In a physics lab experiment, a 6kg box is pushed across a flat table by a horizontal force (F). (i) If the box is moving at a constant speed of 0.30m/s and the coefficient of kinetic friction is 0.12, What is the magnitude of F? (ii) If the box is speeding up with a constant acceleration of 0.18m/s2, what will be the magnitude of F?

Given,

Mass of box (m)=6kg
(i) Speed of box (u)=0.35m/s
Coefficient of kinetic friction (μk)=0.12
Frictional Force (F)=?
We have,

μk=FkR     ⇒   Fk=μkR=μkm.g
Now,
Fu=F+Fk                                       [∵ for Uniform Motion, a=0]
Fu=m.a+Fk=μkm.g=0.12610=7.2N

(ii) When the box moves with acceleration 0.18m/s2. Then
Fu=m.a+mkm/g=60.18+0.12610=8.28N

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