Physics worksheet focusing on work and energy concepts with practice problems and solutions.

Here is the complete solution to all 9 problems on the "Work and Energy" worksheet, with step-by-step explanations.

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Problem 1:

A force of 10 N causes a displacement of 2 m in a body in its own direction. Calculate the work done by force.

Solution:
The formula for work done when force and displacement are in the same direction is:
> W = F × d

Where:
- W = Work done (in Joules, J)
- F = Force (in Newtons, N)
- d = Displacement (in meters, m)

Given:
- F = 10 N
- d = 2 m

So,
> W = 10 N × 2 m = 20 J

✔ Answer: 20 J

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Problem 2:

A body of mass 2 kg is moving with a speed of 20 m/s. Find the kinetic energy.

Solution:
Kinetic energy (KE) is given by:
> KE = ½ mv²

Where:
- m = mass (kg)
- v = velocity (m/s)

Given:
- m = 2 kg
- v = 20 m/s

So,
> KE = ½ × 2 × (20)²
> KE = 1 × 400 = 400 J

✔ Answer: 400 J

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Problem 3:

A moving body of 30 kg has 60 J of KE. Calculate the speed.

Solution:
Use the kinetic energy formula again:
> KE = ½ mv²

We need to solve for v.

Given:
- KE = 60 J
- m = 30 kg

So:
> 60 = ½ × 30 × v²
> 60 = 15 × v²
> v² = 60 / 15 = 4
> v = √4 = 2 m/s

✔ Answer: 2 m/s

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Problem 4:

How much force is applied on the body when 150 joule of work is done in displacing the body through a distance of 10 m in the direction of force?

Solution:
Use the work formula:
> W = F × d

Solve for F:
> F = W / d

Given:
- W = 150 J
- d = 10 m

So:
> F = 150 J / 10 m = 15 N

✔ Answer: 15 N

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Problem 5:

A body of 5 kg raised to 2 m. Find the work done.

Solution:
When lifting an object vertically against gravity, the work done equals the gravitational potential energy gained:
> W = mgh

Where:
- m = mass (kg)
- g = acceleration due to gravity ≈ 9.8 m/s²
- h = height (m)

Given:
- m = 5 kg
- h = 2 m
- g = 9.8 m/s² (standard value unless otherwise specified)

So:
> W = 5 × 9.8 × 2 = 98 J

✔ Answer: 98 J

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Problem 6:

A work of 4900 J is done on a load of mass 50 kg to lift it to a certain height. Calculate the height through which the load is lifted.

Solution:
Again, use:
> W = mgh

Solve for h:
> h = W / (mg)

Given:
- W = 4900 J
- m = 50 kg
- g = 9.8 m/s²

So:
> h = 4900 / (50 × 9.8) = 4900 / 490 = 10 m

✔ Answer: 10 m

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Problem 7:

An engine does 54,000 J of work by exerting a force of 6000 N on it. What is the displacement of the force?

Solution:
Use:
> W = F × d

Solve for d:
> d = W / F

Given:
- W = 54,000 J
- F = 6000 N

So:
> d = 54,000 / 6000 = 9 m

⚠️ Note: The answer key says (10m), but mathematically, 54,000 ÷ 6000 = 9 m, not 10 m. There may be a typo in the provided answer. Unless the problem meant 60,000 J (which would give 10 m), the correct answer is 9 m.

✔ Correct Answer: 9 m *(Answer key likely has error)*

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Problem 8:

A machine does 192 J of work in 240 sec. What is the power of the machine?

Solution:
Power is the rate at which work is done:
> P = W / t

Where:
- P = Power (in Watts, W)
- W = Work (Joules)
- t = time (seconds)

Given:
- W = 192 J
- t = 240 s

So:
> P = 192 / 240 = 0.8 W

⚠️ Note: The answer key says (8w), but 192 ÷ 240 = 0.8, not 8. This appears to be a decimal error in the key.

✔ Correct Answer: 0.8 W *(Answer key likely has error)*

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Problem 9:

A force of 5 N acting on a body at an angle of 30° with the horizontal direction displaces it horizontally through a distance of 6 m. Calculate the work done.

Solution:
When force is applied at an angle, only the component of force in the direction of displacement does work:
> W = F × d × cosθ

Where:
- θ = angle between force and displacement

Given:
- F = 5 N
- d = 6 m
- θ = 30°
- cos(30°) = √3 / 2 ≈ 0.866

So:
> W = 5 × 6 × cos(30°)
> W = 30 × (√3 / 2)
> W = 15√3 J

✔ Answer: 15√3 J

*(This matches the answer key.)*

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## ✔ Final Answers Summary:

1. 20 J
2. 400 J
3. 2 m/s
4. 15 N
5. 98 J
6. 10 m
7. 9 m *(Answer key says 10m — likely incorrect)*
8. 0.8 W *(Answer key says 8w — likely incorrect)*
9. 15√3 J

Let me know if you’d like diagrams or further clarification on any problem!