HW3-solutions - tirotto (ct24472) HW3 mackie (10612) 1 This...

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Unformatted text preview: tirotto (ct24472) HW3 mackie (10612) 1 This print-out should have 25 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A loaded truck can accelerate at 4 . 1 m / s 2 . It loses its load so that it is only 0 . 8 as massive. By what factor must the acceleration change for the same driving force? Correct answer: 1 . 25. Explanation: F net = ma Since the mass changes by a factor of n , and the force does not change, multiply the right side by a clever form of 1 = n 1 n : F net = ma = ( nm ) 1 n a and the acceleration must change by a factor of 1 n . 002 10.0 points A 1552 . 5 kg car is traveling at 22 m / s when the driver takes his foot off the gas pedal. It takes 5 . 4 s for the car to slow down to 20 m / s. How large is the net force slowing the car? Correct answer: 575 N. Explanation: The acceleration of the car is given by a = v- v t = 20 m / s- 22 m / s 5 . 4 s =- . 37037 m / s 2 . Applying Newtons second law yields the force slowing the car: F = | ma | = (1552 . 5 kg)(- . 37037 m / s 2 ) = 575 N . 003 10.0 points Joe pushes down the length of the handle of a 12 . 7 kg lawn spreader. The handle makes an angle of 47 . 8 with the horizontal. Joe wishes to accelerate the spreader from rest to 1 . 31 m / s in 1 . 3 s. What force must Joe apply to the handle? Correct answer: 19 . 0521 N. Explanation: The horizontal component of the force is F h = F cos . Let v be the final velocity of the spreader. According to Newtons second law, F h = ma h so F cos = m v h t F = m v h t cos = mv t cos = (12 . 7 kg) (1 . 31 m / s) (1 . 3 s) cos 47 . 8 = 19 . 0521 N keywords: 004 (part 1 of 2) 10.0 points A 1 . 4 kg mass undergoes an acceleration given by a = a x + a y , where a x = 1 . 7 m / s 2 and a y = 3 . 6 m / s 2 . Find the magnitude of the resultant force. Correct answer: 5 . 57369 N. Explanation: The magnitude of the acceleration is a mag = a 2 x + a 2 y = (1 . 7 m / s 2 ) 2 + (3 . 6 m / s 2 ) 2 = 3 . 98121 m / s 2 . tirotto (ct24472) HW3 mackie (10612) 2 This gives the resultant force as F mag = ma mag = (1 . 4 kg) (3 . 98121 m / s 2 ) = 5 . 57369 N . 005 (part 2 of 2) 10.0 points Find the direction of the resultant force. Express your answer as the counterclock- wise angle from the positive x-axis to the resultant force. Correct answer: 64 . 7223 . Explanation: The direction of the resultant force is the same as the direction of the acceleration. To find this, take the dot product of a and the unit vector along the x-axis a = a x This dot (scalar) product also satisfies the following a = a cos( u ) Here cos u is the angle between the x-axis and the acceleration vector. Since = 1 and a = a mag is known, this can be solved for u ....
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HW3-solutions - tirotto (ct24472) HW3 mackie (10612) 1 This...

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