hanging object?

Question

A 9.00kg hanging object is connected, by a light, inextensible cord over a light, frictionless pulley, to a 5.00kg block that is sliding on a flat table. Taking the coefficient of kinetic friction as 0.200, find the tension in the string.

thank u

Answer 1

Take T to be the tension in the string and a as the acceleration of both blocks

A FBD of the hanging mass
9*9.81-T=9*a

and the one on the table
5*a=T-5*9.81*0.200

solve for T
a=T/5-1.962

T=(88.29+17.658)/2.8
T=37.84 N

j

Answer 2

Letting 9 = M, 5 = m, .2 = µ and 9.8 = g,

a = (Mg - T)/m = (T - µmg)/m →

T = mMg(1 + µ)/(m+M) = 37.8 N