Kinetic Energy Calculations Worksheet by The Clever Chemist | TPT - Free Printable

It looks like you've uploaded an image of a worksheet titled "Kinetic Energy Calculations" with several problems related to kinetic energy. I'll solve each problem step-by-step and explain the solutions clearly.

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🔹 Key Formula:

The formula for kinetic energy (KE) is:

$$
KE = \frac{1}{2}mv^2
$$

Where:
- $ KE $ = kinetic energy (in joules, J)
- $ m $ = mass (in kilograms, kg)
- $ v $ = velocity (in meters per second, m/s)

Also, rearranged forms:
- $ v = \sqrt{\frac{2 \cdot KE}{m}} $
- $ m = \frac{2 \cdot KE}{v^2} $

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✔ Answers to the Questions

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#### 1. What is kinetic energy?
> Answer: Energy a moving object has because of its motion.

✔ This is correct! Kinetic energy is the energy possessed by an object due to its motion.

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#### 2. What is a Joule?
> Answer: A unit of energy.

✔ Correct. The joule (J) is the SI unit of energy, including kinetic energy.
1 joule = 1 kg·m²/s²

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#### 3. What are the SI units for a Joule?
> Answer: kg·m²/s²

✔ Yes! Since:
- $ KE = \frac{1}{2}mv^2 $
- Mass ($ m $) → kg
- Velocity ($ v $) → m/s → $ v^2 $ → m²/s²
- So: $ KE $ → kg × m²/s² = kg·m²/s²

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🧮 Now let’s solve each problem:

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Problem 1:

> Find the kinetic energy of a ball moving at 45 m/s with a mass of 0.58 kg.

Given:
- $ m = 0.58 \, \text{kg} $
- $ v = 45 \, \text{m/s} $

Use:
$$
KE = \frac{1}{2}mv^2 = \frac{1}{2}(0.58)(45)^2
$$

Step-by-step:
- $ 45^2 = 2025 $
- $ \frac{1}{2} \times 0.58 = 0.29 $
- $ 0.29 \times 2025 = 587.25 $

✔ Answer: $ KE = 587.25 \, \text{J} $

✔️ Your answer in the image is correct.

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Problem 2:

> Find the kinetic energy of a skater whose mass is 65 kg and is moving at 4 m/s.

Given:
- $ m = 65 \, \text{kg} $
- $ v = 4 \, \text{m/s} $

$$
KE = \frac{1}{2}(65)(4)^2 = \frac{1}{2}(65)(16) = 32.5 \times 16 = 520 \, \text{J}
$$

✔ Answer: $ KE = 520 \, \text{J} $

✔️ Your answer in the image is correct.

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Problem 3:

> Find the mass of a truck moving at 30 m/s with 455,000 J of energy.

Given:
- $ KE = 455,000 \, \text{J} $
- $ v = 30 \, \text{m/s} $

Rearrange:
$$
m = \frac{2 \cdot KE}{v^2}
$$

Step-by-step:
- $ v^2 = 30^2 = 900 $
- $ 2 \cdot KE = 2 \times 455,000 = 910,000 $
- $ m = \frac{910,000}{900} = 1011.11\ldots \approx 1011.11 \, \text{kg} $

But your image says:
$$
m = \frac{2(455,000)}{(30)^2} = \frac{910,000}{900} = 1011.11 \, \text{kg}
$$

Wait — the image shows 944.4 kg, which seems incorrect.

Let’s double-check:

Is there a typo?

Wait — look again:
You wrote:
$$
m = \frac{2(455,000)}{(30)^2} = \frac{910,000}{900} = 944.4 \, \text{kg}
$$

✘ That’s wrong.
$ \frac{910,000}{900} = 1011.11 $, not 944.4

So either:
- The calculation in the image is incorrect, or
- There's a typo in the problem.

Let’s check: Is it possible that the KE was meant to be 425,000 J?

Try:
$ m = \frac{2 \times 425,000}{900} = \frac{850,000}{900} \approx 944.4 \, \text{kg} $

Ah! So likely, the KE value was miswritten as 455,000 instead of 425,000 J.

✔ Conclusion: The image has a mistake in Problem 3.

If $ KE = 425,000 \, \text{J} $, then:
$$
m = \frac{2 \times 425,000}{900} = \frac{850,000}{900} = 944.4 \, \text{kg}
$$

✔️ So the corrected problem should have 425,000 J, not 455,000 J.

But as written: 455,000 J → mass = 1011.11 kg

⚠️ Error in the worksheet — please verify.

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Problem 4:

> Find the velocity of a runner who has a mass of 75 kg and 3,300 J of energy.

Given:
- $ m = 75 \, \text{kg} $
- $ KE = 3,300 \, \text{J} $

Use:
$$
v = \sqrt{\frac{2 \cdot KE}{m}} = \sqrt{\frac{2 \times 3,300}{75}} = \sqrt{\frac{6,600}{75}} = \sqrt{88} \approx 9.38 \, \text{m/s}
$$

Now check your image:
$$
v = \sqrt{\frac{2 \cdot 3300}{75}} = \sqrt{\frac{6600}{75}} = \sqrt{88} \approx 9.38 \, \text{m/s}
$$

But your image says ~9.39 m/s — very close!

✔ Actually, $ \sqrt{88} \approx 9.3808 $, so rounding to two decimals: 9.38 m/s

Your answer is slightly off — but acceptable if rounded differently.

Alternatively, maybe they used more precise steps.

Let’s compute:
- $ 6600 ÷ 75 = 88 $
- $ \sqrt{88} = \sqrt{4 \times 22} = 2\sqrt{22} \approx 2 \times 4.690 = 9.38 $

So yes, 9.38 m/s is correct.

Your image says 9.39 — probably just a rounding difference.

✔ Close enough, but technically 9.38 m/s is better.

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✔ Final Summary of Answers:

| Problem | Given | Answer |
|--------|-------|--------|
| 1 | $ m=0.58 \, \text{kg}, v=45 \, \text{m/s} $ | $ KE = 587.25 \, \text{J} $ ✔ |
| 2 | $ m=65 \, \text{kg}, v=4 \, \text{m/s} $ | $ KE = 520 \, \text{J} $ ✔ |
| 3 | $ KE=455,000 \, \text{J}, v=30 \, \text{m/s} $ | $ m = 1011.11 \, \text{kg} $ ✘ (Image says 944.4 → error) |
| 4 | $ m=75 \, \text{kg}, KE=3300 \, \text{J} $ | $ v \approx 9.38 \, \text{m/s} $ (Image says 9.39 → minor rounding) |

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🛠️ Fix for Problem 3:

To get $ m = 944.4 \, \text{kg} $, the KE must be:
$$
KE = \frac{1}{2}mv^2 = \frac{1}{2}(944.4)(900) = 425,000 \, \text{J}
$$

So either:
- The KE is 425,000 J, or
- The mass is 1011.11 kg

✔ Recommendation: Check the original problem. If KE is indeed 455,000 J, then the mass should be 1011.11 kg, not 944.4.

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✔ Final Notes:

- All formulas and concepts are correct.
- Only Problem 3 has a numerical error in the given data or solution.
- Problem 4 is nearly correct — just slight rounding.

Let me know if you'd like a corrected version of the worksheet!