Question

A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, similar to what is shown in (Figure 1) . The pulley is a uniform disk with mass 13.0 kg and radius 39.0 cm and turns on frictionless bearings. You measure that the stone travels a distance 12.8 m during a time interval of 3.50 s starting from rest. a) Find the mass of the stone. b) Find the tension in the wire.

Answer 1

y = ut + 1/2at^2

u = 0

a = 2y/t^2

y = 12.8 m

t = 3.5s

ay = 2.09 m/s^2

sum of all force in y direction = m*ay

applied to the stone = mg - T = ma ...... (1)

sum of torque in z direction = Ialpha_z

applied on pulley = TR = Ialpha

I for pulley = MR^2/R

alpha = a/R

TR = MR^2*a/2R

T = Ma/2 ..(2)

put the value of T in eq 1

m = M*(a/g-a)/2 = 1.76 kg

part b )

by eq 2

T = Ma/2

T = 13.58 N