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1. A child bounces in a harness suspended from a door frame by three elastic bands.
(a) If each elastic band stretches 0.290 m while supporting a 5.75-kg child at rest, what is the force constant for each elastic band? Assume that each spring supports 1/3 of the child’s weight.
(b) What is the time for one complete bounce of this child?
(c) What is the child’s maximum velocity if the amplitude of her bounce is 0.290 m?
2. A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel and observes that drops of water fly off tangentially. She measures the heights reached by drops moving vertically (see figure below). A drop that breaks loose from the tire on one turn rises vertically 59.0 cm above the tangent point. A drop that breaks loose on the next turn rises 45.0 cm above the tangent point. The radius of the wheel is 0.365 m.
(a) Why does the first drop rise higher than the second drop?
(b) Neglecting air friction and using only the observed heights and the radius of the wheel, find the wheel’s angular acceleration (assuming it to be constant). (Indicate the direction with the sign of your answer. Take the clockwise direction to be positive.) rad/s2
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3. How much work does the electric field do in moving a proton from a point with a potential of +155V to a point where it is -60V ?
4. Drive lame theory for thick cylinder.
5. Suppose a bank branch has two tellers and their service times for each customer are exponential with parameters 0.2 and 0.25, respectively. When a customer arrives at the branch, he finds that both tellers are serving and no customers are waiting.
(a) What is the distribution of his waiting time?
(b) What is the probability that he will be served by the first teller?
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