Question

"On an essentially frictionless, horizontal ice rink, a skater moving at 4.3 m/s encounters a rough patch that reduces her speed by 42% due to a friction force that is 24% of her weight. Use the work—energy theorem to find the length of this rough patch."

Answer 1

Using work - energy theorem,

work done by all forcec = change in KE

{ work done due to normal and weight force will be zero. }

work done due to friction = f.d = - (0.24 m g ) (d)

- 0.24 m g d = m (0.42v)^2 / 2 - m v^2 /2

- 0.24 x 9.8 x d = - 0.8236 v^2 /2

d = 0.8236 x 4.3^2 / (2 x 0.24 x 9.8) = 3.24 m