Question

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

Please explain thoroughly, with pictures. Thx!

Answer 1

Given data

mass = 300 g = 0.3 kg

distance , d = 54 cm = 0.54 m

time, t = 3 sec

b)

using d = ut + 0.5 at^2
0.54 = 0 + 0.5* a * 3^2

0.54 = 4.5* a
a = 0.12 m/s²

on mass :

mg - T = ma

0.3g - T = 0.3a
T   = 0.3 ( g - a)

     = 0.3 ( 9.8 - 0.12)

    = 2.904 N

c) on pulley :
torque ( rXF) = I x α

and α = a/r

I = 0.5mr^2

So
T*r = ( 0.5*mr^2 ) * a/r
T = 0.5*m*a
2.904 = m (0.5*0.12)
m = 48.4 kg