Q1. A system of two particles has zero total momentum. Which must be true?

Background

Topic: Conservation of Momentum

This question tests your understanding of the vector nature of momentum and what it means for the total momentum of a system to be zero.

Key Terms:

• Momentum (): , where is mass and is velocity.

• Zero Total Momentum:

Step-by-Step Guidance

1. Recall that momentum is a vector quantity, so both magnitude and direction matter.

2. For the total momentum to be zero, the sum of the two particles' momenta must cancel out exactly.

3. Think about what this means for the relationship between the two momenta: .

4. Consider whether this requires the particles to have equal masses, equal speeds, or just opposite velocities.

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Q2. A ball bounces off a wall with the same speed. The change in the ball's momentum:

Background

Topic: Impulse and Change in Momentum

This question tests your understanding of how momentum changes when an object reverses direction after a collision.

Key Terms and Formulas:

• Momentum:

• Change in Momentum:

• Impulse:

Step-by-Step Guidance

1. Assign a direction (e.g., toward the wall is negative, away is positive).

2. Write the initial and final velocities, noting the reversal in direction.

3. Calculate the change in momentum: .

4. Relate this change to the impulse delivered by the wall.

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Q3. In a perfectly elastic head-on collision between equal masses, one initially at rest:

Background

Topic: Elastic Collisions

This question tests your understanding of the outcomes of elastic collisions, especially when masses are equal and one object is initially at rest.

Key Terms and Formulas:

• Elastic Collision: Both momentum and kinetic energy are conserved.

• Conservation of Momentum:

• Conservation of Kinetic Energy:

Step-by-Step Guidance

1. Set up the initial conditions: , .

2. Apply conservation of momentum and kinetic energy to solve for final velocities.

3. Recall the special result for equal masses in elastic collisions.

4. Think about what happens to the moving and stationary objects after the collision.

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Q4. The work done by the normal force on a block sliding along a level surface is:

Background

Topic: Work and Forces

This question tests your understanding of when a force does work, specifically the normal force on a horizontal surface.

Key Terms:

• Work:

• Normal Force: Acts perpendicular to the surface.

Step-by-Step Guidance

1. Recall that work is only done by the component of force in the direction of displacement.

2. Consider the direction of the normal force relative to the block's motion.

3. Calculate the angle between the normal force and the displacement.

4. Use the work formula to determine if the normal force does any work.

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Q5. A spring stretched by distance x has PE = U. If stretched by 3x, the PE is:

Background

Topic: Elastic Potential Energy

This question tests your understanding of how elastic potential energy depends on displacement in a spring.

Key Formula:

• Elastic Potential Energy:

Step-by-Step Guidance

1. Recall the formula for elastic potential energy in a spring.

2. Substitute and into the formula to compare the energies.

3. Calculate the ratio .

4. Express the new potential energy in terms of .

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Q6. A projectile (no air resistance) has minimum kinetic energy at:

Background

Topic: Conservation of Energy in Projectile Motion

This question tests your understanding of how kinetic and potential energy change during projectile motion.

Key Concepts:

• Kinetic Energy:

• At the highest point: Vertical velocity is zero, but horizontal velocity remains.

Step-by-Step Guidance

1. Consider how the projectile's speed changes as it rises and falls.

2. At the highest point, what happens to the vertical component of velocity?

3. Is the kinetic energy ever zero? Why or why not?

4. Compare kinetic energy at launch, at the top, and at impact.

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Q7. Two blocks collide elastically. Block 1 is heavier, Block 2 was at rest. After, Block 1:

Background

Topic: Elastic Collisions with Unequal Masses

This question tests your understanding of the outcome of elastic collisions when one mass is greater than the other and one object is initially at rest.

Key Concepts:

• Elastic Collision Equations: Use conservation of momentum and kinetic energy.

• Relative Masses:

Step-by-Step Guidance

1. Set up the initial conditions: Block 1 moving, Block 2 at rest.

2. Recall the formula for final velocities in elastic collisions.

3. Analyze what happens to Block 1's velocity after the collision if .

4. Consider whether Block 1 stops, reverses, or continues forward.

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Q8. An ideal gas pressure is doubled at constant temperature. Volume:

Background

Topic: Ideal Gas Law

This question tests your understanding of the relationship between pressure and volume at constant temperature (Boyle's Law).

