The rear side of a truck …
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The rear side of a truck is open and a box of 40 kg mass is placed 5m away from the open end. The coefficient of friction between the box and surface below it is 0.15 on a straight road the truck starts from rest and accelerates with 2m/sec. At what distance from the starting point does the box fall off the truck
Posted by Zarsha Arsal 8 years, 2 months ago
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Naveen Sharma 8 years, 2 months ago
Mass of box,m=40 kg
Distance from open end,s=5 m
Coefficient of friction, {tex}\mu{/tex}= 0.15
Acceleration of truck,a=2 ms-2
Value of frictional force,f={tex}\mu mg{/tex} = {tex}0.15 \times 40 \times 10 = 60 N {/tex}
Working in frame of truck,
Pseudo force on block F=ma=(40)(2)=80 N
Acceleration of block,a= {tex}{F-f\over m} ={80-60\over 40}=0.5 \ ms^{-2}{/tex}
Let the time taken be t.
So,
{tex}5 = 0\times t + {1\over 2}\times a\times t^2 \\ => 5 = {1\over 2}\times 0.5\times t^2 \\ => t^2 = 20 \\ => t =\sqrt {20}{/tex}
Distance travlled by truck x = {tex}{1\over2 }\times a \times t^2 {/tex}
{tex}= {1\over 2} \times 2\times (\sqrt {20})^2 = 20 \ m {/tex}
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