Compute minimum value of the horizontal force, Computer Engineering

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Compute minimum value of the horizontal force:

Block A of weight 520N rest on horizontal top of block B having weight of 700N as shown in the figure given below. Block A is tied to support C by cable at 300 horizontally. The coefficient of friction is 0.4 for all the contact surfaces. Compute minimum value of the horizontal force P only to move the block B. How much is the tension in cable then. 

 

353_Compute minimum value of the horizontal force.png

Sol.: Consider First free body diagram of block A

∑H = 0

µR1 = Tcos30°

0.4R1 = 0.866T

R1 = 2.165T                                                                                                                           ...(i)

∑V = 0

W = R1 + Tsin30°

520 = 2.165T + 0.5T

520 = 2.665T

T = 195.12N                                                                                                                       ...(ii)

Putting in equation (i) we get

R1 = 422.43N                                                                                                                      ...(iii)

Consider First free body diagram of block A

∑V = 0

R2 = R1  + WB

R2 = 422.43 + 700

R2 =1122.43N                                                                                                                     ...(iv)

∑H = 0

P = µR1 + µR2

P = 0.4(422.43 + 1122.43)

P = 617.9N                                                  .......ANS


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