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Homework 12-solutions

Homework 12-solutions - kaplan(hmk378 Homework 12...

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kaplan (hmk378) – Homework 12 – Weathers – (17104) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A 3 kg steel ball strikes a wall with a speed of 12 . 8 m / s at an angle of 55 . 4 with the normal to the wall. It bounces off with the same speed and angle, as shown in the figure. x y 12 . 8 m / s 3 kg 12 . 8 m / s 3 kg 55 . 4 55 . 4 If the ball is in contact with the wall for 0 . 206 s, what is the magnitude of the average force exerted on the ball by the wall? Correct answer: 211 . 701 N. Explanation: Let : M = 3 kg , v = 12 . 8 m / s , and θ = 55 . 4 . The y component of the momentum is un- changed. The x component of the momentum is changed by Δ P x = 2 M v cos θ . Therefore, using impulse formula, F = Δ P Δ t = 2 M v cos θ Δ t = 2 (3 kg) (12 . 8 m / s) cos 55 . 4 0 . 206 s bardbl vector F bardbl = 211 . 701 N . Note: The direction of the force is in negative x direction, as indicated by the minus sign. 002 10.0 points A golf ball ( m = 56 . 4 g) is struck a blow that makes an angle of 51 . 6 with the horizontal. The drive lands 201 m away on a flat fairway. The acceleration of gravity is 9 . 8 m / s 2 . If the golf club and ball are in contact for 7 . 06 ms, what is the average force of impact? Neglect air resistance. Correct answer: 359 . 335 N. Explanation: Let : g = 9 . 8 m / s 2 , m = 56 . 4 g , θ = 51 . 6 , and t = 7 . 06 ms . Note that the range of the golf ball is given by L = v 2 sin 2 θ g , so the initial velocity of the ball is v 0 = radicalBigg L g sin(2 θ ) = radicalBigg (201 m) (9 . 8 m / s 2 ) sin(2 × 51 . 6 ) = 44 . 9806 m / s . The average force exerted is the change in its momentum over the time of contact F = m v 0 t = (56 . 4 g) (0 . 001 kg / g) (44 . 9806 m / s) (7 . 06 ms) (0 . 001 s / ms) = 359 . 335 N . 003 10.0 points A 3 . 66 kg particle has a velocity of v x = 1 . 62 m / s and v y = 2 . 59 m / s.
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kaplan (hmk378) – Homework 12 – Weathers – (17104) 2 Find the magnitude of its total momentum. Correct answer: 11 . 181 kg · m / s. Explanation: Let : m = 3 . 66 kg , v x = 1 . 62 m / s , and v y = 2 . 59 m / s .
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