momentum - Name Date Physics - Momentum/Impulse Worksheet Chapter ... - Free Printable

Let’s solve each problem one by one, step by step. We’ll use the formula for momentum:

Momentum (p) = mass (m) × velocity (v)
→ p = m × v

Units: kg·m/s

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Problem 1:

> Calculate the momentum of a car that has a mass of 2.0 × 10³ kg and is moving at 35 m/s.

Step 1: Write down what you know.
mass (m) = 2.0 × 10³ kg = 2000 kg
velocity (v) = 35 m/s

Step 2: Plug into formula.
p = m × v = 2000 kg × 35 m/s

Step 3: Multiply.
2000 × 35 = 70,000

So, momentum = 70,000 kg·m/s

We can also write it as 7.0 × 10⁴ kg·m/s to match scientific notation style.

✔ Final Answer for #1: 7.0 × 10⁴ kg·m/s

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Problem 2:

> If the momentum of the MLB baseball doubles as it leaves the atmosphere in 3.78 s (10 mph/s), what was its initial speed?

Wait — this question seems miswritten or confusing. Let’s read carefully:

It says: “If the momentum of the MLB baseball doubles as it leaves the atmosphere in 3.78 s (10 mph/s)”

That doesn’t make physical sense — baseballs don’t leave the atmosphere. Also, “10 mph/s” is an acceleration unit, but not standard.

Also, we’re missing key info: mass of baseball? Initial momentum? What does “doubles” mean here?

Actually, looking again — maybe there’s a typo. Perhaps it meant:

> “If the momentum of the MLB baseball doubles over 3.78 seconds with an acceleration of 10 mph/s, what was its initial speed?”

But even then, units are messy. Let’s assume they meant:

- Acceleration = 10 miles per hour per second → convert to m/s²?
- Time = 3.78 s
- Momentum doubles → so final velocity = 2 × initial velocity (since mass is constant)

Let’s try that approach.

Assume:
Mass of baseball ≈ 0.145 kg (standard MLB ball — though not given, we may need to assume or see if it cancels)

But wait — if momentum doubles, and mass is constant, then velocity must double.

So:
v_final = 2 × v_initial

Acceleration a = Δv / t = (v_final - v_initial) / t = (2v_i - v_i)/t = v_i / t

Given: a = 10 mph/s → let’s convert to m/s²

1 mile = 1609 meters
1 hour = 3600 seconds

So 10 mph/s = 10 × (1609 m / 3600 s) per second = 10 × 0.447 m/s² ≈ 4.47 m/s²

Now:
a = v_i / t → v_i = a × t = 4.47 m/s² × 3.78 s ≈ ?

Calculate:
4.47 × 3.78

First: 4 × 3.78 = 15.12
0.47 × 3.78 ≈ 0.47 × 3.8 = 1.786 minus 0.47×0.02=0.0094 → ~1.7766
Total ≈ 15.12 + 1.7766 = 16.8966 m/s

Convert back to mph? The question didn’t specify unit for answer.

But original acceleration was given in mph/s, so maybe answer expected in mph?

Wait — let’s re-read: “what was its initial speed?” — no unit specified.

But since input used mph/s, perhaps output should be in mph?

Alternative approach without converting:

If acceleration = 10 mph per second, and time = 3.78 s,

Then change in velocity = a × t = 10 mph/s × 3.78 s = 37.8 mph

And since velocity doubled:
Δv = v_final - v_initial = 2v_i - v_i = v_i

So v_i = Δv = 37.8 mph

Oh! That’s much simpler — and avoids unit conversion.

Because if acceleration is 10 mph every second, then in 3.78 seconds, speed increases by 37.8 mph.

And since momentum doubled → speed doubled → increase equals original speed.

So initial speed = 37.8 mph

✔ Final Answer for #2: 37.8 mph

*(Note: This assumes the "10 mph/s" is literal acceleration in those units, and that doubling momentum means doubling speed — which is true if mass is constant.)*

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Problem 3:

> A 0.05 kg popcorn kernel pops off the base of a hot air balloon (20 kg). After the pop, the balloon is found to be traveling at 1.5 m/s. What is the speed of the popcorn kernel?

This is conservation of momentum!

Before popping: everything is at rest → total momentum = 0

After popping: balloon moves one way, popcorn kernel moves opposite way.

Let’s define direction: say balloon goes positive → popcorn goes negative.

Conservation of momentum:
Initial momentum = Final momentum
0 = m_balloon × v_balloon + m_kernel × v_kernel

Plug in:

0 = (20 kg)(1.5 m/s) + (0.05 kg)(v_kernel)

Compute:

0 = 30 + 0.05 × v_kernel

So:
0.05 × v_kernel = -30

v_kernel = -30 / 0.05 = -600 m/s

Negative sign means opposite direction to balloon.

Speed is magnitude → 600 m/s

✔ Final Answer for #3: 600 m/s

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Problem 4:

> The same popcorn kernel pops off the base of the same balloon, but this time the kernel is already traveling at 2 m/s toward the ground when it pops. The balloon starts from rest and after the pop, it travels upward at 1.5 m/s. What is the speed of the popcorn kernel after the pop?

Again, conservation of momentum.

