Question

Two blocks of mass 2 kg and 5 kg are connected by an ideal string passing over a pulley. The block of mass 2 kg is free to slide on a surface inclined at an angle of 30° with the horizontal whereas 5 kg block hangs freely. Find the acceleration of the system and the tension in the string.

Answer 1

Let a be the acceleration of the system and T be the Tension in the string. Equations of motions for 5 kg and 2 kg blocks are 

5g – T = 5a 

T – 2g sin θ – f = 2a 

where f = force of limiting friction 

= µR = µ mg cos θ = 0.3 x 2 g x cos 30° 

Solving (1) & (2) a = 4.87 m/s²