Question

On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a rough patch that reduces her speed by 45% due to a friction force that is 25% of her weight. Use the work‑energy theorem to find the length of this rough patch.

Answer 1

Answer: 1.25 m

Explanation:

Given

initial velocity$(v_i )=3 m/s$

Final velocity$(v_f)=0.55\times 3=1.65 m/s$

Change in kinetic Energy =work done by Friction

change in Kinetic Energy$=\frac{m}{2}\left ( v_i^2-v_f^2\right )$

work done by friction$=\mu mgL$

$\frac{m}{2}\left ( 3^2-1.65^2\right )=0.25\cdot mg\times L$

$3.135=0.25\times 9.8\times L$

L=1.25