ScienceAges 10-12

Principle of moments & equilibrium

Apply the principle of moments (F₁d₁ = F₂d₂) to balance a uniform beam about a central pivot. Review suitability for your learners before teaching.

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Age band:Ages 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 10-12

Principle of moments & equilibrium

Take your time. Show your thinking.

1. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 9 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
Left: 6 N at 9 m · Right: ? N at 3 m
2. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 4 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
Left: 6 N at 4 m · Right: ? N at 2 m
3. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 9 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
Left: 24 N at 9 m · Right: ? N at 2 m
4. A uniform beam is balanced on a central pivot. A downward force of 50 N acts 9 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 50 N at 9 m · Right: ? N at 5 m
5. A uniform beam is balanced on a central pivot. A downward force of 12 N acts 2 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
Left: 12 N at 2 m · Right: ? N at 2 m
6. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 2 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
Left: 6 N at 2 m · Right: ? N at 3 m
7. A uniform beam is balanced on a central pivot. A downward force of 49 N acts 7 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
Left: 49 N at 7 m · Right: ? N at 7 m
8. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 1 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 24 N at 1 m · Right: ? N at 4 m
9. A uniform beam is balanced on a central pivot. A downward force of 50 N acts 1 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 50 N at 1 m · Right: ? N at 5 m
10. A uniform beam is balanced on a central pivot. A downward force of 30 N acts 8 m to the left of the pivot. What downward force is needed 6 m to the right of the pivot for equilibrium?
Left: 30 N at 8 m · Right: ? N at 6 m
11. A uniform beam is balanced on a central pivot. A downward force of 49 N acts 4 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
Left: 49 N at 4 m · Right: ? N at 7 m
12. A uniform beam is balanced on a central pivot. A downward force of 9 N acts 9 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
Left: 9 N at 9 m · Right: ? N at 3 m

12 questions · Seed 42 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Principle of moments & equilibrium

Answers and reasoning. Review before teaching.

1. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 9 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
18 N
By the principle of moments, anticlockwise moment = clockwise moment: 6 N × 9 m = 54 N·m, so F₂ = 54 ÷ 3 = 18 N.
2. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 4 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
12 N
By the principle of moments, anticlockwise moment = clockwise moment: 6 N × 4 m = 24 N·m, so F₂ = 24 ÷ 2 = 12 N.
3. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 9 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
108 N
By the principle of moments, anticlockwise moment = clockwise moment: 24 N × 9 m = 216 N·m, so F₂ = 216 ÷ 2 = 108 N.
4. A uniform beam is balanced on a central pivot. A downward force of 50 N acts 9 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
90 N
By the principle of moments, anticlockwise moment = clockwise moment: 50 N × 9 m = 450 N·m, so F₂ = 450 ÷ 5 = 90 N.
5. A uniform beam is balanced on a central pivot. A downward force of 12 N acts 2 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
12 N
By the principle of moments, anticlockwise moment = clockwise moment: 12 N × 2 m = 24 N·m, so F₂ = 24 ÷ 2 = 12 N.
6. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 2 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
4 N
By the principle of moments, anticlockwise moment = clockwise moment: 6 N × 2 m = 12 N·m, so F₂ = 12 ÷ 3 = 4 N.
7. A uniform beam is balanced on a central pivot. A downward force of 49 N acts 7 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
49 N
By the principle of moments, anticlockwise moment = clockwise moment: 49 N × 7 m = 343 N·m, so F₂ = 343 ÷ 7 = 49 N.
8. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 1 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
6 N
By the principle of moments, anticlockwise moment = clockwise moment: 24 N × 1 m = 24 N·m, so F₂ = 24 ÷ 4 = 6 N.
9. A uniform beam is balanced on a central pivot. A downward force of 50 N acts 1 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
10 N
By the principle of moments, anticlockwise moment = clockwise moment: 50 N × 1 m = 50 N·m, so F₂ = 50 ÷ 5 = 10 N.
10. A uniform beam is balanced on a central pivot. A downward force of 30 N acts 8 m to the left of the pivot. What downward force is needed 6 m to the right of the pivot for equilibrium?
40 N
By the principle of moments, anticlockwise moment = clockwise moment: 30 N × 8 m = 240 N·m, so F₂ = 240 ÷ 6 = 40 N.
11. A uniform beam is balanced on a central pivot. A downward force of 49 N acts 4 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
28 N
By the principle of moments, anticlockwise moment = clockwise moment: 49 N × 4 m = 196 N·m, so F₂ = 196 ÷ 7 = 28 N.
12. A uniform beam is balanced on a central pivot. A downward force of 9 N acts 9 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
27 N
By the principle of moments, anticlockwise moment = clockwise moment: 9 N × 9 m = 81 N·m, so F₂ = 81 ÷ 3 = 27 N.

