Up and Down the Hill. A 28-kg rock approaches the foot of a hill with a speed of 15 m/s. This hill slopes upward at a constant angle of 40.0 ? above the horizontal. The coefficients of static and kinetic friction between the hill and the rock are 0.75 and 0.20, respectively. (a) Use energy conservation to find the maximum height above the foot of the hill reached by the rock. (b) Will the rock remain at rest at its highest point, or will it slide back down the hill? (c) If the rock does slide back down, find its speed when it returns to the bottom of the hill.
Solution 48P Introduction We have to first calculate the height of the rock that the rock can reach by equating the initial kinetic energy with the work done by friction and the potential energy at that height. Now at the top, if the static frictional force is greater than the component of the gravity along the surface, then the wood will not slide down, otherwise it will come down. If it comes down, we have to calculate velocity at the bottom of the hill. Step 1 The following is the schematic diagram of the given problem. The initial kinetic energy of the rock was Now let us consider that the stone can climb a height of h. So the potential energy of stone at that height is Hence the frictional force on the rock is Now, if the height of the stone is h, then the distance travelled by the stone is So the work done by the frictional force is Hence the equating all the energies we have So the maximum height reached by the rock is 9.27 m. Step 2 At this height the downward force along the surface And the force due to static friction is Since the downward force along the surface due to gravity is higher than the static friction force, the rock will slide back down.