friction and the pully?

Question

An 8.0-kg hanging block is connected by a string over a pulley to a 6.5-kg block sliding on a flat table (Fig.P5.47). If the coefficient of sliding friction is 0.28, find the tension in the string.

no figure included (sorry)

Answer 1

Assume the pulley is mass-less and frictionless. String is frictionless

Using FBDs of each block with positive in the direction of motion and T= tension in the string, a is the acceleration of each block, which are equal because of the string and mass-less pulley.

8*9.81-T=8*a

T-6.5*9.81*0.28=6.5*a

solve for T

(8*9.81-T)/8=a

(T-6.5*9.81*0.28)/6.5=a

(8*9.81-T)/8=(T-6.5*9.81*0.28)/6.5

6.5*(8*9.81-T)=8*(T-6.5*9.81*0.28)

T=6.5*9.81*8*1.28/14.5

T=45.0 N

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