Question

three masses are connected by a light string that passes over a frictionless pulley as shown. (a) what is there acceleration of the system? (b) what are the tensions in the string?​

Answer 1

The mass on the left has a downslope weight of  

W1 = 3.5kg * 9.8m/s² * sin35º = 19.7 N  

The mass on the right has a downslope weight of  

W2 = 8kg * 9.8m/s² * sin35º = 45.0 N  

The net is 25.3 N pulling downslope to the right.  

(a) Therefore we need 25.3 N of friction force.  

Ff = 25.3 N = µ(m1 + m2)gcosΘ = µ * 11.5kg * 9.8m/s² * cos35º  

25.3N = µ * 92.3 N  

µ = 0.274  

(b) total mass is 11.5 kg, and the net force is 25.3 N, so  

acceleration a = F / m = 25.3N / 11.5kg = 2.2 m/s²  

tension T = 8kg * (9.8sin35 - 2.2)m/s² = 27 N  

Check: T = 3.5kg * (9.8sin35 + 2.2)m/s² = 27 N √

hope this helps.   :)