The Ultimate Conservation of Momentum Worksheet - Free Printable
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Step-by-step solution for: The Ultimate Conservation of Momentum Worksheet
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Step-by-step solution for: The Ultimate Conservation of Momentum Worksheet
Let's go through each of the conceptual problems on "The Ultimate Conservation of Momentum Worksheet" and provide clear, detailed explanations.
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1. To win a prize at the county fair, you're trying to knock down a milk bottle by hitting it with a thrown object. Should you choose to throw a rubber ball or a beanbag of equal size and weight? Explain.
Answer:
You should choose to throw the beanbag.
Explanation:
Momentum is conserved in collisions, but the effectiveness in knocking down the bottle depends on how much impulse is delivered. Impulse is the change in momentum (Δp = FΔt), and for a given mass and velocity, the key factor is whether the object bounces or sticks.
- A rubber ball bounces off the bottle, meaning its velocity reverses direction. This results in a larger change in momentum (from +v to -v), so a greater impulse is delivered to the bottle.
- However, in this case, the goal is to knock the bottle over, not just transfer momentum. But since the rubber ball rebounds, it transfers less net momentum to the bottle because it takes some back. The beanbag, being inelastic, sticks to the bottle, transferring all of its momentum to the bottle.
Wait — actually, this is a common misconception. Let’s clarify:
- If the rubber ball bounces, it changes direction, meaning the change in momentum is larger than if it stops. So the force exerted on the bottle is greater during impact.
- Thus, the rubber ball delivers more impulse due to the reversal of momentum.
But here’s the catch: if the bottle is light, the rebound effect might be more effective in tipping it over due to higher force. However, if the bottle is sturdy, the beanbag may be better because it stays attached and applies a sustained force.
But generally, for maximum impulse, the rubber ball is better because it has a larger Δp.
✔ Correct Answer: Choose the rubber ball.
Reason: When the rubber ball hits and bounces, its change in momentum is greater than that of the beanbag, which stops or sticks. This means a larger impulse is delivered to the bottle, increasing the chance of knocking it down.
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2. A wet snowball is thrown at a large concrete wall and sticks. Does this violate the law of conservation of momentum? Explain.
Answer: No, it does not violate the law of conservation of momentum.
Explanation:
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.
In this case:
- The snowball has initial momentum toward the wall.
- After impact, it sticks to the wall → its momentum becomes zero (relative to the ground).
- But the wall (and the Earth) are massive and can absorb the momentum without noticeable motion.
So, the momentum is transferred to the wall and ultimately to the Earth. Since the Earth is so massive, the change in its velocity is negligible, but momentum is still conserved.
✔ Conclusion: Momentum is conserved — it’s just transferred to the Earth.
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3. When a sprinter bursts from the starting blocks, he/she generates considerable forward momentum. Is this an example where momentum is not conserved?
Answer: No, momentum is conserved.
Explanation:
The sprinter pushes backward against the starting blocks, and the blocks push forward on the sprinter (Newton’s third law). The sprinter gains forward momentum, but the blocks (and the Earth) gain an equal amount of backward momentum.
Since the Earth is extremely massive, its velocity change is imperceptible, but the momentum is still conserved.
✔ Conclusion: Momentum is conserved — the system includes the sprinter and the Earth.
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4. An ice boat is coasting along a frozen lake. Friction between the ice and the boat is negligible, and so is air resistance. Nothing is propelling the boat. From a bridge, someone jumps straight down and lands in the boat, which continues to coast straight ahead.
a. Does the horizontal momentum of the boat change?
b. Does the speed of the boat increase, decrease, or remain the same? Explain.
Answer:
a. No, the horizontal momentum of the boat does not change.
b. The speed of the boat decreases.
Explanation:
- Initially, the boat has some horizontal momentum: $ p = m_{\text{boat}} v $
- The person jumps straight down, so their horizontal momentum is zero before landing.
- When they land in the boat, they add mass to the system, but no horizontal momentum is added.
- Total horizontal momentum is conserved: $ m_{\text{boat}} v = (m_{\text{boat}} + m_{\text{person}}) v' $
- Solving for $ v' $: $ v' = \frac{m_{\text{boat}}}{m_{\text{boat}} + m_{\text{person}}} v $
So the speed decreases because the denominator increases, while momentum remains the same.
✔ Summary:
- Horizontal momentum: unchanged (no external horizontal force)
- Speed: decreases due to increased mass
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5. When analyzing a collision, how can you tell if the collision is inelastic or elastic? Explain.
