HW 02-solutions

# HW 02-solutions - cooper(mlc4285 HW 02 florin(55245 This...

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cooper (mlc4285) – HW 02 – florin – (55245) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points A small object is sliding along a level surface with negligible friction, and has mass m , and constant speed v 0 , when it collides with a brick resting on the surface. If the object recoils backward at v 0 3 , and is in contact with the brick for time Δ t , assum- ing the force is constant, what force did the brick exert on the object? Assume the object is moving along x -direction. 1.F net = parenleftbigg 2 m v 0 3 Δ t parenrightbigg ˆ x 2.F net = parenleftbigg 3 m v 0 Δ t parenrightbigg ˆ x 3.F net = vector 0 4.F net = parenleftBig m v 0 3 Δ t parenrightBig ˆ x 5.F net = parenleftBig m v 0 Δ t parenrightBig ˆ x 6.F net = parenleftbigg 3 m v 0 2 Δ t parenrightbigg ˆ x 7.F net = parenleftbigg 4 m v 0 3 Δ t parenrightbigg ˆ x correct Explanation: We need to apply the momentum principle which states Δ p = F net Δ t , and here we have Δ p = parenleftBig m v 0 3 parenrightBig ˆ x + ( m v 0 x , so F net = Δ p Δ t = parenleftBig m v 0 3 Δ t parenrightBig ˆ x parenleftBig m v 0 Δ t parenrightBig ˆ x = parenleftbigg 4 m v 0 3 Δ t parenrightbigg ˆ x . 002 10.0points A ball moves in the direction of the arrow labeled c in the following diagram. The ball is struck by a stick that briefly exerts a force on the ball in the direction of the arrow labeled e . Which arrow best describes the direction of Δ vectorp , the change in the ball’s momentum? a b c d e f g h 1. c 2. h 3. f 4. e correct 5. a 6. d 7. g 8. b Explanation: Recall the definition of impulse: Impulse = vector F net Δ t = Δ vectorp. Therefore, whatever direction the net force points in, that will be the direction of the change in the ball’s momentum. We are told that the force is in the direction of e , so that is the correct answer. 003(part1of3)10.0points In outer space a rock of mass 6 kg is acted on by a constant net force vector F net = ( 27 , 16 , 40 ) N , during a 3 s time interval. At the end of this time interval, the rock has a velocity of vectorv f = ( 114 , 94 , 112 ) m / s .

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cooper (mlc4285) – HW 02 – florin – (55245) 2 Find the initial velocity of the rock. Start by finding the x component, v i,x . Correct answer: 100 . 5 m / s. Explanation: Let’s go ahead and do the vector algebra to solve for all three components. We can derive an expression for the initial velocity from the Momentum Principle: vector F net Δ t = Δ vectorp = m Δ vectorv = mvectorv f mvectorv i vectorv i = vectorv f vector F net m Δ t = ( 114 , 94 , 112 ) m / s parenleftbigg ( 27 , 16 , 40 ) N 6 kg parenrightbigg (3 s) = ( 100 . 5 , 102 , 92 ) m / s . 004(part2of3)10.0points Find v i,y . Correct answer: 102 m / s. Explanation: See the explanation to part 1. 005(part3of3)10.0points Find v i,z ..
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