First slide

Static friction

Question

In case of pulling & pushing minimum forces required are $\fn_cm \large \frac{{w\cos \alpha }}{{\cos (\theta - \alpha )}}$ & $\large \frac{{w\cos \alpha }}{{\cos (\theta + \alpha )}}$ then accelerations are (Here α = Angle of friction and θ is the angle with horizontal at which the force is applied).

Moderate

A

a = g, a = g/ µ
B

a = 0, a = 0
C

a = g/ µ , a = µ g
D

none

Solution

When the body is on the verge of motion , it is in equilibrium . For pulling ,
$\fn_cm \large Fcos\theta=\mu[W-Fsin\theta]\; tan\alpha=\mu$
For pushing , $\large Fcos\theta=\mu[W+Fsin\theta]\;tan\alpha=\mu$
For pulling , $\large F=\frac{\mu W}{cos\theta+usin\theta}=\frac{W.tan\alpha}{cos\theta+tan\alpha.sin\theta}=\frac{Wsin\alpha}{cos(\theta-\alpha)};$
Similarly for pushing $\large F=\frac{Wsin\alpha}{cos(\theta+\alpha)}$

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