In a physics lab experiment, a $6\;kg$ box is pushed across a flat table by a horizontal force $(F)$. (i) If the box is moving at a constant speed of $0.30\;m/s$ 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 $0.18\;m/s^2$, what will be the magnitude of $F$?

Given,

Mass of box $(m) = 6\;kg$

(i) Speed of box $(u) = 0.35\;m/s$

Coefficient of kinetic friction $(\mu_k) = 0.12$

Frictional Force $(F) = \;?$

We have,

$\mu_k = $$\frac{F_k}{R}$     ⇒   $F_k = \mu_k\;R = \mu_k\;m.g$

Now,

$F_u = F + F_k$                                       [∵ for Uniform Motion, $a = 0$]

$F_u = m.a + F_k = \mu_k\;m.g = 0.12\;*\; 6\;*\;10  = 7.2\;N$

(ii) When the box moves with acceleration $0.18\;m/s^2$. Then

$F_u = m.a + m_k\;m/g = 6\;*\;0.18 + 0.12\;*\;6\;*10 = 8.28\;N$

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