Answer:
You can determine the type of collision by checking whether kinetic energy is conserved.
- Elastic collision: Both momentum and kinetic energy are conserved.
- Example: Two billiard balls colliding with little deformation.
- Inelastic collision: Momentum is conserved, but kinetic energy is not.
- In perfectly inelastic collisions, objects stick together after impact.
How to tell:
Compare the total kinetic energy before and after the collision:
- If $ KE_{\text{before}} = KE_{\text{after}} $ → elastic
- If $ KE_{\text{before}} > KE_{\text{after}} $ → inelastic
Note: All real collisions lose *some* kinetic energy (to heat, sound, deformation), so perfectly elastic collisions are idealized.
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6. What is impulse defined as?
Answer:
Impulse is defined as the change in momentum of an object.
Mathematically:
$$
\text{Impulse} = \Delta p = m \Delta v = F \Delta t
$$
Where:
- $ \Delta p $ = change in momentum
- $ F $ = average force applied
- $ \Delta t $ = time interval over which the force acts
So, impulse is also equal to the product of force and time.
It’s a vector quantity and has units of kg·m/s or N·s.
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7. When kicking a field goal, kickers are coached to follow through after the kick. Explain how this is beneficial.
Answer:
Following through increases the time of contact between the foot and the football.
From the impulse-momentum theorem:
$$
F \Delta t = \Delta p
$$
By increasing $ \Delta t $, the average force needed to achieve a certain change in momentum (i.e., give the ball high speed) is reduced, but more importantly, a longer contact time allows for greater impulse, leading to:
- Higher ball speed
- Greater distance traveled
- Better control and accuracy
Also, following through helps maintain proper form and ensures the force is applied in the correct direction.
✔ Conclusion: Follow-through increases impulse, resulting in a more powerful and accurate kick.
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| Question | Answer |
|--------|--------|
| 1 | Rubber ball — it bounces, giving larger Δp and more impulse. |
| 2 | No — momentum is transferred to Earth. |
| 3 | No — Earth gains equal backward momentum. |
| 4a | No — horizontal momentum unchanged. |
| 4b | Speed decreases — mass increases, momentum conserved. |
| 5 | Elastic: KE conserved; Inelastic: KE not conserved. |
| 6 | Impulse = change in momentum = $ F \Delta t $. |
| 7 | Increases contact time → greater impulse → higher ball speed. |
Let me know if you'd like these formatted as a printable answer key!
---
1. To win a prize at the county fair, you're trying to knock down a milk bottle by hitting it with a thrown object. Should you choose to throw a rubber ball or a beanbag of equal size and weight? Explain.
Answer:
You should choose to throw the beanbag.
Explanation:
Momentum is conserved in collisions, but the effectiveness in knocking down the bottle depends on how much impulse is delivered. Impulse is the change in momentum (Δp = FΔt), and for a given mass and velocity, the key factor is whether the object bounces or sticks.
- A rubber ball bounces off the bottle, meaning its velocity reverses direction. This results in a larger change in momentum (from +v to -v), so a greater impulse is delivered to the bottle.
- However, in this case, the goal is to knock the bottle over, not just transfer momentum. But since the rubber ball rebounds, it transfers less net momentum to the bottle because it takes some back. The beanbag, being inelastic, sticks to the bottle, transferring all of its momentum to the bottle.
Wait — actually, this is a common misconception. Let’s clarify:
- If the rubber ball bounces, it changes direction, meaning the change in momentum is larger than if it stops. So the force exerted on the bottle is greater during impact.
- Thus, the rubber ball delivers more impulse due to the reversal of momentum.
But here’s the catch: if the bottle is light, the rebound effect might be more effective in tipping it over due to higher force. However, if the bottle is sturdy, the beanbag may be better because it stays attached and applies a sustained force.
But generally, for maximum impulse, the rubber ball is better because it has a larger Δp.
✔ Correct Answer: Choose the rubber ball.
Reason: When the rubber ball hits and bounces, its change in momentum is greater than that of the beanbag, which stops or sticks. This means a larger impulse is delivered to the bottle, increasing the chance of knocking it down.
---
2. A wet snowball is thrown at a large concrete wall and sticks. Does this violate the law of conservation of momentum? Explain.
Answer: No, it does not violate the law of conservation of momentum.
Explanation:
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.
In this case:
- The snowball has initial momentum toward the wall.
- After impact, it sticks to the wall → its momentum becomes zero (relative to the ground).
- But the wall (and the Earth) are massive and can absorb the momentum without noticeable motion.
