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Chapter 6: Q. 47 (page 156)

A truck with a heavy load has a total mass of 7500kg. It is climbing a 15°incline at a steady 15m/s when, unfortunately, the poorly secured load falls off! Immediately after losing the load, the truck begins to accelerate at 1.5 m/s2. What was the mass of the load? Ignore rolling friction.

Short Answer

Expert verified

Mass of the load is 2800Kg

Step by step solution

01

Step 1. Given Information 

Total load of truck m+M=7500Kg

Mass of load=M

Mass of truck=m

Incline of the shapeθ=15°

Speed of truck with loadv=15 m/s

Acceleration of truck without loada=1.5 m/s

02

Step 2. Find the mass of the Load

We need to determine the mass of the load by ignoring the fact that rolling friction is there.

Refer force identification diagram below

Truck force=T

when a load is there

localid="1647674523836" FGsinθ=T(m+M)gsinθ=T

when the load falls:

localid="1647674538677" T-FGsinθ=FnetT=Fnet+FGsinθT=ma+mgsinθ⇒(m+M)gsinθ=ma+mgsinθ7500×9.8×sin15°=m(1.5+9.8×sin15°)m=19023.24.04

localid="1647674555126" m=4712.88kg

localid="1647674569546" M=7500-mM=7500-4712.88

localid="1647674575808" M=2787Kg

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