Final answer:
To calculate the vertical height reached by the ball when treated as a spherical shell, we can use the principle of conservation of mechanical energy. When the ball slides up the hill without rolling, kinetic friction is involved and the ball will not reach the same height as it would when rolling without slipping.
Step-by-step explanation:
To calculate the vertical height reached by the ball when treated as a spherical shell, we can use the principle of conservation of mechanical energy. The initial kinetic energy of the ball is converted into potential energy as it moves up the hill. The potential energy at the top of the hill is given by the equation: PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the vertical height. To find the height, we can use the formula: h = KE / (mg).
When the ball slides up the hill without rolling, kinetic friction is involved. This frictional force opposes the motion of the ball and converts kinetic energy into heat. Therefore, the ball will not reach the same height as it would when rolling without slipping. To find the height in this case, we need to subtract the work done by friction from the initial kinetic energy. The work done by friction can be calculated using the equation: Work = frictional force x distance, where the distance is equal to the vertical height of the hill.