Problem 1

A sled of mass

m=2.0,\,\mathrm{kg}

starts from rest on a smooth ramp of length

L=5.0,\,\mathrm{m}

30^\circ

to the horizontal. It enters a rough horizontal track with kinetic-friction coefficient

\mu=0.20

. Neglect air resistance and use

g=9.8,\,\mathrm{m/s^2}

. (a) Find acceleration and speed at the ramp bottom. (b) Find stopping distance on the horizontal track. (c) If that track is only

4.0,\,\mathrm{m}

long, does the sled stop before its edge? Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

a_1=g\sin\alpha

problems.proof.analysis

Apply the governing law for the stated model, using the sign convention in the problem. This provides the starting equation for the later parts.

problems.proof.pitfall. Do not assume the ramp-exit speed remains constant; friction slows the sled on the horizontal track.