A string is wrapped around a uniform solid cylinder of radius 4.60 cm, as shown in the figure. The cylinder can rotate...
A string is wrapped around a uniform solid cylinder of radius
4.60 cm, as shown in the figure. The cylinder can rotate freely
about its axis. The loose end of the string is attached to a block.
The block has mass 19.6 kg, and the cylinder has mass 12.3
kg.
a) Find the magnitude α of the angular acceleration of the cylinder
as the block descends.
b)What is the acceleration of the block?
c)What is the tension in the string?
Homework Answers
Applying newton's 2nd law of motion on the block,
a = mg-T
19.6*a = 192.08 - T ------------- (1)
Applying torque on wheel, τ = Iα
TR = 1/2MR^2*a/R
∴ T = 1/2*12.3*a
T = 6.15*a ------------ (2)
substituting equation (2) in (1),
a = 7.459 m/s^2 and T = 45.875 N
the acceleration of the block is 7.459 m/s^2 and the tension in the string is 45.875 N.
(a) the angular acceleration of the cylender , α = a/R = 7.459/4.60*10^-2 m
∴ α = 162.15 rad/s
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