Answer to Question #200876 in Physics for Joel Katu

Question

A small rock with mass 0.20kg is released from rest at point A, which is at the top edge of a large hermisperical bowl with radius, r = 0.50m. Assume that the size of the rock is small compared to the radius, so that the rock can be treated as a particle, and assume that the rock slides rather than roll. The work done by friction on the rock when it moves from point A to point B at the bottom of the bowl has a magnitude of 0.22J.

a). Between points A to point B, how much work is done on the rock by;

i). The normal force and ii). The gravity?

b). What is the speed of the rock as it reaches point B?

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

d). Just as the rock reaches point B, what is the normal force on it due to the bottom of the bowl?

Answer 1

a) i) Since the normal force is perpendicular to the displacement at every point of motion, then the work done by the normal force is zero.

ii)

$$W_g=0.2(9.8)(0.5)=0.98\ J$$

b)

$$K_2=0.98-0.22=0.76\ J\\0.76=0.5(0.2)v_2^2\\v_2=2.76\frac{m}{s}$$

c) Constant: gravity.

Not constant: normal force, friction force.

d)

$$N=0.2(9.8)+0.5\frac{2.76^2}{0.5}=5\ N$$