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What is the time required for a block to...

What is the time required for a block to slide down from the top to the bottom ofan inclined plane 6.4 m long if the inclination of the plane with the horizonta l is 30° and the coefficient of friction= 0.2?

A

2s

B

1.5s

C

3s

D

2.5s

Text Solution

Verified by Experts

The correct Answer is:
A
The downward component of force mg `sintheta` is opposed by the frictional force `F=muR=mumgcostheta`
`:.` Resultant downward force=mg`(sintheta-mucostheta)`
`:." "a=F/m=g(sintheta-mucostheta)`
But(`sintheta-musintheta)=sin30^(@)-mucos30^(@)`
`=[0.5-2/(10)xx(1.732)/(2)]`
=0.3268
When the block slides from the top to the bottom of the inclined plane,
`s=1/2at^2`
`:." "6.4=1/2g(sintheta-mucostheta)t^2`
`:." "6.4=1/2xx9.8xx0.3268xxt^2=1.6t^2`
`:." "t^2=(6.4)/(1.6)=4`
`:." "t=2s`
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