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 how the momenta of individual particles combine to give the total momentum of a system.

Key Terms:

• Momentum ():

• Conservation of Momentum: The total momentum of a system remains constant if no external forces act.

Step-by-Step Guidance

1. Recall that momentum is a vector quantity, so direction matters as well as magnitude.

2. For the total momentum to be zero, the sum of the individual momenta must cancel out.

3. Consider what must be true about the velocities and masses of the particles for their momenta to add to zero.

4. Think about whether both particles must be at rest, or if they can be moving with equal and opposite momenta.

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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 Momentum Change

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

Key Terms:

• Momentum ():

• Impulse ():

Step-by-Step Guidance

1. Consider the initial and final velocities of the ball before and after hitting the wall.

2. Since the speed is the same but the direction is reversed, the velocity changes sign.

3. Calculate the change in momentum: .

4. Think about how this relates 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 how velocities are exchanged in elastic collisions between equal masses.

Key Terms:

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

• Conservation of Momentum:

• Conservation of Kinetic Energy:

Step-by-Step Guidance

1. Set up the conservation equations for momentum and kinetic energy.

2. Plug in the values: , (one at rest).

3. Solve for the final velocities and .

4. Interpret the physical meaning of the result: what happens to the moving and stationary objects?

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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 how work is calculated for forces perpendicular to displacement.

Key Terms:

• Work ():

• Normal Force: Acts perpendicular to the surface.

Step-by-Step Guidance

1. Recall the definition of work and the angle between force and displacement.

2. For the normal force, the angle between force and displacement is .

3. Calculate and see how it affects the work done.

4. Consider whether the normal force does any work as the block moves horizontally.

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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 potential energy in a spring depends on displacement.

Key Formula:

• Elastic Potential Energy:

Step-by-Step Guidance

1. Write the expression for potential energy for displacement and for .

2. Compare for and for .

3. Calculate and relate it to .

4. Determine the factor by which the potential energy increases.

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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 Terms:

• Kinetic Energy ():

• At the highest point, vertical velocity is zero.

Step-by-Step Guidance

1. Consider how the velocity components change as the projectile rises and falls.

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 KE is minimum.

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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 and Mass Ratio

This question tests your understanding of how mass affects the outcome of elastic collisions.

Key Terms:

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

• Mass ratio:

Step-by-Step Guidance

1. Set up the conservation equations for momentum and kinetic energy.

2. Consider the case where and Block 2 is initially at rest.

3. Analyze the final velocity of Block 1 after the collision.

4. Determine whether Block 1 stops, bounces back, 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.

Key Formula:

• Ideal Gas Law:

Step-by-Step Guidance

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

2. At constant and , and are inversely related.

3. Express the relationship: .

4. Set and solve for in terms of .

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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 how temperature relates to molecular speed.

Key Formula:

• Root-mean-square speed:

• Average kinetic energy:

Step-by-Step Guidance

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

2. As temperature increases, kinetic energy and rms speed increase.

3. Examine the formula for and see how it depends on .

4. Identify which explanation matches this relationship.

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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 how net work relates to changes in kinetic energy.

Key Formula:

• Work-Energy Theorem:

Step-by-Step Guidance

1. Recall the work-energy theorem and what it says about net work and kinetic energy.

2. Consider the effects of friction on the block's energy as it moves onto the rough surface.

3. Determine how the net work relates to the change in kinetic energy.

4. Compare the options to see which matches the theorem.

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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 Speed and Kinetic Energy

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

Key Formula:

Step-by-Step Guidance

1. Compare the molar masses of N2 and O2.

2. Use the formula to see how mass affects speed.

3. Use the formula to see how temperature affects kinetic energy.

4. Determine which properties are the same and which 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 how heat pumps operate and the role of external work.

Key Terms:

• Second Law of Thermodynamics: Heat naturally flows from hot to cold, not the reverse without work.

• Heat Pump: Moves heat from cold to warm by doing work.

Step-by-Step Guidance

1. Recall the second law and how it applies to heat transfer.

2. Consider whether external work is required to move heat from cold to warm.

3. Determine which options correctly describe the process.

4. Eliminate options that violate physical laws.

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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: Comparing Momentum

This question tests your ability to calculate and compare momentum for different masses and velocities.

Key Formula:

• Momentum:

Step-by-Step Guidance

1. Calculate and .

2. Compare the values to see which is greater.

3. Consider whether direction matters in this comparison.

4. Determine if the momenta are equal, or if one is larger.

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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 stopping time affects force during a collision.

Key Formula:

• Impulse:

• Average force:

Step-by-Step Guidance

1. Recall that impulse is the change in momentum.

2. Increasing the time over which the ball is stopped reduces the average force.

3. Consider how moving your hands backward affects stopping time and force.

4. Identify which option matches this reasoning.

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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 force exerted by gas molecules.

Key Formula:

• Pressure:

• Ideal Gas Law:

• Force is proportional to pressure, which is proportional to temperature at constant volume.

Step-by-Step Guidance

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

2. Doubling temperature doubles pressure.

3. Since force is related to pressure, consider how force changes when temperature doubles.

4. Determine the relationship between force and temperature.

Try solving on your own before revealing the answer!