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Solved: An elaborate pulley consists of four identical
Chapter 9, Problem 18DQ(choose chapter or problem)
An elaborate pulley consists of four identical balls at the ends of spokes extending out from a rotating drum (Fig. Q9.18). A box is connected to a light thin rope wound around the rim of the drum. When it is released from rest, the box acquires a speed V after having fallen a distance d. Now the four balls are moved inward closer to the drum,and the box is again released from rest. After it has fallen a distance d,will its speed be equal to V, greater than V, or less than V? Show or explain why.
Questions & Answers
QUESTION:
An elaborate pulley consists of four identical balls at the ends of spokes extending out from a rotating drum (Fig. Q9.18). A box is connected to a light thin rope wound around the rim of the drum. When it is released from rest, the box acquires a speed V after having fallen a distance d. Now the four balls are moved inward closer to the drum,and the box is again released from rest. After it has fallen a distance d,will its speed be equal to V, greater than V, or less than V? Show or explain why.
ANSWER:
Solution 18DQ
Step 1 of 4:
This problem can be solved using the law of conservation of energy;
That is
Loss in potential energy of box = rotational KE of drum + translational Kinetic energy of box
M g h = +
Using h = d and
M g d= +