Question

Two blocks with masses M1 and M2 are connected by a massless string that passes over a massless pulley as shown. M1 has a mass of 2.25 kg and is on an incline of θ1=42.5 with coefficient of kinetic friction μ1=0.205. M2 has a mass of 7.25 kg and is on an incline of θ2=31.5 with coefficient of kinetic friction μ2=0.105. The two‑block system is in motion with the block of mass M2 sliding down the ramp.

Find the magnitude a2 of the acceleration of M2 down the incline.

Answer 1

This is the diagram which I made as per the question description

m1 is moving up and m2 is moving down

for m1, we have

T - m1gsin 42.5 - um1gcos45 = m1a

put in the values,

T - 2.25 * 9.8 * sin 42.5 - 0.205 * 2.25 * 9.8 * cos 42.5 = 2.25 * a

T - 11.564 = 2.25a ---------- (1)

for mass m2

m2gsin31.5 - T - um2gcos31.5 = m2 * a

7.25 * 9.8 * sin 31.5 - T - 0.105 * 7.25 * 9.8 * cos 31.5 = 7.25 * a

-T + 30.7626 = 7.25a ----------- (2)

solving (1) and (2),

I got

a = 0.4948 m/s²