A skier weighing 600 N goes over a frictionless circular hill of radius R=20 m (Fig. 8-62). As

step 1 So here we're going to use equation 817 or simply apply the law of conservation of energy. So we

A skier weighing 600 N goes over a frictionless circular...

A skier weighing $600 \mathrm{~N}$ goes over a frictionless circular hill of radius $R=20 \mathrm{~m}$ (Fig. 8-62). Assume that the effects of air resistance on the skier are negligible. As she comes up the hill, her speed is $8.0 \mathrm{~m} / \mathrm{s}$ at point $B$, at angle $\theta=20^{\circ}$. (a) What is her speed at the hilltop (point $A$ ) if she coasts without using her poles? (b) What minimum speed can she have at $B$ and still coast to the hilltop? (c) Do the answers to these two questions increase, decrease, or remain the same if the skier weighs $700 \mathrm{~N}$ instead of $600 \mathrm{~N} ?$

Key Concepts

Gravitational Potential Energy

This is the energy associated with the position of an object in a gravitational field and is given by the product of mass, gravitational acceleration, and height. In the context of the problem, as the skier ascends the hill, a portion of her kinetic energy is transformed into gravitational potential energy.

Conservation of Mechanical Energy

This principle states that when non-conservative forces (like friction or air resistance) are negligible, the sum of kinetic and potential energy remains constant throughout the motion. It allows us to relate the skier's speed at different points on the hill by equating the initial kinetic plus potential energy to the final kinetic plus potential energy.

Circular Motion and Centripetal Force

When an object moves along a circular path, it experiences a centripetal force that keeps it moving in that curve. Determining the conditions under which the skier remains in contact with the hill involves ensuring that the gravitational and normal forces provide the necessary centripetal acceleration.

Mass Independence in Energy and Circular Motion Problems

In many problems involving gravitational potential energy and circular motion, the mass of the object often cancels out when solving for speeds or forces, meaning that the dynamics of the motion, such as energy conservation and the required centripetal force, are independent of the object's mass.

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