Question

A small rock with mass 0.30 kg k g is released from rest at point A A , which is at the top edge of a large, hemispherical bowl with radius R R = 0.48 m m (the figure (Figure 1)). Assume that the size of the rock is small compared to R R , so that the rock can be treated as a particle, and assume that the rock slides rather than rolls. The work done by friction on the rock when it moves from point A A to point B B at the bottom of the bowl has magnitude 0.22 J J .

a. Between points AA and BB, how much work is done on the rock by the normal force?

c. What is the speed of the rock as it reaches point BB?

d.Of the three forces acting on the rock as it slides down the bowl, which (if any) are constant and which are not? Explain.

e. just as the rock reaches point BB, what is the normal force on it due to the bottom of the bowl?

Answer 1

Part A) As the normal force is perpendicular to the displacement vector, so the work done on the rock between points A and B by the normal force is zero.

Part B) Speed of the rock, using the energy conservation

Potential Energy at the Top = Kinetic energy at the Bottom + Work Done against friction.

Part D) The three forces acting on the rock are Gravitational Force, Normal Force, and Frictional Force.

As the gravitational force depends on the mass and gravitational acceleration so remains constant throughout.

The normal force depends upon the angle of contact with the surface so it does not remains constant. And we know that frictional force is proportional to the normal force, hence frictional force does not remain constant.

Part E) Normal force at the bottom is provided by the gravitational force and centripetal force so