Calculating Net Force worksheet - Free Printable

To solve the problems in the worksheet, we need to calculate the net force acting on an object. The net force is the vector sum of all forces acting on the object. If the forces are in opposite directions, we subtract their magnitudes. If they are in the same direction, we add their magnitudes.

Let's solve each problem step by step:

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Problem 1:

- Forces:
- Pushing: 39 N (to the right)
- Pulling: 29 N (to the left)
- Net Force:
\[
\text{Net Force} = 39 \, \text{N} - 29 \, \text{N} = 10 \, \text{N}
\]
Direction: To the right (since pushing is greater than pulling).

Answer: \( \boxed{10 \, \text{N}} \)

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Problem 2:

- Forces:
- Pushing: 24 N (to the right)
- Pulling: 65 N (to the left)
- Net Force:
\[
\text{Net Force} = 24 \, \text{N} - 65 \, \text{N} = -41 \, \text{N}
\]
Direction: To the left (since pulling is greater than pushing).

Answer: \( \boxed{-41 \, \text{N}} \)

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Problem 3:

- Forces:
- Pushing: 13 N (to the right)
- Pulling: 16 N (to the left)
- Net Force:
\[
\text{Net Force} = 13 \, \text{N} - 16 \, \text{N} = -3 \, \text{N}
\]
Direction: To the left (since pulling is greater than pushing).

Answer: \( \boxed{-3 \, \text{N}} \)

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Problem 4:

- Forces:
- Pushing: 29 N (to the right)
- Pushing: 30 N (to the right)
- Net Force:
\[
\text{Net Force} = 29 \, \text{N} + 30 \, \text{N} = 59 \, \text{N}
\]
Direction: To the right (both forces are in the same direction).

Answer: \( \boxed{59 \, \text{N}} \)

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Problem 5:

- Forces:
- Pulling: 10 N (to the left)
- Pulling: 41 N (to the left)
- Net Force:
\[
\text{Net Force} = 10 \, \text{N} + 41 \, \text{N} = 51 \, \text{N}
\]
Direction: To the left (both forces are in the same direction).

Answer: \( \boxed{51 \, \text{N}} \)

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Problem 6:

- Forces:
- Pulling: 76 N (to the left)
- Pulling: 76 N (to the right)
- Net Force:
\[
\text{Net Force} = 76 \, \text{N} - 76 \, \text{N} = 0 \, \text{N}
\]
Direction: No net force (forces cancel each other out).

Answer: \( \boxed{0 \, \text{N}} \)

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Problem 7:

- Forces:
- 45 N East
- 45 N West
- 40 N South
- 20 N North
- Net Force in the East-West direction:
\[
\text{East-West Net Force} = 45 \, \text{N} - 45 \, \text{N} = 0 \, \text{N}
\]
- Net Force in the North-South direction:
\[
\text{North-South Net Force} = 20 \, \text{N} - 40 \, \text{N} = -20 \, \text{N}
\]
Direction: To the South (since South is greater than North).

Answer: \( \boxed{-20 \, \text{N}} \)

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Problem 8:

- Forces:
- 12 N West
- 9 N East
- 10 N South
- 10 N North
- Net Force in the East-West direction:
\[
\text{East-West Net Force} = 9 \, \text{N} - 12 \, \text{N} = -3 \, \text{N}
\]
- Net Force in the North-South direction:
\[
\text{North-South Net Force} = 10 \, \text{N} - 10 \, \text{N} = 0 \, \text{N}
\]
Direction: To the West (since West is greater than East).

Answer: \( \boxed{-3 \, \text{N}} \)

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Problem 9:

- Forces:
- 24 N West
- 12 N East
- 7 N North
- 7 N South
- Net Force in the East-West direction:
\[
\text{East-West Net Force} = 12 \, \text{N} - 24 \, \text{N} = -12 \, \text{N}
\]
- Net Force in the North-South direction:
\[
\text{North-South Net Force} = 7 \, \text{N} - 7 \, \text{N} = 0 \, \text{N}
\]
Direction: To the West (since West is greater than East).

Answer: \( \boxed{-12 \, \text{N}} \)

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Problem 10:

- Forces:
- 30 N West
- 30 N East
- 0 N South
- 0 N North
- Net Force in the East-West direction:
\[
\text{East-West Net Force} = 30 \, \text{N} - 30 \, \text{N} = 0 \, \text{N}
\]
- Net Force in the North-South direction:
\[
\text{North-South Net Force} = 0 \, \text{N} - 0 \, \text{N} = 0 \, \text{N}
\]
Direction: No net force (forces cancel each other out).

Answer: \( \boxed{0 \, \text{N}} \)

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Final Answers:

1. \( \boxed{10 \, \text{N}} \)
2. \( \boxed{-41 \, \text{N}} \)
3. \( \boxed{-3 \, \text{N}} \)
4. \( \boxed{59 \, \text{N}} \)
5. \( \boxed{51 \, \text{N}} \)
6. \( \boxed{0 \, \text{N}} \)
7. \( \boxed{-20 \, \text{N}} \)
8. \( \boxed{-3 \, \text{N}} \)
9. \( \boxed{-12 \, \text{N}} \)
10. \( \boxed{0 \, \text{N}} \)