Engineering & Physics CalcyZone Calculator
Work Calculator (W = Fd cosθ)
Calculate mechanical work from force, displacement and the angle between them.
Work done
433.0127 J
Force component along motion
43.3013 N
Step-by-step working
- W = F d cosθ = 50 × 10 × cos(30°)
- = 433.0127 J
Mathematical Formula
W = F d cos θ (joules).
Overview & Explanation
Only the force component along the motion does work.
How It Works
- Resolve force along motion.
- Multiply by displacement.
Practical Applications
- Pulling a sled.
- Lifting loads.
Example 1: 50 N at 30° over 10 m
Pulling a cart.
1
Inputs
Force (N): 50 · Displacement (m): 10 · Angle between force and motion (°): 30
= entered
2
Step 1
W = F d cosθ = 50 × 10 × cos(30°)
3
Step 2
= 433.0127 J
4
Work done
Result
= 433.0127 J
Example 2: 200 N straight for 3 m
Pushing a box.
1
Inputs
Force (N): 200 · Displacement (m): 3 · Angle between force and motion (°): 0
= entered
2
Step 1
W = F d cosθ = 200 × 3 × cos(0°)
3
Step 2
= 600 J
4
Work done
Result
= 600 J
Frequently Asked Questions
Can work be negative?
Yes, when the angle is over 90° (e.g. friction).
Work at 90°?
Zero — a perpendicular force does no work.
Joule?
1 J = 1 N·m.
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