R$.

4. Once $F_R$ is found, use the sum of forces to find $F_L$.

Try solving on your own before revealing the answer!

Q13. A student holds a 40.0 N textbook in their hand with their arm extended horizontally. The hand is 35.0 cm from the elbow (pivot). The biceps muscle attaches 4.0 cm from the elbow. What upward force must the biceps exert to hold the book stationary? (Ignore the weight of the forearm.)

Background

Topic: Torque and Static Equilibrium

This question tests your ability to analyze torques and forces in a lever system (the human arm).

Key Formula:

• Torque equilibrium: $\sum \tau = 0$

• Torque by biceps: $\tau_{\text{biceps}} = F_{\text{biceps}} \times r_{\text{biceps}}$

• Torque by book: $\tau_{\text{book}} = W_{\text{book}} \times r_{\text{hand}}$

Step-by-Step Guidance

1. Set the sum of torques about the elbow to zero (since the arm is stationary).

2. Write the torque equation: $F_{\text{biceps}} \times r_{\text{biceps}} = W_{\text{book}} \times r_{\text{hand}}$

3. Plug in the given distances (converted to meters) and the weight of the book.

4. Rearrange to solve for $F_{\text{biceps}}$.

Try solving on your own before revealing the answer!