On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a rough patch that reduces her speed to 1.65 m/s due to a friction force that is 25% of her weight. Use the work–energy theorem to find the length of this rough patch.

Solution 89P Step 1 of 1: According to work energy theorem, work done = change in kinetic energy W total= (K.E) 2(K.E) 1 (K.E) 1 m v1 2 2 0 1 2 (K.E) 2 m v2 2 = m(0.55 v ) 2 2 0 1 = 0.3025 ( m2 ) 2 0 The work energy relation gives (0.25 mg)s = 0.3025 ( mv ) 2 2 0 0.3025 ( mv ) s = 2 0 (0.25 mg The mass divides out, and solving gives , s=1.3 m