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Unformatted text preview: reyes (mr29667) Homework 6 chelikowsky (59005) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Batman, whose mass is 78 . 8 kg, is holding on to the free end of a 15 . 8 m rope, the other end of which is fixed to a tree limb above. He is able to get the rope in motion as only Batman knows how, eventually getting it to swing enough that he can reach a ledge when the rope makes a 77 . 7 angle with the vertical. The acceleration of gravity is 9 . 8 m / s 2 . How much work was done against the force of gravity in this maneuver? Correct answer: 9602 . 12 J. Explanation: The work done is given by the expression, W = m g y . The change in height, y , is y = - cos . Thus W = mg ( - cos ) = mg (1- cos ) = (78 . 8 kg) (9 . 8 m / s 2 ) (15 . 8 m) (1- cos 77 . 7 ) = 9602 . 12 J . 002 10.0 points A force F is exerted by a broom handle on the head of the broom, which has a mass m . The handle is at an angle to the horizontal, as shown below. F What is the work done by the force on the head of the broom as it moves a distance d across a horizontal floor? 1. W = F d cos correct 2. W = F d sin 3. W = F md sin 4. W = F m cos 5. W = F m tan Explanation: By definition, the work done by a force is given by the formula W = vector F vector d = F d cos , where vector d is the displacement vector, and is the angle between vector F and vector d . Simply apply the definition, the work is W = F d cos . 003 10.0 points You drag a(n) 19 . 3 kg steamer trunk over a rough surface by a constant force of 162 N acting at an angle of 30 . 1 above the horizon- tal. You move the trunk over a distance of 7 . 99 m in a straight line, and the coefficient of kinetic friction is 0 . 186. The acceleration of gravity is 9 . 8 m / s 2 . 19 . 3 kg = 0 . 186 1 6 2 N 3 . 1 How much is the work done on the block by the net force? Correct answer: 959 . 487 J. Explanation: reyes (mr29667) Homework 6 chelikowsky (59005) 2 F mg n f k Work is W = vector F vectors , where vectors is the distance traveled. In this problem vectors = 5 x is only in the x direction. W F = vector F x vectors x = F s x cos = (162 N) (7 . 99 m) cos30 . 1 = 1119 . 83 J . To find the frictional force, F friction = N , we need to find N from vertical force balance. Note: N is in the same direction as the y component of F and opposite the force of gravity. Thus F sin + N = mg , so that N = mg- F sin . Thus the friction force is vector F friction =- N x =- ( mg- F sin ) x , and the work done by friction is W = vector F friction vectors =-| F f | | s | =- ( mg- F sin ) s x =- . 186 bracketleftBig (19 . 3 kg) (9 . 8 m / s 2 )- (162 N) sin30 . 1 bracketrightBig (7 . 99 m) =- 160 . 347 J ....
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- Fall '09