The two blocks in the figure are connected by a massless rope that passes over a pulley. The pulley is 14cm in diameter and has a mass of 2.4 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.54 Nm .
so m1 = 4.0kg
m2= 2.0 kg
M = 2.4kg
Tf (torque due to friction) = 0.54 Nm
ƩFy (for mass 1)= T2 - m1*g
m1*ay1 +m1*g= T2 so T2 = m1(ay1+g) this becomes T2= m1(ay + g)
ƩFy (for mass 2)= T1 - m2*g
m1*ay2 + m2*g = T1 so T1 = m2(ay2 + g)
but since ay1 = -ay2 = ay this becomes T1 = m2(g - ay)
Ʃτ= T2*R - T1*R - Tf
The Attempt at a Solution
Using what i put up there i get the following formula
τnet = R(T2 - T1) - Tf = R(m1(ay+g) - m2(g-ay)) - Tf .... equation 1
since τ= Iα, I= 1/2 MR^2 and since α= -ay/R
equation 1 becomes..
1/2MR^2 * (-ay)R = R(m1(ay+g) - m2(g-ay)) - Tf ..... solving for ay with the given data i found ay=-1.65 and thus using the kinematic equation i found Δt= 1.55s but this is wrong.. :( i would appreciate if anyone points out my error or mistake, thanks
EDIT: sorry about this, they are asking us to find the time it takes for mass 1 to hit the floor, starting at rest.