Question

Pushing force making an angle $\theta$ to the horizontal is applied on a block of weight W placed on a horizontal table. If the angle of friction is $\varphi$, the magnitude of force required to move the body is equal to:

• A. $\frac{Wcos\theta }{cos(\theta -\varphi )}$
• B. $\frac{Wsin\varphi }{cos(\theta +\varphi )}$
• C. $\frac{Wtan\varphi }{sin(\theta -\varphi )}$
• D. $\frac{Wsin\varphi }{tan(\theta -\varphi )}$

Answer 1

The correct option is B $\frac{Wsin\varphi }{cos(\theta +\varphi )}$

$N=W+F\sin \theta$

$\therefore f_{max}=\mu N=\left(\tan \varphi \right)(W+F\sin \theta )$

To move the body;

$F\cos \theta =f_{max}=\left(\tan \varphi \right)(W+F\sin \theta )$

Solving this equation we get,

$f=\frac{W\sin \varphi }{\cos (\theta +\varphi )}$