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Question

A variable force F is applied on a block such that Ft, at an angle θ with the horizontal as shown in figure. Given (μs>μk). Find the correct graph between frictional force and time. (where t= time)


A
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B
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C
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D
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Solution

The correct option is A
Given, Ft
Force F is increasing with time t.
From FBD:


N=mgFsinθ
f=Fcosθ
Block is initially at rest,
At t=0,f=0
Hence, graph will start from origin and increase linearly.
i.e ft

Maximum static frictional force that can act,
(fs)max=μsN
(fs)max=μs(mgFsinθ)
At time t when maximum static friction (fs)max will be equal to Fcosθ, then block will just start moving.

When block starts moving, kinetic friction will act
fk=μkNfk=μk(mgFsinθ)(1)
As, given μk<μs. Hence (fk<fs)

Here, F is increasing linearly with time.
Hence, fk will decrease linearly with time and will eventually become zero according to equation (1).
So, graph will decrease linearly, after attending the maximum value.
Hence option (a) is correct.

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