Question

If the coefficient of kinetic friction be $\mu_{k}$ in above question then the initial acceleration of the crate will be :

• A. $\left[\left(\frac{T}{m g}\right)\left(\cos \theta+\mu_{k} \sin \theta\right)+\mu_{k}\right] g$
• B. $\left[\left(\frac{T}{m g}\right)\left(\cos \theta+\mu_{k} \sin \theta\right)-\mu_{k}\right] g$
• C. $\left[\left(\frac{T}{m g}\right)\left(\sin \theta+\mu_{k} \cos \theta\right)-\mu_{k}\right] g$
• D. $\left[\left(\frac{T}{m g}\right)\left(\sin \theta+\mu_{k} \cos \theta\right)+\mu_{k}\right] g$

Answer 1

Answer: (B)

$F \cos \theta-\mu_{k} N=m a$
$ F \cos \theta-\mu_{k}(m g-F \sin \theta)=m a $
$\Rightarrow F \cos \theta-\mu_{k} m g+\mu_{k} F \sin \theta=m a$
$\Rightarrow F\left(\cos \theta+\mu_{k} \sin \theta\right)-\mu_{k} m g=m a $
$\Rightarrow a=\left[\left(\frac{F}{m g}\right)\left(\cos \theta+\mu_{k} \sin \theta\right)-\mu_{k}\right] g$