angular acceleration of pulley with two masses.

1. The problem statement, all variables and given/known data





The system shown in the diagram contains two blocks, of masses 1.9 kg and 5.7 kg, connected by a light string over a pulley of radius 0.15 m and rotational inertia 2.8 kg m 2 . The block of mass 5.7 kg is free to slide on a horizontal frictionless surface and the pulley is free to rotate on a frictionless fixed horizontal axle passing through its center. Find the magnitude of the angular acceleration α of the pulley once the system is released from rest. The string connecting the blocks does not slip on the pulley. Enter your answer in rad/s 2 and use g = 9.8 m/s 2 .












2. Relevant equations

τ=Torque

t=tension

A=linear acceleration

a_Θ=Angular acceleration

r=radius



τ=I*a_Θ

A=r*a_Θ

F=A*m










3. The attempt at a solution

box with mass m is box 1

box with mass 3m is box 2



ok so, drawing a FBD of both boxes we get. F₁=m*g-t=m*a. t=m*g-m*a.

and F₂=3*m*a=t. Since tension and acceleration is the same throughout.

m*g-m*a=3*m*a. So we get a=g/4.



Now since we know acceleration we can use it in a equation.



τ=r*t.where t= (m*g-m*a) or (3*m*a).

rearranging the formula τ=I*a_Θ.



we substitute the variables in. we get τ/I=a_Θ. = r*(3*m*a)/I = a_Θ.

and we know all the variables there substituting them we get. 0.15*(3*1.9*2.45)/2.8 = a_Θ.



and the final answer is a_Θ= 0.748125.

but when I put it down as the answer it marks me incorrect. Could someone help me out to see where I went wrong ? thank you :)