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Question

What minimum force is required to move it up the incline with constant speed?

238269_b6e70ca7c64345bb8062dfb80da655fe.png

A
23mg
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B
mg2
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C
7mg6
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D
5mg6
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Solution

The correct option is D 5mg6
There will be three equations.
1) Initially at rest: μsmgcos30mgsin302μktan30μk123
2) Start moving when F applied: F+mgsin30=μsmgcos30F=mg(3μk+0.5)
3) Block is sliding with constant speed: F=mgsin30μkmgcos30F=mg2(13μk)
From (2) & (3): mg2(13μk)=mg(3μk+0.5)2=33μkμk=233

Therefore the minimum value of force required to move it up the incline with constant speed:
F=mg2(1+3233)=5mg6.


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