- #1
rahularvind06
- 10
- 0
Homework Statement
A given pulley has a radius of 20 cm and moment of inertia 0.2 kgm2. The string going over it is attached to a vertical spring of spring constant 50 N/m on one end and a 1 kg mass on the other end. The system is released from rest with the spring at natural length. Find the speed of the block when it has descended 10 cm.
Homework Equations
Γ = r x F
Γnet=Iα
F=ma
The Attempt at a Solution
i let T2 be the tension in the rope pulling the spring upward and T1 be the tension pulling the mass upward.
then mg - T1 = ma ----- (1)
and T2 = kx
then for the pulley,
T1R -T2R =Iα
T1R -T2R = Ia/R
then T1 -T2 = 5a (substituting known values)
then T1 - kx = 5a ---- (2)
eliminating T1 between (1) and (2)
mg - kx - 5a = ma
substituting for m,k and x = 10 cm,
a = 5/6 m/s2
v=√2as
= 5/2√15
the correct answer, however is 0.5.
any conceptual errors or oversights in my answer? please help..