I cannot figure out Part A. Please help. Thank you. Exercise 10.14 A stone is su

Question

I cannot figure out Part A. Please help. Thank you.

Exercise 10.14 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 (see the figure (Figure 1) ). The pulley is a uniform disk with mass 11.0 kg and radius 45.0 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. Part A Find the mass of the stone. Take the free fall acceleration to be 9.80 m/s2. Part B Find the tension in the wire. Take the free fall acceleration to be 9.80 m/s2.

Explanation / Answer

here ,

mass of the pulley, mp = 11 kg

radius of the pulley , rp = 0.45 m

distance , d = 12.8 m

time taken , t = 3.50 s

using second equation of motion

d = 0.5 * a*t^2

12.8 = 0.5 * a * 3.50^2

a = 2.1 m/s^2

Now, for the pulley - system ,

using second law of motion and effective mass

a = total force /(total effective mass)

a = m*g/( m + Ipulley/rp^2)

a = m*g/( m + 0.5 mp*rp^2/rp^2)

2.1 = m * 9.8 /( m + 0.5 * 11)

solving for m

m = 1.5 Kg

the mass of block is 1.5 Kg

part B)
let the tension in the string is T

mg - T = ma

1.5 * 9.8 - T = 1.5 * 2.1

T = 11.5 N

the tension in the wire is 11.5 N

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