Need a step by step solution for this problem. A stone is suspended from the fre

Question

Need a step by step solution for this problem.

A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, as shown in the figure (from figure). The pulley is a uniform disk with mass 12.0 kg and radius 55.0 cm and turns on frictionless bearings. You measure that the stone travels a distance 12.6 m during a time interval of 3.30 s starting from rest. Find the mass of the stone Find the tension in the wire. In both cases, take the free fall acceleration to be 9.80 m/s

Explanation / Answer

1)
let a is the acceleration of the stone.

apply, h = 0.5*a*t^2

a = 2*h/t^2

= 2*12.6/3.3^2

= 2.31 m/s^2

angular acceleration of the pulley, alfa = a/R

= 2.31/0.55

= 4.2 rad/s^2

let T is the tension in the string.

net torque = I*alfa

T*R = I*alfa

T = I*alfa/R

= 0.5*M*R^2*alfa/R

= 0.5*M*R*alfa

= 0.5*12*0.55*4.2

= 13.86 N <<<<<<<<<<<<<<<<<<---------------Answer

2) let m is the mass of the stone.

T = m*g - m*a

==> m = T/(g-a)

= 13.86/(9.8 - 2.31)

= 1.85 kg <<<<<<<<<<<<<<<<<<---------------Answer

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