As part of your civil engineering summer internship, you work on a site where a

Question

As part of your civil engineering summer internship, you work on a site where a pail of sand (mass 65.0kg) hangs from a massless rope that passes over a frictionless pulley. The rope is connected to an 80.0kg container on a horizontal truss as shown in the figure Container to the right. Bag of Cement 6. The rope pulls horizontally on the container and a 50.0 kg bag of cement rest on top of the container. The coefficient of friction between the container and the truss is 0.70 for the static friction and 0.40 for kinetic friction. a) Find the friction fore on the bag of cement. b) Find the friction force on the container c) Suddenly the bag of cement is lifted from the Pai container. Using 0.50m from its rest position. energy conservation, determine the speed of the pail after it has fallen

Explanation / Answer

6. (A) on system of container and bag,

N = (80 + 50)g = 130 g

maximum frictional force, fs_max = us N

fs_max = 0.70 (130 g) = 91 g

fs_max is sufficient to prevent it from sliding.

so a = 0

T = m_pail g = 65 g

hence fs= T = 65 g = 637 N  

there is no other force on cement , f = 0 .....Ans

(B) fs = 637 N .....Ans

(c) Work done by friction + work done by gravity = change in KE

(- uk M g d) + (m g d) = ( M + m) v^2 / 2

(-0.40 x 80 x 9.8 x 0.50) + (65 x 9.8 x 0.50) = (80 + 65)v^2 / 2

v = 1.50 m/s

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