Let's solve each problem step by step using the
work formula:
$$
\text{Work} = \text{Force} \times \text{Distance} \quad \text{or} \quad W = F \cdot d
$$
Where:
- $ W $ is work in joules (J)
- $ F $ is force in newtons (N)
- $ d $ is distance in meters (m)
We’ll solve for the missing variable in each case.
---
1. You must exert a force of 4.5 N on a book to slide it across a table. If you do 2.7 J of work in the process, how far have you moved the book?
Given:
- $ F = 4.5 \, \text{N} $
- $ W = 2.7 \, \text{J} $
- Find: $ d = ? $
Use:
$$
d = \frac{W}{F} = \frac{2.7 \, \text{J}}{4.5 \, \text{N}} = 0.6 \, \text{m}
$$
✔ Answer: $ \boxed{0.6 \, \text{m}} $
---
2. A child pulls a sled up a snow-covered hill. The child does 405 J of work on the sled. If the child walks 15 m up the hill, how large of a force must the child exert?
Given:
- $ W = 405 \, \text{J} $
- $ d = 15 \, \text{m} $
- Find: $ F = ? $
$$
F = \frac{W}{d} = \frac{405 \, \text{J}}{15 \, \text{m}} = 27 \, \text{N}
$$
✔ Answer: $ \boxed{27 \, \text{N}} $
---
3. How much work is done on a small car if a 31.50 N force is exerted to move it 75.5 m to the side of the road?
Given:
- $ F = 31.50 \, \text{N} $
- $ d = 75.5 \, \text{m} $
- Find: $ W = ? $
$$
W = F \cdot d = 31.50 \, \text{N} \times 75.5 \, \text{m} = 2382.75 \, \text{J}
$$
✔ Answer: $ \boxed{2382.75 \, \text{J}} $
---
4. A crate is being lifted into a truck. If it is moved with a 2470 N force and 3650 J of work is done, then how far is the crate being lifted?
Given:
- $ F = 2470 \, \text{N} $
- $ W = 3650 \, \text{J} $
- Find: $ d = ? $
$$
d = \frac{W}{F} = \frac{3650 \, \text{J}}{2470 \, \text{N}} \approx 1.477 \, \text{m}
$$
Rounded to two decimal places: $ \boxed{1.48 \, \text{m}} $
✔ Answer: $ \boxed{1.48 \, \text{m}} $
---
5. If 16,700 J of work is done to shoot the human cannonball down a 3.05 m barrel, then how much force is applied to the person to fire them out the cannon?
Given:
- $ W = 16,700 \, \text{J} $
- $ d = 3.05 \, \text{m} $
- Find: $ F = ? $
$$
F = \frac{W}{d} = \frac{16,700 \, \text{J}}{3.05 \, \text{m}} \approx 5,475.41 \, \text{N}
$$
Rounded to nearest whole number: $ \boxed{5,475 \, \text{N}} $
✔ Answer: $ \boxed{5,475 \, \text{N}} $
---
6. An elephant pushes with 2000 N on a load of trees. It then pushes these trees for 150 m. How much work did the elephant do?
Given:
- $ F = 2000 \, \text{N} $
- $ d = 150 \, \text{m} $
- Find: $ W = ? $
$$
W = F \cdot d = 2000 \, \text{N} \times 150 \, \text{m} = 300,000 \, \text{J}
$$
✔ Answer: $ \boxed{300,000 \, \text{J}} $
---
✔ Final Answers Summary:
1. $ \boxed{0.6 \, \text{m}} $
2. $ \boxed{27 \, \text{N}} $
3. $ \boxed{2382.75 \, \text{J}} $
4. $ \boxed{1.48 \, \text{m}} $
5. $ \boxed{5,475 \, \text{N}} $
6. $ \boxed{300,000 \, \text{J}} $
Let me know if you'd like this formatted as a completed worksheet!
Parent Tip: Review the logic above to help your child master the concept of calculating work worksheet.
