Question

which factors below will increase the momentum of a rolling ball of constant mass m? (select only the answers that will increase the momentum of the ball.)
colliding with a ball of much lower mass moving in the opposite direction of the ball.
moving from a flat surface to moving downhill.
rolling uphill onto an inclined surface.
a moving object traveling in the same direction as the ball colliding with it.
rolling onto a surface with high amounts of friction with the ball.

Explanation:

To determine which factors increase the momentum (\(p = mv\), where \(m\) is mass and \(v\) is velocity) of a ball with constant mass, we analyze each option by checking if velocity increases:

1. **Colliding with a lower - mass ball (opposite direction):**
In a collision, the ball will experience an impulse (change in momentum) from the other ball. Since the other ball has lower mass and is moving opposite, the collision will transfer momentum to our ball, increasing its velocity (and thus momentum).

2. **Moving from flat to downhill:**
Gravity acts downhill, so the ball will accelerate (gain velocity) as it moves downhill. With \(m\) constant, higher \(v\) means higher momentum.

3. **Rolling uphill:**
Gravity acts against the motion, so the ball will decelerate (lose velocity), decreasing momentum.

4. **Collision with same - direction object:**
If the colliding object is moving in the same direction, depending on speeds, but generally, a collision with an object moving in the same direction (especially if it’s adding to the ball’s motion) can transfer momentum, increasing the ball’s velocity. Wait, actually, if the colliding object is moving in the same direction and has momentum, the interaction can increase our ball’s velocity. But more accurately, for the purpose of this question, when an object moving in the same direction collides with the ball, it can push the ball, increasing its velocity.

5. **High - friction surface:**
Friction opposes motion, so the ball will slow down (decrease velocity), decreasing momentum.

After re - evaluating:
- The correct options are:
- Colliding with a ball of much lower mass moving in the opposite direction of the ball.
- Moving from a flat surface to moving downhill.
- A moving object traveling in the same direction as the ball colliding with it. Wait, no, let's correct this. When a ball collides with an object moving in the same direction, if the colliding object has a higher velocity, it can transfer momentum. But in the case of a ball rolling and another object moving in the same direction colliding, the key is that for the ball’s momentum to increase, the collision should impart a net positive impulse. However, the most straightforward correct ones are:

- Colliding with a ball of much lower mass moving in the opposite direction of the ball (the lower - mass ball moving opposite will hit the ball and push it, increasing its velocity).
- Moving from a flat surface to moving downhill (gravity causes acceleration, so velocity increases).
- A moving object traveling in the same direction as the ball colliding with it (if the colliding object is moving faster in the same direction, it will push the ball, increasing its velocity; if it's moving slower, maybe not, but the question’s context implies that this collision increases momentum). And the option of rolling uphill is incorrect, and high - friction is incorrect.

But to match the standard understanding of such problems:
The correct options are:
- Colliding with a ball of much lower mass moving in the opposite direction of the ball.
- Moving from a flat surface to moving downhill.
- A moving object traveling in the same direction as the ball colliding with it. Wait, no, actually, the first two and the fourth? No, let's do it step by step.

Momentum \(p=mv\). Mass is constant, so we need to find what increases \(v\).

1. Colliding with lower - mass opposite - direction ball: The ball will be pushed, so \(v\) increases. Correct.
2. Flat to downhill: Acceleration due to gravity, \(v\) increases. Correct.
3. Uphill: \(v\) decreases. Incorrect.
4. Same - direction collision: If the colliding object is moving in the same direction, the interaction can increase the ball’s \(v\) (e.g., a faster object hitting from behind). Correct.
5. High friction: \(v\) decreases. Incorrect.

So the correct checkboxes to select are:
- Colliding with a ball of much lower mass moving in the opposite direction of the ball.
- Moving from a flat surface to moving downhill.
- A moving object traveling in the same direction as the ball colliding with it.

Answer:

• Colliding with a ball of much lower mass moving in the opposite direction of the ball.
• Moving from a flat surface to moving downhill.
• A moving object traveling in the same direction as the ball colliding with it.