Question

A wooden block of mass M resting on a rough horizontal surface is pulled with a force T at an angle $\theta$ to the horizontal. If $\mu$ is coefficient of kinetic friction between the block and the surface, the acceleration of the block is

• A. $\frac{Tcos\theta }{M}-\mu g$
• B. $\frac{T}{M}(cos\theta -sin\theta )-\mu g$
• C. $\frac{T}{M}(cos\theta +\mu sin\theta )-\mu g$
• D. $\frac{\mu Tcos\theta }{M}-\mu g$

Answer 1

Answer: (C)

$\frac{T}{M}(cos\theta +\mu sin\theta )-\mu g$

Normal force, $N=mg-Tsin\theta$
$Tcos\theta -\mu N=ma$
From above equations:

$a=\frac{T}{M}(cos\theta +\mu sin\theta )-\mu g$