Before pop:
Balloon is at rest → momentum = 0
Kernel is moving downward at 2 m/s → momentum = m_kernel × (-2) [if up is positive]

Total initial momentum = 0 + (0.05 kg)(-2 m/s) = -0.1 kg·m/s

After pop:
Balloon moves up at 1.5 m/s → momentum = 20 kg × 1.5 = +30 kg·m/s
Kernel has unknown velocity v → momentum = 0.05 × v

Total final momentum = 30 + 0.05v

Set equal to initial:

30 + 0.05v = -0.1

Solve:

0.05v = -0.1 - 30 = -30.1

v = -30.1 / 0.05 = -602 m/s

Speed = |v| = 602 m/s

✔ Final Answer for #4: 602 m/s

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Problem 5:

> The Titanic is sinking downward at half its max speed. Before hitting the iceberg, the Titanic was going 20 knots (1 knot = 0.514 m/s). As it hits the iceberg, the ship stops completely. During the collision, the iceberg gains some speed. If the iceberg has a mass of 1.0 × 10⁶ kg, and the Titanic has a mass of 4.0 × 10⁷ kg, find the speed of the iceberg after the collision. Assume the iceberg was initially at rest.

First, find Titanic’s speed before collision.

Max speed = 20 knots → but it’s sinking at *half* max speed → so speed = 10 knots

Convert to m/s:
10 knots × 0.514 m/s per knot = 5.14 m/s downward

Define direction: let’s take downward as positive (since Titanic is moving down).

Initial momentum:

Titanic: m_t = 4.0e7 kg, v_t = +5.14 m/s → p_t = 4.0e7 × 5.14 = ?

Calculate:
4.0 × 5.14 = 20.56 → so 2.056 × 10⁸ kg·m/s

Iceberg: initially at rest → p_i = 0

Total initial momentum = 2.056 × 10⁸ kg·m/s

After collision:
Titanic stops → v_t_final = 0 → p_t_final = 0
Iceberg moves with unknown speed v_i → p_i_final = (1.0e6 kg) × v_i

Conservation of momentum:

Initial = Final
2.056 × 10⁸ = 0 + (1.0 × 10⁶) × v_i

So:
v_i = (2.056 × 10⁸) / (1.0 × 10⁶) = 2.056 × 10² = 205.6 m/s

Wait — that’s super fast! 205 m/s is like 740 km/h — unrealistic for an iceberg.

Did I misread?

“The Titanic is sinking downward at half its max speed.” Max speed is 20 knots → half is 10 knots → 5.14 m/s — that’s correct.

Masses: Titanic 4e7 kg, iceberg 1e6 kg — ratio 40:1

So if Titanic stops, iceberg should move faster — but 40 times faster? 5.14 × 40 = 205.6 m/s — math checks out.

But physically, icebergs don’t fly off at supersonic speeds — so either the masses are wrong, or scenario is idealized.

In physics problems, we go with the numbers given.

So answer is 205.6 m/s — but let’s round appropriately.

Input values: 20 knots (exact?), 0.514 exact? Probably keep 3 sig figs.

20 knots → half is 10.0 knots → 10.0 × 0.514 = 5.14 m/s (3 sig figs)

Titanic mass: 4.0 × 10⁷ → 2 sig figs? Wait, written as 4.0 → two sig figs? But often in such problems, trailing zero after decimal counts.

Actually, 4.0 × 10⁷ has 2 sig figs, 1.0 × 10⁶ has 2 sig figs, 0.514 has 3.

Limiting is 2 sig figs? But 5.14 has 3.

Better to compute exactly and round at end.

v_i = (4.0e7 * 5.14) / 1.0e6 = (2.056e8) / 1.0e6 = 205.6 m/s

With sig figs: masses have 2 sig figs (4.0 and 1.0), speed 5.14 has 3 → limiting is 2 sig figs? But 4.0 might be considered 2, but in context, probably expect 3.

Looking at other problems, they use 2 or 3.

Perhaps report as 206 m/s? Or 2.1 × 10² m/s?

But let’s check calculation again.

4.0e7 × 5.14 = 4.0 × 5.14 × 10^7 = 20.56 × 10^7 = 2.056 × 10^8

Divide by 1.0e6 = 2.056 × 10^2 = 205.6

Since 4.0 and 1.0 both have two significant figures, answer should have two: 210 m/s? But 205.6 rounded to two sig figs is 210? No — 205.6 to two sig figs is 2.1 × 10² = 210 m/s.

But 205.6 is closer to 210 than 200? Actually, 205.6 rounded to two significant figures: first digit is 2, second is 0, third is 5 — so round up → 210.

But let’s see: 4.0 has two, 1.0 has two, 5.14 has three — the product should have two sig figs.

Alternatively, perhaps the problem expects exact calculation.

In many textbooks, they’d leave it as 206 m/s or something.

But to be safe, let’s use 206 m/s — or better, calculate precisely.

Another thought: “half its max speed” — max speed is 20 knots, so half is exactly 10 knots.

10 knots × 0.514 m/s/knot = 5.14 m/s — exact as given.

Masses: 4.0 × 10^7 and 1.0 × 10^6 — likely intended as exact for calculation.

So I’ll go with 206 m/s (rounded from 205.6)

But 205.6 is 205.6 — perhaps report as 206 m/s.

Wait, 4.0e7 * 5.14 = let's compute numerically:

40,000,000 × 5.14 = 40e6 × 5.14 = 205,600,000

Divide by 1,000,000 = 205.6

So 205.6 m/s

In physics, often keep one decimal if inputs allow.

But let’s see the answer format — others were whole numbers.

Perhaps they want 206 m/s.

I think it’s fine to put 206 m/s.

But let me double-check direction.

We assumed downward positive. Iceberg gains speed — in which direction? Since Titanic was moving down and stopped, iceberg should move down too — so positive.

Yes.

✔ Final Answer for #5: 206 m/s (or 205.6, but rounded)

Actually, let's use 206 m/s for consistency.

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Now, compiling all answers:

Final Answer:
1. 7.0 × 10⁴ kg·m/s
2. 37.8 mph
3. 600 m/s
4. 602 m/s
5. 206 m/s