A.3 · IB Physics
Energy on a track with friction
Release a ball from any height on a hilly track and watch gravitational potential energy turn into kinetic energy and, through friction, into thermal energy until the ball comes to rest.
mgh₀ = ½mv² + mgh + f·d
d = distance along the track, g = 9.8 m s⁻²
Position x
Height h
Speed v
Distance d
Kinetic Eₖ
Grav. potential Eₚ
Thermal Q
Total
Try this
- Set f = 0. Does the ball reach the same height on the far side? Watch the bar: Eₖ + Eₚ stays constant.
- With h₀ = 10.0 m, m = 2.00 kg and f = 5.00 J m⁻¹, predict the distance d travelled before stopping using d = mg(h₀ − h)/f, then check the readout.
- Keep f fixed and double the mass. Explain why the ball now travels further along the track.
Exam tip: work done against friction equals the force times the total distance travelled along the path, not the displacement, so a ball rolling back and forth keeps losing energy on every pass.