So, the momentum is transferred to the wall and ultimately to the Earth. Since the Earth is so massive, the change in its velocity is negligible, but momentum is still conserved.
✔ Conclusion: Momentum is conserved — it’s just transferred to the Earth.
---
3. When a sprinter bursts from the starting blocks, he/she generates considerable forward momentum. Is this an example where momentum is not conserved?
Answer: No, momentum is conserved.
Explanation:
The sprinter pushes backward against the starting blocks, and the blocks push forward on the sprinter (Newton’s third law). The sprinter gains forward momentum, but the blocks (and the Earth) gain an equal amount of backward momentum.
Since the Earth is extremely massive, its velocity change is imperceptible, but the momentum is still conserved.
✔ Conclusion: Momentum is conserved — the system includes the sprinter and the Earth.
---
4. An ice boat is coasting along a frozen lake. Friction between the ice and the boat is negligible, and so is air resistance. Nothing is propelling the boat. From a bridge, someone jumps straight down and lands in the boat, which continues to coast straight ahead.
a. Does the horizontal momentum of the boat change?
b. Does the speed of the boat increase, decrease, or remain the same? Explain.
Answer:
a. No, the horizontal momentum of the boat does not change.
b. The speed of the boat decreases.
Explanation:
- Initially, the boat has some horizontal momentum: $ p = m_{\text{boat}} v $
- The person jumps straight down, so their horizontal momentum is zero before landing.
- When they land in the boat, they add mass to the system, but no horizontal momentum is added.
- Total horizontal momentum is conserved: $ m_{\text{boat}} v = (m_{\text{boat}} + m_{\text{person}}) v' $
- Solving for $ v' $: $ v' = \frac{m_{\text{boat}}}{m_{\text{boat}} + m_{\text{person}}} v $
So the speed decreases because the denominator increases, while momentum remains the same.
✔ Summary:
- Horizontal momentum: unchanged (no external horizontal force)
- Speed: decreases due to increased mass
---
5. When analyzing a collision, how can you tell if the collision is inelastic or elastic? Explain.
Answer:
You can determine the type of collision by checking whether kinetic energy is conserved.
- Elastic collision: Both momentum and kinetic energy are conserved.
- Example: Two billiard balls colliding with little deformation.
- Inelastic collision: Momentum is conserved, but kinetic energy is not.
- In perfectly inelastic collisions, objects stick together after impact.
How to tell:
Compare the total kinetic energy before and after the collision:
- If $ KE_{\text{before}} = KE_{\text{after}} $ → elastic
- If $ KE_{\text{before}} > KE_{\text{after}} $ → inelastic
Note: All real collisions lose *some* kinetic energy (to heat, sound, deformation), so perfectly elastic collisions are idealized.
---
6. What is impulse defined as?
Answer:
Impulse is defined as the change in momentum of an object.
Mathematically:
$$
\text{Impulse} = \Delta p = m \Delta v = F \Delta t
$$
Where:
- $ \Delta p $ = change in momentum
- $ F $ = average force applied
- $ \Delta t $ = time interval over which the force acts
So, impulse is also equal to the product of force and time.
It’s a vector quantity and has units of kg·m/s or N·s.
---
7. When kicking a field goal, kickers are coached to follow through after the kick. Explain how this is beneficial.
Answer:
Following through increases the time of contact between the foot and the football.
From the impulse-momentum theorem:
$$
F \Delta t = \Delta p
$$
By increasing $ \Delta t $, the average force needed to achieve a certain change in momentum (i.e., give the ball high speed) is reduced, but more importantly, a longer contact time allows for greater impulse, leading to:
- Higher ball speed
- Greater distance traveled
- Better control and accuracy
Also, following through helps maintain proper form and ensures the force is applied in the correct direction.
✔ Conclusion: Follow-through increases impulse, resulting in a more powerful and accurate kick.
---
Summary of Answers:
| Question | Answer |
|--------|--------|
| 1 | Rubber ball — it bounces, giving larger Δp and more impulse. |
| 2 | No — momentum is transferred to Earth. |
| 3 | No — Earth gains equal backward momentum. |
| 4a | No — horizontal momentum unchanged. |
| 4b | Speed decreases — mass increases, momentum conserved. |
| 5 | Elastic: KE conserved; Inelastic: KE not conserved. |
| 6 | Impulse = change in momentum = $ F \Delta t $. |
| 7 | Increases contact time → greater impulse → higher ball speed. |
Let me know if you'd like these formatted as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of worksheet conservation of momentum.
