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

f_k=\mu mg,\quad a_2=-\mu g

problems.proof.analysis

Combine equations to eliminate intermediate quantities and isolate the desired result. This uses the system’s constraint or conservation law.