Question

Two blocks of mass 3.5 kg, and 8.0 kg are connected by a massless string that passes over a frictionless pulley. The inclines are frictionless. Find (a) the magnitude of acceleration of each block and (b) the tension in the string.

answer should be: (2.45m/s2 , 30.6 N) please show me how to get those answers

Answer 1

m1 = 3.5 kg

m2 = 8 kg

for mass m1

net force = m1*a

T - m1*g*sintheta = m1*a ..............(1)

for mass m2

net force = m2*a

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

adding 1 and 2

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

acceleration a = g*(m2 - m1)*sintheta/(m1+m2)

acceleration a = 9.8*(8-3.5)*sin40/(3.5+8) = 2.45 m/s <<<<<-------------answer

--------------------------------

from equation 1

T = m1*a + m1*g*sintheta

T = (3.5*2.45) + (3.5*9.8*sin40)

T = 30.6 N <<<<<-------------answer