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 what it means for a system to have zero total momentum and how the momenta of individual particles relate to the total.

Key Terms:

• Momentum (): The product of mass and velocity, .

• System: The collection of particles being considered.

Step-by-Step Guidance

1. Recall that the total momentum of a system is the vector sum of the momenta of all particles: .

2. If , then (equal in magnitude, opposite in direction).

3. Consider whether both particles must be at rest, or if they can be moving with equal and opposite momenta.

4. Think about whether equal masses are required, or if only the momenta need to be equal and opposite.

Try solving on your own before revealing the answer!

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

Background

Topic: Impulse and Momentum Change

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

Key Terms and Formulas:

• Momentum:

• Impulse:

Step-by-Step Guidance

1. Let the ball's initial velocity toward the wall be ; after bouncing, its velocity is (opposite direction, same speed).

2. Calculate the change in momentum: .

3. Simplify the expression to see how the change relates to the original momentum.

4. Recall that impulse delivered by the wall equals the change in momentum.

Try solving on your own before revealing the answer!

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 between equal masses, especially when one is initially at rest.

Key Concepts:

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

• Equal Masses:

Step-by-Step Guidance

1. Write conservation of momentum: , with .

2. Write conservation of kinetic energy: .

3. Solve the equations for and .

4. Interpret the physical meaning: what happens to each mass 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 Concepts:

• Work:

• Normal Force: Acts perpendicular to the surface.

Step-by-Step Guidance

1. Recall that work is the dot product of force and displacement vectors.

2. On a level surface, the normal force is vertical, while displacement is horizontal.

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

4. Determine if the normal force does any work based on the angle.

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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 the potential energy stored in a spring depends on the amount it is stretched.

Key Formula:

Step-by-Step Guidance

1. Write the expression for potential energy at stretch : .

2. Substitute for to find the new potential energy: .

3. Simplify the expression to see how relates to .

4. Compare the new energy to the original energy .

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

Background

Topic: Projectile Motion and Energy

This question tests your understanding of how kinetic energy changes during projectile motion.

Key Concepts:

• Kinetic Energy:

• At the highest point, vertical velocity is zero.

Step-by-Step Guidance

1. Recall that as a projectile rises, its speed decreases due to gravity.

2. At the highest point, the vertical component of velocity is zero, but the horizontal component remains.

3. Calculate kinetic energy at launch, at the highest point, and at impact.

4. Compare these values to determine where kinetic energy is minimized.

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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, Conservation of Momentum

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

Key Concepts:

• Momentum and kinetic energy are conserved in elastic collisions.

• Relative masses affect the final velocities.

Step-by-Step Guidance

1. Write the equations for conservation of momentum and kinetic energy for two masses, , with .

2. Solve for the final velocity of Block 1, , in terms of and .

3. Analyze the result for to see if Block 1 stops, bounces back, or continues forward.

4. Consider the special case when .

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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:

Step-by-Step Guidance

1. At constant temperature and number of moles, .

2. If pressure doubles (), substitute into the equation to solve for .

3. Compare to to see how volume changes.

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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:

• Temperature is proportional to average kinetic energy.

Step-by-Step Guidance

1. Recall that temperature is a measure of the average kinetic energy of molecules.

2. As temperature increases, average kinetic energy increases, leading to higher rms speed.

3. Review the formula for rms speed and see how it depends on temperature.

Try solving on your own before revealing the answer!

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:

Step-by-Step Guidance

1. Recall the work-energy theorem: net work done on an object equals its change in kinetic energy.

2. Consider the work done by friction on the rough surface and how it affects the block's kinetic energy.

3. Relate the net work to the change in kinetic energy as the block moves from the ramp to the rough surface.

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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: Kinetic Theory of Gases

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

Key Formula:

• Average kinetic energy per molecule: (independent of mass)

Step-by-Step Guidance

1. Compare the molar masses of N2 and O2.

2. Use the rms speed formula to see how increasing molar mass affects speed at constant temperature.

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

Try solving on your own before revealing the answer!

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 how heat pumps work and the requirements for moving heat against a temperature gradient.

Key Concepts:

• Heat naturally flows from hot to cold unless work is done.

• Second Law of Thermodynamics: Heat cannot spontaneously flow from cold to hot without external work.

Step-by-Step Guidance

1. Recall the direction of natural heat flow and what is required to reverse it.

2. Consider whether a heat pump can operate without external work.

3. Determine which statement best matches the second law 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 .

2. Calculate .

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

4. Consider if direction is relevant 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 average force experienced.

Key Formula:

Step-by-Step Guidance

1. Recall that impulse equals change in momentum, and can also be written as average force times time.

2. If you increase the time () over which the ball is stopped, what happens to the average force?

3. Consider the effect on your hands if you "give" with the ball versus stopping it abruptly.

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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 of Gases

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

Key Formula:

Step-by-Step Guidance

1. At constant volume, pressure is directly proportional to temperature ().

2. If temperature doubles, pressure doubles, so the average force on the wall also doubles.

3. Relate this to the molecular collisions with the wall.

Try solving on your own before revealing the answer!