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Work done by gravity on incline
Intermediate
Gravity's work depends only on vertical height change.
inclineGravity's work is mg·Δh regardless of slope length: W = mg·d·sinθ = mgh. Steeper slopes just reach the same height faster.
A 5 kg block sliding down 10 m of a 30° slope: W = 5·9.8·5 = 245 J.
The normal force does no work on a fixed slope.
In more detail
On an incline, gravity does work on an object sliding down it equal to mgh, regardless of the slope's shape or length. Only the height change matters for conservative gravity.
Real-world uses
- Designing a slide so children reach the bottom at a safe speed.
- Estimating the speed at the bottom of a ramp in a physics lab.
- Ski slope designers calculate the speed of a skier at the bottom from the vertical drop, without needing the slope length.
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Frequently asked questions
Does the length of the slope matter?
Not for the work done by gravity, only the height drop.
Why is speed at the bottom the same for different slopes?
Because the height drop is the same, so the energy available is the same, if friction is ignored.
Does a longer slope with the same drop change the bottom speed?
No, if friction is negligible. Gravity's work depends only on vertical height change, so the final speed is the same.
Related topics in Work, Energy & Power
Work in rotation · Rotational kinetic energy · Rolling without slipping energy · Heat as energy transfer · Mechanical equivalent of heat · Mass–energy equivalence