ScienceAges 13-15

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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Worksheet StudioPractice pack · Ages 13-15

Principle of moments & equilibrium

Take your time. Show your thinking.

1. A uniform beam is balanced on a central pivot. A downward force of 36 N acts 3 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 36 N at 3 m · Right: ? N at 4 m
2. A uniform beam is balanced on a central pivot. A downward force of 60 N acts 4 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 60 N at 4 m · Right: ? N at 5 m
3. A uniform beam is balanced on a central pivot. A downward force of 56 N acts 5 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
Left: 56 N at 5 m · Right: ? N at 7 m
4. A uniform beam is balanced on a central pivot. A downward force of 25 N acts 8 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 25 N at 8 m · Right: ? N at 5 m
5. A uniform beam is balanced on a central pivot. A downward force of 44 N acts 6 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 44 N at 6 m · Right: ? N at 4 m
6. A uniform beam is balanced on a central pivot. A downward force of 10 N acts 3 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 10 N at 3 m · Right: ? N at 5 m
7. 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 6 m to the right of the pivot for equilibrium?
Left: 12 N at 2 m · Right: ? N at 6 m
8. A uniform beam is balanced on a central pivot. A downward force of 40 N acts 4 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 40 N at 4 m · Right: ? N at 5 m
9. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 4 m to the left of the pivot. What downward force is needed 8 m to the right of the pivot for equilibrium?
Left: 24 N at 4 m · Right: ? N at 8 m
10. A uniform beam is balanced on a central pivot. A downward force of 96 N acts 7 m to the left of the pivot. What downward force is needed 8 m to the right of the pivot for equilibrium?
Left: 96 N at 7 m · Right: ? N at 8 m
11. A uniform beam is balanced on a central pivot. A downward force of 28 N acts 1 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
Left: 28 N at 1 m · Right: ? N at 7 m
12. A uniform beam is balanced on a central pivot. A downward force of 72 N acts 7 m to the left of the pivot. What downward force is needed 6 m to the right of the pivot for equilibrium?
Left: 72 N at 7 m · Right: ? N at 6 m

12 questions · Seed 43 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Principle of moments & equilibrium

Answers and reasoning. Review before teaching.

1. A uniform beam is balanced on a central pivot. A downward force of 36 N acts 3 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
27 N
By the principle of moments, anticlockwise moment = clockwise moment: 36 N × 3 m = 108 N·m, so F₂ = 108 ÷ 4 = 27 N.
2. A uniform beam is balanced on a central pivot. A downward force of 60 N acts 4 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
48 N
By the principle of moments, anticlockwise moment = clockwise moment: 60 N × 4 m = 240 N·m, so F₂ = 240 ÷ 5 = 48 N.
3. A uniform beam is balanced on a central pivot. A downward force of 56 N acts 5 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
40 N
By the principle of moments, anticlockwise moment = clockwise moment: 56 N × 5 m = 280 N·m, so F₂ = 280 ÷ 7 = 40 N.
4. A uniform beam is balanced on a central pivot. A downward force of 25 N acts 8 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
40 N
By the principle of moments, anticlockwise moment = clockwise moment: 25 N × 8 m = 200 N·m, so F₂ = 200 ÷ 5 = 40 N.
5. A uniform beam is balanced on a central pivot. A downward force of 44 N acts 6 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
66 N
By the principle of moments, anticlockwise moment = clockwise moment: 44 N × 6 m = 264 N·m, so F₂ = 264 ÷ 4 = 66 N.
6. A uniform beam is balanced on a central pivot. A downward force of 10 N acts 3 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
6 N
By the principle of moments, anticlockwise moment = clockwise moment: 10 N × 3 m = 30 N·m, so F₂ = 30 ÷ 5 = 6 N.
7. 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 6 m to the right of the pivot for equilibrium?
4 N
By the principle of moments, anticlockwise moment = clockwise moment: 12 N × 2 m = 24 N·m, so F₂ = 24 ÷ 6 = 4 N.
8. A uniform beam is balanced on a central pivot. A downward force of 40 N acts 4 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
32 N
By the principle of moments, anticlockwise moment = clockwise moment: 40 N × 4 m = 160 N·m, so F₂ = 160 ÷ 5 = 32 N.
9. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 4 m to the left of the pivot. What downward force is needed 8 m to the right of the pivot for equilibrium?
12 N
By the principle of moments, anticlockwise moment = clockwise moment: 24 N × 4 m = 96 N·m, so F₂ = 96 ÷ 8 = 12 N.
10. A uniform beam is balanced on a central pivot. A downward force of 96 N acts 7 m to the left of the pivot. What downward force is needed 8 m to the right of the pivot for equilibrium?
84 N
By the principle of moments, anticlockwise moment = clockwise moment: 96 N × 7 m = 672 N·m, so F₂ = 672 ÷ 8 = 84 N.
11. A uniform beam is balanced on a central pivot. A downward force of 28 N acts 1 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
4 N
By the principle of moments, anticlockwise moment = clockwise moment: 28 N × 1 m = 28 N·m, so F₂ = 28 ÷ 7 = 4 N.
12. A uniform beam is balanced on a central pivot. A downward force of 72 N acts 7 m to the left of the pivot. What downward force is needed 6 m to the right of the pivot for equilibrium?
84 N
By the principle of moments, anticlockwise moment = clockwise moment: 72 N × 7 m = 504 N·m, so F₂ = 504 ÷ 6 = 84 N.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Principle of moments & equilibrium

Take your time. Show your thinking.

