Question

On an essentially frictionless, horizontal ice rink, a skater moving at 5.0 m/s encounters a rough patch that reduces her speed by 45 % due to a friction force that is 45 % of her weight.

Part A. Use the work-energy theorem to find the length of this rough patch. Express your answer using two significant figures.

Answer 1

To find the length of the rough patch, we can use the work-energy theorem.

Step-by-step explanation:

To find the length of the rough patch, we can use the work-energy theorem. The work done by the friction force is equal to the change in kinetic energy of the skater. The initial kinetic energy is given by (1/2)mv12, where m is the mass of the skater and v1 is her initial velocity. The final kinetic energy is given by (1/2)mv22, where v2 is her final velocity. The work done by the friction force can be calculated using the formula: work = force x distance. In this case, the force is 45% of the skater's weight, which can be calculated using the formula: force = mass x acceleration due to gravity. By equating the work done by the friction force to the change in kinetic energy, we can solve for the distance traveled on the rough patch.