Work Calculator

Trigonometry · Axiom Academy

Calculate work done by force along displacement. See why only the component along motion contributes! In everyday language, "work" means any effort or task. But in physics, work has a very specific meaning! Work is done when a force causes an object to move in the direction of the force. If you push a box across the floor, you're doing work. But if you push against a wall that doesn't move, you're doing zero work (in the physics sense)! The key insight: Work happens when force and motion are in the same direction. But What If Force Isn't Along the Motion? Here's where it gets interesting! What if you're pulling a suitcase at an angle? Or pushing a lawnmower downward while it moves forward? Key Discovery: Only the horizontal component of the force does work! The vertical component doesn't contribute because the suitcase doesn't move vertically. This is where trigonometry comes in! We use cosine to find the component of force along the direction of motion. The formula for work when force is at an angle is beautiful and simple: Think about it: What happens to the work when... θ = 0° (force along motion)? → cos(0°) = 1 → Maximum work! θ = 90° (force perpendicular to motion)? → cos(90°) = 0 → Zero work! θ = 180° (force opposite to motion)? → cos(180°) = -1 → Negative work! Now it's your turn! Adjust the sliders to see how force, distance, and angle affect the work done.

This is the written version of the interactive lesson above. See the full Trigonometry course.