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.

New variation Try interactive challenge Browse templates

Age band:Ages 10-12 Ages 13-15

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

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 12 N acts 8 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 12 N at 8 m · Right: ? N at 4 m
2. A uniform beam is balanced on a central pivot. A downward force of 30 N acts 6 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
Left: 30 N at 6 m · Right: ? N at 3 m
3. A uniform beam is balanced on a central pivot. A downward force of 20 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: 20 N at 8 m · Right: ? N at 5 m
4. A uniform beam is balanced on a central pivot. A downward force of 28 N acts 3 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 3 m · Right: ? N at 7 m
5. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 6 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 6 m · Right: ? N at 8 m
6. A uniform beam is balanced on a central pivot. A downward force of 16 N acts 5 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 16 N at 5 m · Right: ? N at 4 m
7. A uniform beam is balanced on a central pivot. A downward force of 36 N acts 7 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
Left: 36 N at 7 m · Right: ? N at 3 m
8. A uniform beam is balanced on a central pivot. A downward force of 20 N acts 7 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 20 N at 7 m · Right: ? N at 4 m
9. A uniform beam is balanced on a central pivot. A downward force of 48 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: 48 N at 2 m · Right: ? N at 6 m
10. A uniform beam is balanced on a central pivot. A downward force of 12 N acts 9 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 9 m · Right: ? N at 6 m
11. A uniform beam is balanced on a central pivot. A downward force of 40 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: 40 N at 3 m · Right: ? N at 5 m
12. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 3 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 3 m · Right: ? N at 2 m

12 questions · Seed 104729 · 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 12 N acts 8 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
24 N
By the principle of moments, anticlockwise moment = clockwise moment: 12 N × 8 m = 96 N·m, so F₂ = 96 ÷ 4 = 24 N.
2. A uniform beam is balanced on a central pivot. A downward force of 30 N acts 6 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
60 N
By the principle of moments, anticlockwise moment = clockwise moment: 30 N × 6 m = 180 N·m, so F₂ = 180 ÷ 3 = 60 N.
3. A uniform beam is balanced on a central pivot. A downward force of 20 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?
32 N
By the principle of moments, anticlockwise moment = clockwise moment: 20 N × 8 m = 160 N·m, so F₂ = 160 ÷ 5 = 32 N.
4. A uniform beam is balanced on a central pivot. A downward force of 28 N acts 3 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
12 N
By the principle of moments, anticlockwise moment = clockwise moment: 28 N × 3 m = 84 N·m, so F₂ = 84 ÷ 7 = 12 N.
5. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 6 m to the left of the pivot. What downward force is needed 8 m to the right of the pivot for equilibrium?
18 N
By the principle of moments, anticlockwise moment = clockwise moment: 24 N × 6 m = 144 N·m, so F₂ = 144 ÷ 8 = 18 N.
6. A uniform beam is balanced on a central pivot. A downward force of 16 N acts 5 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
20 N
By the principle of moments, anticlockwise moment = clockwise moment: 16 N × 5 m = 80 N·m, so F₂ = 80 ÷ 4 = 20 N.
7. A uniform beam is balanced on a central pivot. A downward force of 36 N acts 7 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
84 N
By the principle of moments, anticlockwise moment = clockwise moment: 36 N × 7 m = 252 N·m, so F₂ = 252 ÷ 3 = 84 N.
8. A uniform beam is balanced on a central pivot. A downward force of 20 N acts 7 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
35 N
By the principle of moments, anticlockwise moment = clockwise moment: 20 N × 7 m = 140 N·m, so F₂ = 140 ÷ 4 = 35 N.
9. A uniform beam is balanced on a central pivot. A downward force of 48 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?
16 N
By the principle of moments, anticlockwise moment = clockwise moment: 48 N × 2 m = 96 N·m, so F₂ = 96 ÷ 6 = 16 N.
10. A uniform beam is balanced on a central pivot. A downward force of 12 N acts 9 m to the left of the pivot. What downward force is needed 6 m to the right of the pivot for equilibrium?
18 N
By the principle of moments, anticlockwise moment = clockwise moment: 12 N × 9 m = 108 N·m, so F₂ = 108 ÷ 6 = 18 N.
11. A uniform beam is balanced on a central pivot. A downward force of 40 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?
24 N
By the principle of moments, anticlockwise moment = clockwise moment: 40 N × 3 m = 120 N·m, so F₂ = 120 ÷ 5 = 24 N.
12. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 3 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
36 N
By the principle of moments, anticlockwise moment = clockwise moment: 24 N × 3 m = 72 N·m, so F₂ = 72 ÷ 2 = 36 N.

