Notcs Ask Your Teacher A hlock or mass mi-21 B kg ls at rest on a plana inclined

Question

Notcs Ask Your Teacher A hlock or mass mi-21 B kg ls at rest on a plana inclined at between block 1 and he inclined plana are M D 109 and Rk rone and massless pulay system to another block cf mass m2-17,1 kg, as shown In the fguna·Tha coatticiants of static and cinetic friction hat istha dsplacement of block 2 in the vertical direction after 1 89 s? Use positive um bes tor tha up ard direction and negative numbers rar t 30.0° aac e tha harlzontal. Tra hlcck ls connected Via 0.086, respectivaly. Tr the blocks are released from rest,

Explanation / Answer

Given value of us = 0.109 and uk = 0.086 are quite small, so we can assume from the get-go that "us" will be overcome, and that the block hanging from the pulley will move downward.

Again, once the system is in motion, the frictional force along the incline is -
F = uk N
= (0.086) (21.8 kg) (9.8 m/s^2)(cos 30)
= 15.91 N

Weight of hanging block = m2*g = 17.1*9.8 = 167.58 N

Therefore, the acceleration of the system = (15.91 N - 167.58 N)/(38.9 kg) = - 3.90 m/s^2

So, displacement of block m2 after 1.89 s -

y = (1/2)at^2 = 0.5*(-3.90)*(1.89)^2 = -6.96 m

The negative sign shows that the displacement is in the downward direction.

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