The figure below shows two blocks of mass m1 = 250g and m2 = 400g are connected
ID: 1384696 • Letter: T
Question
The figure below shows two blocks of mass m1 = 250g and m2 = 400g are connected by a massleas cord wrapped around a uniform disk of of mass M = 740g and radius R = 11.0cm. Assume the disk rotates without friction about a horizontal axis through its center and that the cord does not slip on the disk When the blocks are released from rest find the tension in the left cord (T1), the tension in the right cord (T2), the magnitude of the angular acceleration of the disk, and the magnitude of the (linear) acceleration of the blocks.Explanation / Answer
On Block 1
m1g-T1 =m1a------------1
on Block 2
T2-m2g =m2a------------------2
On pulley
T =T1R -T2R =I*a/R------------------3
1+2
(m1-m2)g-(T1-T2) =(m1+m2)a
(m1-m2)g-I*a/R =(m1+m2)a
Moment of inertia of pulley
I=(1/2)MR2
=>(m1-m2)g-(1/2)MR2*a/R =(m1+m2)a
=>a =(m1-m2)g/(m1+m2+(1/2)M)
a =(250-400)*9.8/(250+400+(1/2)*740)
a=-1.44 m/s2 (linear acceleration)
Tension on left cord from 1
T1 =(250*10-3)(9.8-(-1.44))
T1=2.81 N
Tension on right string
T2 =(400*10-3)(9.8-1.44)
T2=3.34 N
angular acceleration
alpha =a/r =-1.44/0.11
alpha =-13.1 rad/s2