Work along a path

A sliding object on a stationary surface

Forces and displacement

dr→GravityNormal forceFriction

Force arrows share a scale. The displacement arrow shows direction, not distance to scale.

Work done so far

From the top of the surface to the object's current position

Gravity0.00 J
Normal force0.00 J
Friction0.00 J
Net work0.00 J

The normal force is perpendicular to dr→ at every point, so it does no work. Gravity does positive work as the object descends; friction opposes the motion.

0%

About these models

All three motions use point objects and neglect air resistance. Playback moves through positions for inspection, rather than representing elapsed time. Force arrows share a scale within each motion; the displacement arrow indicates direction, not a scaled distance.

Down a curve: a 1 kg object starts from rest on a fixed quarter-circle of radius 4 m. Optional kinetic friction has coefficient 0.20; its work is integrated along the curve. At the initial instant friction shows the direction it takes once sliding starts.

Over a hill: the ball has the Chapter 17 exercise's mass 0.2 kg, initial speed 5 m/s and heights 2.5 m initially, 3.5 m at the summit, and 0 m at the bottom. The horizontal dimensions are illustrative. Friction is neglected and the ball remains on the surface.

Pendulum: a 1 kg bob on a massless 2 m string is released from rest at 55 degrees. String tension does no work. The five-point arrows show the first half of the swing; displacement reverses on the return. At the turning points the instantaneous displacement direction is not shown.