Question

Two blocks with masses 4.0kg and 8.0kg are connected by a string and slide down a 30 degree inclined plane. The coefficient of kinetic friction between the 4.0kg block and the plane is 0.25: that between 8.0kg block and the plane is 0.35.

a)       Calculate the acceleration of each block

b)      Calculate the tension in the string.

Answer 1

for mass m1

Fnet = m1*a

m1*g*sintheta - T - uk1*m1*g*costheta = m1*a ............(1)

for mass m2

Fnet = m2*a

m2*g*sintheta + T - uk2*m2*g*costheta = m2*a..................(2)

from 1 and 2

(m1+m2)*g*sintheta - g*costheta*(uk1*m1 + uk2*m2) = (m1+m2)*a

acceleration a = g*sintheta - g*costheta*(uk1*m1+uk2*m2)/(m1+m2)

acceleration = 9.8*sin30 - 9.8*cos30*(0.25*4 + 0.35*8)/(4+8) = 2.21 m/s^2

(b)

from equation 1

T = m1*g*sintheta - uk1*m1*g*costheta - m1*a

T = 4*9.8*sin30 - 0.25*4*9.8*cos30 - 4*2.21

Tension T = 2.27 N