Chapter 8, Problem 93AP

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# An object of mass m1 = 4.00 kg is connected by a light cord to an object of mass m2 = 3.00 kg on a frictionless surface (Fig. P8.93). The pulley- rotates about a friction-less axle and has a moment of inertia of 0.500 kg · m2 and a radius of 0.300 m. Assuming that the cord does not slip on the pulley, find (a) the acceleration of the two masses and (b) the tensions T1 and T2.Figure P8.93

(a)

To determine
The acceleration of the two masses.

Explanation
The tension in the card due to acceleration of masses (m1,â€‰m2) are âˆ‘Fy=mayâ‡’T1âˆ’mg=m1(âˆ’a)â‡’T1=m1(gâˆ’a) and âˆ‘Fx=maxâ‡’T2=m2a .

The resultant torque of the pulley is âˆ‘Ï„=IÎ±â‡’T2râˆ’T1r=I(âˆ’a/r)â‡’T1âˆ’T2=a/r2 , by solving these three expressions we can calculate the acceleration of the given masses such that a=m1g/[(I/r)2+m1+m2] .

Given info: The masses of the objects are 4.00â€‰kg and 3.00â€‰kg , moment of inertia of the pulley is 0.500â€‰kgâ‹…m2 , radius of the pulley is 0.300â€‰m , and acceleration due to gravity is 9.80â€‰m/s2

(b)

To determine
The tensions T1 and T2 .

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