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Question

A pulling force of 100 N is acting at an angle of 300 with the horizontal on a body of mass 50 kg placed on a rough horizontal surface. Will the same force cause the body to move if it is a pushing force for the body? If not, what should be the value of the force (acting at the same angle) to cause the body to just move? Take g=10 m/s2.

A
77 N
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B
124.84 N
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C
88 N
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D
119 N
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Solution

The correct option is B 124.84 N

From the FBD, when the force is pulling the body.
Applying equations for the equilibrium of the body in horizontal and vertical direction:

For just moving condition, fmax=μsN will act on the body.

N=mgFsin300.....(i)Fcos300=μsN.....(ii)

Substituting the values, we get:
F cos30=μs(mgFsin30)
F=μsmgcos30+μssin30
100=μs×50×1032+μs×12
μs=0.192

FBD in case of pushing force (with same force at same angle with horizontal):


Following same procedure for the pushing case:

N=mg+Fsin300.....(i)Fcos300=μsN.....(ii)

Substituting (i) in (ii), we get:
F=μsmgcos30μssin30
F=500×0.1920.769=124.84 N

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