hw 16 sol - Patel(pnp223 homework 16 Turner(92160 This...

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Patel (pnp223) – homework 16 – Turner – (92160) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Suppose you want to ride your mountain bike up a steep hill. Two paths lead From the base to the top, one twice as long as the other. Compared to the average Force you would exert iF you took the short path, the average Force you exert along the longer path is 1. Four times as small 2. halF as small correct 3. the same 4. three times as small 5. undetermined-it depends on the time taken Explanation: The gravitational potential energy gained is the same in both cases and is equal to the average Force exerted times the distance traveled. 002 (part 1 oF 6) 10.0 points A heavy ball swings on a string in a circular arc oF radius 1 m. Q 1 m Q P 35 The two highest points oF the ball’s trajec- tory are Q and Q ; at these points the string is ± 35 From the vertical. Point P is the lowest point oF the ball’s trajectory where the string hangs vertically down. The acceleration oF gravity is 9 . 8 m / s 2 . What is the ball’s speed at the point P ? Ne- glect air resistance and other Frictional Forces. Correct answer: 1 . 88272 m / s. Explanation: Let : g = 9 . 8 m / s 2 , m = 3 kg , = 1 m , and θ = 35 . The diagram For the velocity and accelera- tion oF the ball at point P is as Follows, x y v a The di±erence oF gravitational potential en- ergy oF the ball between point Q and point P is Δ U = U Q U P = mg ℓ (1 cos θ ). The velocity oF the ball at point Q is zero, so K P + U P = K Q + U Q K P + U P = 0 + U Q .
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hw 16 sol - Patel(pnp223 homework 16 Turner(92160 This...

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