1. A uniform beam is balanced on a central pivot. A downward force of 36 N acts 3 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 36 N at 3 m · Right: ? N at 4 m
2. A uniform beam is balanced on a central pivot. A downward force of 60 N acts 4 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 60 N at 4 m · Right: ? N at 5 m
3. A uniform beam is balanced on a central pivot. A downward force of 56 N acts 5 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
Left: 56 N at 5 m · Right: ? N at 7 m
4. A uniform beam is balanced on a central pivot. A downward force of 25 N acts 8 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 25 N at 8 m · Right: ? N at 5 m
5. A uniform beam is balanced on a central pivot. A downward force of 44 N acts 6 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 44 N at 6 m · Right: ? N at 4 m
6. A uniform beam is balanced on a central pivot. A downward force of 10 N acts 3 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 10 N at 3 m · Right: ? N at 5 m
7. 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 6 m to the right of the pivot for equilibrium?
Left: 12 N at 2 m · Right: ? N at 6 m
8. A uniform beam is balanced on a central pivot. A downward force of 40 N acts 4 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
Left: 40 N at 4 m · Right: ? N at 5 m
9. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 4 m to the left of the pivot. What downward force is needed 8 m to the right of the pivot for equilibrium?
Left: 24 N at 4 m · Right: ? N at 8 m
10. A uniform beam is balanced on a central pivot. A downward force of 96 N acts 7 m to the left of the pivot. What downward force is needed 8 m to the right of the pivot for equilibrium?
Left: 96 N at 7 m · Right: ? N at 8 m
11. A uniform beam is balanced on a central pivot. A downward force of 28 N acts 1 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
Left: 28 N at 1 m · Right: ? N at 7 m
12. A uniform beam is balanced on a central pivot. A downward force of 72 N acts 7 m to the left of the pivot. What downward force is needed 6 m to the right of the pivot for equilibrium?
Left: 72 N at 7 m · Right: ? N at 6 m

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Principle of moments & equilibrium

Answers and reasoning. Review before teaching.

1. A uniform beam is balanced on a central pivot. A downward force of 36 N acts 3 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
27 N
By the principle of moments, anticlockwise moment = clockwise moment: 36 N × 3 m = 108 N·m, so F₂ = 108 ÷ 4 = 27 N.
2. A uniform beam is balanced on a central pivot. A downward force of 60 N acts 4 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
48 N
By the principle of moments, anticlockwise moment = clockwise moment: 60 N × 4 m = 240 N·m, so F₂ = 240 ÷ 5 = 48 N.
3. A uniform beam is balanced on a central pivot. A downward force of 56 N acts 5 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
40 N
By the principle of moments, anticlockwise moment = clockwise moment: 56 N × 5 m = 280 N·m, so F₂ = 280 ÷ 7 = 40 N.
4. A uniform beam is balanced on a central pivot. A downward force of 25 N acts 8 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
40 N
By the principle of moments, anticlockwise moment = clockwise moment: 25 N × 8 m = 200 N·m, so F₂ = 200 ÷ 5 = 40 N.
5. A uniform beam is balanced on a central pivot. A downward force of 44 N acts 6 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
66 N
By the principle of moments, anticlockwise moment = clockwise moment: 44 N × 6 m = 264 N·m, so F₂ = 264 ÷ 4 = 66 N.
6. A uniform beam is balanced on a central pivot. A downward force of 10 N acts 3 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
6 N
By the principle of moments, anticlockwise moment = clockwise moment: 10 N × 3 m = 30 N·m, so F₂ = 30 ÷ 5 = 6 N.
7. 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 6 m to the right of the pivot for equilibrium?
4 N
By the principle of moments, anticlockwise moment = clockwise moment: 12 N × 2 m = 24 N·m, so F₂ = 24 ÷ 6 = 4 N.
8. A uniform beam is balanced on a central pivot. A downward force of 40 N acts 4 m to the left of the pivot. What downward force is needed 5 m to the right of the pivot for equilibrium?
32 N
By the principle of moments, anticlockwise moment = clockwise moment: 40 N × 4 m = 160 N·m, so F₂ = 160 ÷ 5 = 32 N.
9. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 4 m to the left of the pivot. What downward force is needed 8 m to the right of the pivot for equilibrium?
12 N
By the principle of moments, anticlockwise moment = clockwise moment: 24 N × 4 m = 96 N·m, so F₂ = 96 ÷ 8 = 12 N.
10. A uniform beam is balanced on a central pivot. A downward force of 96 N acts 7 m to the left of the pivot. What downward force is needed 8 m to the right of the pivot for equilibrium?
84 N
By the principle of moments, anticlockwise moment = clockwise moment: 96 N × 7 m = 672 N·m, so F₂ = 672 ÷ 8 = 84 N.
11. A uniform beam is balanced on a central pivot. A downward force of 28 N acts 1 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
4 N
By the principle of moments, anticlockwise moment = clockwise moment: 28 N × 1 m = 28 N·m, so F₂ = 28 ÷ 7 = 4 N.
12. A uniform beam is balanced on a central pivot. A downward force of 72 N acts 7 m to the left of the pivot. What downward force is needed 6 m to the right of the pivot for equilibrium?
84 N
By the principle of moments, anticlockwise moment = clockwise moment: 72 N × 7 m = 504 N·m, so F₂ = 504 ÷ 6 = 84 N.

12 questions · Seed 43 · Age guidance, not curriculum certification