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Solved: CP A small rock with mass 0.20 kg is released from
Chapter 7, Problem 9E(choose chapter or problem)
CP A small rock with mass 0.20 kg is released from rest at point A, which is at the top edge of a large, hemispherical bowl with radius R = 0.50m (Fig. E7.9). 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 point A to point B at the bottom of the bowl has magnitude 0.22 J. (a) Between points A and B, how much work is done on the rock by (i) the normal force and (ii) 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?
Equation Transcription:
Text Transcription:
0.20 kg
Questions & Answers
QUESTION:
CP A small rock with mass 0.20 kg is released from rest at point A, which is at the top edge of a large, hemispherical bowl with radius R = 0.50m (Fig. E7.9). 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 point A to point B at the bottom of the bowl has magnitude 0.22 J. (a) Between points A and B, how much work is done on the rock by (i) the normal force and (ii) 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?
Equation Transcription:
Text Transcription:
0.20 kg
ANSWER:Solution 9E
Introduction
The stone is sliding along the bowl. We have to calculate the total work done by gravity and normal force. We have to also calculate the speed of the rock at the bottom of the bowl. We have to also discuss which force remains constant during the motion.
Step 1
(a)
(i)
The normal force always act perpendicular to the surface, and the rock is sliding along the bowl. Hence the force and displacement is always perpendicular to each other hence the work done by normal force is zero.
(ii)
The work done by the gravity is the change in the potential energy of the rock. Initial potential energy of the stone was
The final potential energy of the rock is
So the change in potential energy is
This potential energy will be converted to work, hence the work done is