12 questions · Seed 104729 · 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 12 N acts 8 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 12 N at 8 m · Right: ? N at 4 m
2. A uniform beam is balanced on a central pivot. A downward force of 30 N acts 6 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
Left: 30 N at 6 m · Right: ? N at 3 m
3. A uniform beam is balanced on a central pivot. A downward force of 20 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: 20 N at 8 m · Right: ? N at 5 m
4. A uniform beam is balanced on a central pivot. A downward force of 28 N acts 3 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 3 m · Right: ? N at 7 m
5. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 6 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 6 m · Right: ? N at 8 m
6. A uniform beam is balanced on a central pivot. A downward force of 16 N acts 5 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 16 N at 5 m · Right: ? N at 4 m
7. A uniform beam is balanced on a central pivot. A downward force of 36 N acts 7 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
Left: 36 N at 7 m · Right: ? N at 3 m
8. A uniform beam is balanced on a central pivot. A downward force of 20 N acts 7 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
Left: 20 N at 7 m · Right: ? N at 4 m
9. A uniform beam is balanced on a central pivot. A downward force of 48 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: 48 N at 2 m · Right: ? N at 6 m
10. A uniform beam is balanced on a central pivot. A downward force of 12 N acts 9 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 9 m · Right: ? N at 6 m
11. A uniform beam is balanced on a central pivot. A downward force of 40 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: 40 N at 3 m · Right: ? N at 5 m
12. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 3 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 3 m · Right: ? N at 2 m

12 questions · Seed 104729 · 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 12 N acts 8 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
24 N
By the principle of moments, anticlockwise moment = clockwise moment: 12 N × 8 m = 96 N·m, so F₂ = 96 ÷ 4 = 24 N.
2. A uniform beam is balanced on a central pivot. A downward force of 30 N acts 6 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
60 N
By the principle of moments, anticlockwise moment = clockwise moment: 30 N × 6 m = 180 N·m, so F₂ = 180 ÷ 3 = 60 N.
3. A uniform beam is balanced on a central pivot. A downward force of 20 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?
32 N
By the principle of moments, anticlockwise moment = clockwise moment: 20 N × 8 m = 160 N·m, so F₂ = 160 ÷ 5 = 32 N.
4. A uniform beam is balanced on a central pivot. A downward force of 28 N acts 3 m to the left of the pivot. What downward force is needed 7 m to the right of the pivot for equilibrium?
12 N
By the principle of moments, anticlockwise moment = clockwise moment: 28 N × 3 m = 84 N·m, so F₂ = 84 ÷ 7 = 12 N.
5. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 6 m to the left of the pivot. What downward force is needed 8 m to the right of the pivot for equilibrium?
18 N
By the principle of moments, anticlockwise moment = clockwise moment: 24 N × 6 m = 144 N·m, so F₂ = 144 ÷ 8 = 18 N.
6. A uniform beam is balanced on a central pivot. A downward force of 16 N acts 5 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
20 N
By the principle of moments, anticlockwise moment = clockwise moment: 16 N × 5 m = 80 N·m, so F₂ = 80 ÷ 4 = 20 N.
7. A uniform beam is balanced on a central pivot. A downward force of 36 N acts 7 m to the left of the pivot. What downward force is needed 3 m to the right of the pivot for equilibrium?
84 N
By the principle of moments, anticlockwise moment = clockwise moment: 36 N × 7 m = 252 N·m, so F₂ = 252 ÷ 3 = 84 N.
8. A uniform beam is balanced on a central pivot. A downward force of 20 N acts 7 m to the left of the pivot. What downward force is needed 4 m to the right of the pivot for equilibrium?
35 N
By the principle of moments, anticlockwise moment = clockwise moment: 20 N × 7 m = 140 N·m, so F₂ = 140 ÷ 4 = 35 N.
9. A uniform beam is balanced on a central pivot. A downward force of 48 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?
16 N
By the principle of moments, anticlockwise moment = clockwise moment: 48 N × 2 m = 96 N·m, so F₂ = 96 ÷ 6 = 16 N.
10. A uniform beam is balanced on a central pivot. A downward force of 12 N acts 9 m to the left of the pivot. What downward force is needed 6 m to the right of the pivot for equilibrium?
18 N
By the principle of moments, anticlockwise moment = clockwise moment: 12 N × 9 m = 108 N·m, so F₂ = 108 ÷ 6 = 18 N.
11. A uniform beam is balanced on a central pivot. A downward force of 40 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?
24 N
By the principle of moments, anticlockwise moment = clockwise moment: 40 N × 3 m = 120 N·m, so F₂ = 120 ÷ 5 = 24 N.
12. A uniform beam is balanced on a central pivot. A downward force of 24 N acts 3 m to the left of the pivot. What downward force is needed 2 m to the right of the pivot for equilibrium?
36 N
By the principle of moments, anticlockwise moment = clockwise moment: 24 N × 3 m = 72 N·m, so F₂ = 72 ÷ 2 = 36 N.

12 questions · Seed 104729 · Age guidance, not curriculum certification