Change in momentum worksheet|KS4 Physics|Teachit - Free Printable

Let's solve each question step by step using the key concept:

> Change in momentum = Force × Time
> or
> Δp = F × t

We'll also use:
- Momentum (p) = mass × velocity (p = m × v)
- Acceleration (a) = (v – u)/t
- Newton’s second law: F = m × a

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1. A mountain-biker and his bike have a total momentum of 600 kg·m/s. When the brakes are applied, the bike stops in 5 seconds. What force must the brakes have exerted?

Given:
- Initial momentum = 600 kg·m/s
- Final momentum = 0 (since it stops)
- So, change in momentum (Δp) = 600 kg·m/s
- Time (t) = 5 s

Using:
Δp = F × t
→ F = Δp / t = 600 / 5 = 120 N

✔ Answer: 120 N

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2. A cricket ball of mass 0.4 kg is travelling at 10 m/s. It is caught by a fielder. Calculate the force on the fielder’s hand if the time of impact is:

#### a) 0.1 seconds

Step 1: Find initial momentum
p = m × v = 0.4 × 10 = 4 kg·m/s

Final momentum = 0 (ball stops)

So, Δp = 4 kg·m/s

Time = 0.1 s

F = Δp / t = 4 / 0.1 = 40 N

✔ Answer: 40 N

#### b) 0.5 seconds

Same Δp = 4 kg·m/s
t = 0.5 s

F = 4 / 0.5 = 8 N

✔ Answer: 8 N

> ✔ Note: Longer stopping time → smaller force.

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3. A cricket player hits a ball (mass 0.2 kg) with a force of 20 N. If the force is applied for 0.5 seconds, calculate:

#### i) The change in momentum

Use:
Δp = F × t = 20 N × 0.5 s = 10 kg·m/s

✔ Answer: 10 kg·m/s

#### ii) The change in velocity of the ball

We know:
Δp = m × Δv
→ Δv = Δp / m = 10 / 0.2 = 50 m/s

✔ Answer: 50 m/s

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4. In a crash test, a dummy’s head collides with the steering wheel, coming to a complete standstill in 0.05 s. If the head has a mass of 8 kg and is initially travelling at 20 m/s, how much force is exerted on the head?

Step 1: Find change in momentum
Initial momentum = m × v = 8 × 20 = 160 kg·m/s
Final momentum = 0
→ Δp = 160 kg·m/s

Time = 0.05 s

F = Δp / t = 160 / 0.05 = 3200 N

✔ Answer: 3200 N

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5. An airbag is deployed in a second crash test, using the same dummy and same initial velocity as Q4. This time the head comes to a standstill in 0.2 s. What force is exerted this time?

Same Δp = 160 kg·m/s
t = 0.2 s

F = 160 / 0.2 = 800 N

✔ Answer: 800 N

> ✔ Airbag increases stopping time → reduces force → safer.

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6. Explain what a “crumple zone” is, and why they are included in all modern car designs.

Crumple zone:
A crumple zone is a specially designed area in a car (usually front and rear) that is meant to deform or collapse during a collision.

Why included?
- It increases the time over which the car stops during a crash.
- Since force = change in momentum / time, increasing time reduces the force experienced by the occupants.
- This helps reduce injury by spreading out the deceleration.

✔ Answer: Crumple zones absorb energy and increase stopping time, reducing the force on passengers.

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7. Extension Question: Show how you can derive the change in momentum formula by combining Newton’s second law (F = m × a) and a = (v – u)/t

Start with Newton’s second law:
F = m × a

Substitute acceleration:
a = (v – u) / t

So:
F = m × [(v – u) / t]

Multiply both sides by t:
F × t = m × (v – u)

But m × (v – u) is the change in momentum (final momentum – initial momentum)

So:
F × t = change in momentum

✔ Therefore:
Change in momentum = Force × Time

This is the impulse-momentum theorem.

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✔ Summary of Answers:

| Question | Answer |
|--------|--------|
| 1 | 120 N |
| 2a | 40 N |
| 2b | 8 N |
| 3i | 10 kg·m/s |
| 3ii | 50 m/s |
| 4 | 3200 N |
| 5 | 800 N |
| 6 | Crumple zones increase stopping time, reducing force on passengers. |
| 7 | Derived: F = m×a → F = m×(v−u)/t → F×t = m(v−u) = Δp |

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