Answer to Question #1674 in Mechanics | Relativity for Brian

Question

A child of mass 30 kg skates down from the top of a ramp having a constant slope of 15°. The child’s speed increases from 1.5 ms−1 to 3.0 ms−1 as she reaches the bottom of the ramp. A force of kinetic friction of magnitude 50 N opposes her motion. Determine the length of the ramp. Take g = 10 ms−2.

Answer 1

The moving force is mg*sin 15 = 300 sin15 = 77.65 N, the resultative force that causes the motion downward is 77.65 - 50= 27.65 N. The
acceleration is F/m = 27.65/30 =0.92 m/s².
According equations of the motion
h = h₀ + v₀t + at²/2
v = v₀ + at, where v = 3m/s, v₀ = 1.5 m/s, h₀ = 0, a = 0.92 m/s².
t = (v-v0)/a = (3-1.5)/0.92 = 1.63 s.
Thus h = 1.5*1.63 + 0.92* 1.63²/2 = 3.67 m.