- #1
Valerie Prowse
- 25
- 0
Homework Statement
- A light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string, as shown. When released, the mass falls a distance 54 cm in 3.0 s.
a. Draw free-body diagrams for the block and the cylinder. b. Calculate the tension in the string.
c. Calculate the mass of the cylinder
Homework Equations
τ = rF
I = 1/2mr^2
mg - Ft = ma
τ = Iα
The Attempt at a Solution
[/B]
I'm pretty sure I have figured out part a) and b) (tension in the rope = 2.9 N), but I'm not sure about part c).
I know that r needs to be canceled out at some point, because we are not given the radius of the cylinder. I am thinking it goes something like this, but I get lost somewhere in here:
F = Force of tension in the rope {and, from part a., F = m(g-a) }
M = mass of cylinder
m = 3.0 kg
α = a = 0.12 m/s^2
τ = rF = Iα
rF = 1/2Mr^2 * α
r (m[g-a]) = 1/2Mr^2 * α (this is where I get lost, I'm not sure what to do)
2rm(g-a) / r^2 * α = M
I'm not sure if this is the right thing to do... I'm not sure how I could make sure that r cancels out. Or maybe it is the wrong equation to use in general. Any help in the right direction is appreciated! :)