posted by Casey .
An object slides without friction in a bowl shaped like a hemisphere. It is released from rest at one edge of the bowl, slides up the other side before stopping right on the edge of the bowl. During which part of this process is the power being delivered by the gravitational force at is greatest? Not that we want the greatest positive power.
A. At the beginning
B. When the object is at the bottom of the bowl.
C. At the end
D. Sometime between the start and when the object reaches the bottom of the bowl.
E. Sometime between when the object reaches the bottom of the bowl and the end.
I am really not sure about this problem.. My guess is D.
Power delivered by gravity is the product of speed and the gravity (weight) component along the side of the bowl.
Let A be the angle to the object, measured from the center of the hemisphere.
Speed = sqrt(2gRsinA)
Weight component along direction of motion:
M g cos A
Power = M g cosA*sqrt(2 g R sin A)
Power is zero at A = 0 and 90 degrees, and is a maximum somewhere in between. To be positive, the answer must be D.
Thank you for such a wonderful explanation