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dynamics and inertia

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The vehicle s used to transport supplies to and from the bottom of the 25-present grade. Each par of wheels one at A and the other at B has a mass of 140 kg with a radius of gyration of 100 mm. The total mass of the vehicle s 520 g. The vehicle is released from rest with a restraining force T of 500 N n the control cable which passes around the drum and is secured at D. The wheels roll without slipping.
a) Calculate the inertia of wheel A about its centre in kg.m^2
b) Calculate the inertia of wheel C about its centre in kg.m^2
c) Determine the initial acceleration a of the vehicle in m/s^2

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Solution Preview

a)
mass of A, mA = 140 kg
Radius of gyration, kA = 150 mm == 0.15 m

inertia I = m*k^2

inertia of A,
IA = mA * kA^2 = 140*0.15^2 = 3.15 kg.m^2

b)
mass of C, mC= 40 kg
radius of gyration of C, kC = 100 mm = 0.1 m

Hence, inertia of C,
IC = mC*kC^2 = 40*0.1^2 = 0.4 kg.m^2

c)
Vehicle moving downward.
Let us assume, acceleration of the vehicle = ...

Solution Summary

A problem of rolling of a vehicle without slipping is solved.

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