Balanced and Unbalanced Forces Worksheet | PDF - Free Printable

To solve the problems on the "Balanced and Unbalanced Forces Worksheet," we need to calculate the net force acting on each object. The net force is the vector sum of all forces acting on an 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: \( 4 \, \text{N} \) (left)
- Net Force:
- Since there is only one force acting, the net force is simply \( 4 \, \text{N} \) to the left.
- Net Force: \( 4 \, \text{N} \) (left)

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Problem 2:

- Forces: \( 7 \, \text{N} \) (left), \( 2 \, \text{N} \) (right)
- Net Force:
- The forces are in opposite directions. Subtract the smaller force from the larger force:
\[
7 \, \text{N} - 2 \, \text{N} = 5 \, \text{N}
\]
- The direction of the net force is the same as the larger force, which is to the left.
- Net Force: \( 5 \, \text{N} \) (left)

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Problem 3:

- Forces: \( 4 \, \text{N} \) (right), \( 4 \, \text{N} \) (left)
- Net Force:
- The forces are equal in magnitude but opposite in direction. They cancel each other out.
- Net Force: \( 0 \, \text{N} \)

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Problem 4:

- Forces: \( 6 \, \text{N} \) (right), \( 3 \, \text{N} \) (right)
- Net Force:
- The forces are in the same direction. Add their magnitudes:
\[
6 \, \text{N} + 3 \, \text{N} = 9 \, \text{N}
\]
- The direction of the net force is to the right.
- Net Force: \( 9 \, \text{N} \) (right)

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Problem 5:

- Forces: \( 8 \, \text{N} \) (left), \( 4 \, \text{N} \) (right)
- Net Force:
- The forces are in opposite directions. Subtract the smaller force from the larger force:
\[
8 \, \text{N} - 4 \, \text{N} = 4 \, \text{N}
\]
- The direction of the net force is the same as the larger force, which is to the left.
- Net Force: \( 4 \, \text{N} \) (left)

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Problem 6:

- Forces: \( 4 \, \text{N} \) (right), \( 5 \, \text{N} \) (left)
- Net Force:
- The forces are in opposite directions. Subtract the smaller force from the larger force:
\[
5 \, \text{N} - 4 \, \text{N} = 1 \, \text{N}
\]
- The direction of the net force is the same as the larger force, which is to the left.
- Net Force: \( 1 \, \text{N} \) (left)

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Problem 7:

- Forces: \( 3 \, \text{N} \) (left), \( 3 \, \text{N} \) (left)
- Net Force:
- The forces are in the same direction. Add their magnitudes:
\[
3 \, \text{N} + 3 \, \text{N} = 6 \, \text{N}
\]
- The direction of the net force is to the left.
- Net Force: \( 6 \, \text{N} \) (left)

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Problem 8:

- Forces: \( 2 \, \text{N} \) (right), \( 4 \, \text{N} \) (right), \( 5 \, \text{N} \) (left)
- Net Force:
- First, add the forces in the same direction (right):
\[
2 \, \text{N} + 4 \, \text{N} = 6 \, \text{N} \, (\text{right})
\]
- Then, subtract the force in the opposite direction (left):
\[
6 \, \text{N} - 5 \, \text{N} = 1 \, \text{N}
\]
- The direction of the net force is to the right.
- Net Force: \( 1 \, \text{N} \) (right)

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Problem 9:

- Forces: \( 6 \, \text{N} \) (left), \( 3 \, \text{N} \) (right)
- Net Force:
- The forces are in opposite directions. Subtract the smaller force from the larger force:
\[
6 \, \text{N} - 3 \, \text{N} = 3 \, \text{N}
\]
- The direction of the net force is the same as the larger force, which is to the left.
- Net Force: \( 3 \, \text{N} \) (left)

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Problem 10:

- Forces: \( 7 \, \text{N} \) (left), \( 4 \, \text{N} \) (right), \( 4 \, \text{N} \) (right)
- Net Force:
- First, add the forces in the same direction (right):
\[
4 \, \text{N} + 4 \, \text{N} = 8 \, \text{N} \, (\text{right})
\]
- Then, subtract the force in the opposite direction (left):
\[
8 \, \text{N} - 7 \, \text{N} = 1 \, \text{N}
\]
- The direction of the net force is to the right.
- Net Force: \( 1 \, \text{N} \) (right)

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Final Answers:

1. \( 4 \, \text{N} \) (left)
2. \( 5 \, \text{N} \) (left)
3. \( 0 \, \text{N} \)
4. \( 9 \, \text{N} \) (right)
5. \( 4 \, \text{N} \) (left)
6. \( 1 \, \text{N} \) (left)
7. \( 6 \, \text{N} \) (left)
8. \( 1 \, \text{N} \) (right)
9. \( 3 \, \text{N} \) (left)
10. \( 1 \, \text{N} \) (right)

\boxed{
\begin{array}{ll}
1. & 4 \, \text{N} \, (\text{left}) \\
2. & 5 \, \text{N} \, (\text{left}) \\
3. & 0 \, \text{N} \\
4. & 9 \, \text{N} \, (\text{right}) \\
5. & 4 \, \text{N} \, (\text{left}) \\
6. & 1 \, \text{N} \, (\text{left}) \\
7. & 6 \, \text{N} \, (\text{left}) \\
8. & 1 \, \text{N} \, (\text{right}) \\
9. & 3 \, \text{N} \, (\text{left}) \\
10. & 1 \, \text{N} \, (\text{right})
\end{array}
}