A small rock with mass 0.23 kg is released from rest at point A, which is at the

Question

A small rock with mass 0.23 kg is released from rest at point A, which is at the top edge of a large hemispherical bowl with radius R = 0.46 m (see figure). Assume that the size of the rock is small compared to 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 points to point B at the bottom of the bowl has magnitude 0.18 J. Between points A and B, how much work is done on the rock by the following the normal force J gravity J What is the speed of the rock as it reaches point B? m/s Of the three forces acting on the rock as it slides down the bowl, which (if any) are constant? (Select all that apply.) gravity normal force friction force Which are not constant? (Select all that apply.) gravity normal force friction force Explain. Just as the rock reaches point B, what is the normal force on it due to the bottom of the bowl? N

Explanation / Answer

a )

work done by gravity is W = m g R

W = 0.23 X 9.8 X 0.46

W = 1.036 J

b )

1/2 m v2 = 1.036 - 0.18

0.5 X 0.23 x v2 = 0.856

v = 2.728 m/sec

c )

the gravity is constant

but normal and friction force is not constant.

d )

F= m g + m v2 / R

F = 0.23 X 9.8 + 0.23 X 2.7282 / 0.46

F = 2.254 + 3.72

F = 5.974 N

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