Question

In the figure below, a block of 1.67 slides on a track with different levels, which has friction only at the highest point where the kinetic coefficient of friction is uk = 0.35. If the block has an initial speed V0 = 7.5m/s and the highest point of the track is at ℎ = 2.1 above the initial position of the block, calculate the distance where the friction force for the block is.

Answer 1

2.0 m

Step-by-step explanation:

Energy is conserved.

Initial KE = Final PE + Work done by friction

½ mv² = mgh + Fd

½ mv² = mgh + mgμd

½ v² = gh + gμd

½ v² − gh = gμd

d = (½ v² − gh) / (gμ)

d = (½ (7.5 m/s)² − (10 m/s²) (2.1 m)) / ((10 m/s²) (0.35))

d = 2.0 m