The double inclined plane supports two blocks A and B, each having a weight of 10 lb. If the coefficient of kinetic friction between the blocks and the plane is 0.1, determine the acceleration of each block. (The blocks are connected to each other by a string and pulley system so their accelerations are equal, block on the left is on an incline of 60 degrees and the block on the right is on an incline of 30 degrees.)

Explanation:

Left block is on surface with higher inclination so it will go down . If T be tension

For motion of block A ,

net force = mgsin60 - (T + mg cos 60 x μ ) , μ is coefficient of friction .

ma =  mgsin60 - T -  mg cos 60 x .1

10a = 277.13  - T - 16

= 261.13 - T

T = 261.13 - 10a

For motion of block B

T - mg sin30 - mgcos30 x μ = ma

T- 160 - 27.71 = 10 a

261.13 - 10a - 160 - 27.71 = 10a

73.42 = 20a

a = 3.67 ft / s²

common acceleration = 3.67 ft / s²