Key Formula:

• At constant and ,

Step-by-Step Guidance

1. Write the ideal gas law and identify which variables are constant.

2. Set up the proportional relationship between pressure and volume.

3. If pressure doubles, solve for the new volume in terms of the original volume.

4. Determine whether the volume increases, decreases, or stays the same.

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Q9. Which best explains why rms speed of gas molecules increases with temperature?

Background

Topic: Kinetic Theory of Gases

This question tests your understanding of the relationship between temperature and molecular motion in gases.

Key Formula:

• Root Mean Square Speed:

• Average Kinetic Energy:

Step-by-Step Guidance

1. Recall how temperature relates to the average kinetic energy of molecules.

2. Understand that higher temperature means higher average kinetic energy.

3. Relate kinetic energy to rms speed using the formulas above.

4. Choose the explanation that directly connects temperature and rms speed.

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Q10. A block slides from rest down a frictionless ramp onto a rough surface. The work-energy theorem says:

Background

Topic: Work-Energy Theorem

This question tests your understanding of the work-energy theorem and how it applies to a block moving from a frictionless to a rough surface.

Key Formula:

• Work-Energy Theorem:

Step-by-Step Guidance

1. Recall that the work done by all forces equals the change in kinetic energy.

2. Consider the forces acting on the block on both surfaces.

3. Think about what happens to the block's kinetic energy as it moves onto the rough surface.

4. Relate the net work to the change in kinetic energy.

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Q11. Compared to N2 (M = 28 g/mol), O2 (M = 32 g/mol) molecules at the same temperature have:

Background

Topic: Molecular Speeds and Kinetic Energy

This question tests your understanding of how molecular mass affects rms speed and average kinetic energy at a given temperature.

Key Formulas:

• (independent of mass)

Step-by-Step Guidance

1. Compare the molar masses of N2 and O2.

2. Recall that rms speed is inversely proportional to the square root of molar mass.

3. Remember that average kinetic energy depends only on temperature, not mass.

4. Determine which gas has higher rms speed and whether their average kinetic energies differ.

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Q12. A heat pump moves heat from cold to warm reservoir. This process:

Background

Topic: Second Law of Thermodynamics

This question tests your understanding of the requirements for heat transfer from cold to hot reservoirs.

Key Concepts:

• Second Law: Heat does not flow spontaneously from cold to hot without external work.

• Heat Pump: Requires work input to move heat against the temperature gradient.

Step-by-Step Guidance

1. Recall what the second law says about spontaneous heat flow.

2. Consider what is required for a heat pump to move heat from cold to hot.

3. Decide whether this process is possible without work input.

4. Eliminate options that violate the laws of thermodynamics.

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Q13. A 1 kg object at 2 m/s has momentum p1. A 2 kg object at 1 m/s has momentum p2. Which is correct?

Background

Topic: Linear Momentum

This question tests your ability to calculate and compare the momenta of two objects with different masses and velocities.

Key Formula:

Step-by-Step Guidance

1. Calculate for the 1 kg object: .

2. Calculate for the 2 kg object: .

3. Compare the two values to determine which is greater, or if they are equal.

4. Consider if direction matters based on the information given.

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Q14. When catching a fast ball, moving your hands backward as you catch it:

Background

Topic: Impulse and Force

This question tests your understanding of how increasing the time over which a force acts affects the force experienced.

Key Formula:

Step-by-Step Guidance

1. Recall that impulse equals the change in momentum.

2. Understand that for a given change in momentum, increasing the time reduces the average force.

3. Think about what moving your hands backward does to the stopping time.

4. Relate this to the force felt by your hands.

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Q15. An ideal gas molecule in a cubic box: if temperature doubles at constant volume, the average force on the wall by each molecule:

Background

Topic: Kinetic Theory and Pressure

This question tests your understanding of how temperature affects the pressure (and thus force) exerted by gas molecules at constant volume.

Key Formula:

• At constant ,

Step-by-Step Guidance

1. Recall that pressure is proportional to temperature at constant volume.

2. Since force on the wall is related to pressure, consider how force changes as temperature doubles.

3. Set up the proportional relationship between force and temperature.

4. Determine the factor by which the force changes.

Try solving on your own before revealing the answer!