Question

Two masses are connected by a massless string and a frictionless pulley. The masses of the blocks are; m1=500 g and m2= 150g. The coefficiant of friction between m1 and the surface is 0.25. (a) What is the acceleration of the masses? (b) What is the tension in the string?

Answer 1

a)
m1 = 500 g = 0.5 kg
m2 = 150 g = 0.15 kg
mue_k = 0.25
Let T is the tension in the string and a is the acceleration if the blocks.

Net force acting on m1,

Fnetx = T - fk

m1*a = T - mue_k*m1*g

T = m1*a + mue_k*m1*g ----(1)

Net force acting on m2,

Fnety = m2*g - T

m2*a = m2*g - T

T = m2*g - m2*a ---(2)

from equations 1 and 2

m1*a + mue_k*m1*g = m2*g - m2*a

a*(m1 + m2) = g*(m2 - m1*mue_k)

a = g*(m2 - m1*mue_k)/(m1 - m2)

= 9.8*(0.15 - 0.5*0.25)/(0.5 + 0.15)

= 0.377 m/s^2

b) from equation 1

T = m2*g - m2*a

= 0.15*9.8 - 0.15*0.377

= 1.41 N