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Principle of moments & equilibrium

Take your time. Show your thinking.

1. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 9 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
Left: 6 N at 9 m · Right: ? N at 3 m
2. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 4 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
Left: 6 N at 4 m · Right: ? N at 2 m
3. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 9 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
Left: 24 N at 9 m · Right: ? N at 2 m
4. A uniform beam is balanced on a central pivot. A downward force of 50 N acts 9 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 50 N at 9 m · Right: ? N at 5 m
5. A uniform beam is balanced on a central pivot. A downward force of 12 N acts 2 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
Left: 12 N at 2 m · Right: ? N at 2 m
6. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 2 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
Left: 6 N at 2 m · Right: ? N at 3 m
7. A uniform beam is balanced on a central pivot. A downward force of 49 N acts 7 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
Left: 49 N at 7 m · Right: ? N at 7 m
8. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 1 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 24 N at 1 m · Right: ? N at 4 m
9. A uniform beam is balanced on a central pivot. A downward force of 50 N acts 1 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 50 N at 1 m · Right: ? N at 5 m
10. A uniform beam is balanced on a central pivot. A downward force of 30 N acts 8 m to the left of the pivot. What downward force is needed 6 m to the right of the pivot for equilibrium?
Left: 30 N at 8 m · Right: ? N at 6 m
11. A uniform beam is balanced on a central pivot. A downward force of 49 N acts 4 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
Left: 49 N at 4 m · Right: ? N at 7 m
12. A uniform beam is balanced on a central pivot. A downward force of 9 N acts 9 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
Left: 9 N at 9 m · Right: ? N at 3 m

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Principle of moments & equilibrium

Answers and reasoning. Review before teaching.

1. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 9 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
18 N
By the principle of moments, anticlockwise moment = clockwise moment: 6 N × 9 m = 54 N·m, so F₂ = 54 ÷ 3 = 18 N.
2. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 4 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
12 N
By the principle of moments, anticlockwise moment = clockwise moment: 6 N × 4 m = 24 N·m, so F₂ = 24 ÷ 2 = 12 N.
3. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 9 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
108 N
By the principle of moments, anticlockwise moment = clockwise moment: 24 N × 9 m = 216 N·m, so F₂ = 216 ÷ 2 = 108 N.
4. A uniform beam is balanced on a central pivot. A downward force of 50 N acts 9 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
90 N
By the principle of moments, anticlockwise moment = clockwise moment: 50 N × 9 m = 450 N·m, so F₂ = 450 ÷ 5 = 90 N.
5. A uniform beam is balanced on a central pivot. A downward force of 12 N acts 2 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
12 N
By the principle of moments, anticlockwise moment = clockwise moment: 12 N × 2 m = 24 N·m, so F₂ = 24 ÷ 2 = 12 N.
6. A uniform beam is balanced on a central pivot. A downward force of 6 N acts 2 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
4 N
By the principle of moments, anticlockwise moment = clockwise moment: 6 N × 2 m = 12 N·m, so F₂ = 12 ÷ 3 = 4 N.
7. A uniform beam is balanced on a central pivot. A downward force of 49 N acts 7 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
49 N
By the principle of moments, anticlockwise moment = clockwise moment: 49 N × 7 m = 343 N·m, so F₂ = 343 ÷ 7 = 49 N.
8. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 1 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
6 N
By the principle of moments, anticlockwise moment = clockwise moment: 24 N × 1 m = 24 N·m, so F₂ = 24 ÷ 4 = 6 N.
9. A uniform beam is balanced on a central pivot. A downward force of 50 N acts 1 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
10 N
By the principle of moments, anticlockwise moment = clockwise moment: 50 N × 1 m = 50 N·m, so F₂ = 50 ÷ 5 = 10 N.
10. A uniform beam is balanced on a central pivot. A downward force of 30 N acts 8 m to the left of the pivot. What downward force is needed 6 m to the right of the pivot for equilibrium?
40 N
By the principle of moments, anticlockwise moment = clockwise moment: 30 N × 8 m = 240 N·m, so F₂ = 240 ÷ 6 = 40 N.
11. A uniform beam is balanced on a central pivot. A downward force of 49 N acts 4 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
28 N
By the principle of moments, anticlockwise moment = clockwise moment: 49 N × 4 m = 196 N·m, so F₂ = 196 ÷ 7 = 28 N.
12. A uniform beam is balanced on a central pivot. A downward force of 9 N acts 9 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
27 N
By the principle of moments, anticlockwise moment = clockwise moment: 9 N × 9 m = 81 N·m, so F₂ = 81 ÷ 3 = 27 N.

12 questions · Seed 42 · Age guidance, not curriculum certification