Name: WID) Recitation Recitation Time: TA: Question:The surface of a lab bench i

Question

Name: WID) Recitation Recitation Time: TA: Question:The surface of a lab bench is 5.0 m long and 0.90 m above the floor. A 2.0 kg block, starting from rest, is pulled from one end of the bench to the other by a student holding a string that has a tension of 11 N and is 60 degrees above the horizontal. For the first 2.5 meters, the bench is smooth and frictionless, and for the next 2.5 meters the bench is rough with a coefficient of kinetic friction of 0.40 Note: to receive credit for parts (c) and (d) you must use energy considerations when obtaining a solution. a) Determine the work done by the tension over the length of the bench b) Calculate the work done by friction over the length of the bench. c) What is the speed of the box after being pulled the length of the bench? d) When the block reaches the end of the bench, the student lets go of the string and the block falls to the ground. What is its speed just before it hits the ground?

Explanation / Answer

work done by temsion WT = T*L = 11*5 = 55 J

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(b)

frictional force fk = uk*m*g = 0.4*2*9.8 = 7.84 N

wok done by friction Wf = fk*x*cos180 = 7.84*2.5*cos180 = -19.6 J

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c)

from work energy relation

work done = change in KE

WT + Wf = dKE

WT + Wf = (1/2)*m*(vf^2 - vi^2)

55 - 19.6 = (1/2)*2*(vf^2-0^2)

vf = 5.95 m/s

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d)

total mechanical energy at top = total mechanical energy at the bottom

(1/2)*m*vf^2 + m*g*h = (1/2)*m*v^2

v = sqrt(vf^2 + 2*g*h)

v = sqrt(5.95^2 + (2*9.8*0.9))

v = 7.28 m/s <<<<-------------ANSWER

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