Acceleration Of Block Against Friction - Practice Questions & MCQ

• Case 1:- Acceleration of a block on a horizontal surface

• When the body is moving under the application of force P, then kinetic friction opposes its motion.

              Let a is the net acceleration of the body.

From the figure,

$
\begin{aligned}
& \mathrm{P}-\mathrm{f}_{\mathrm{k}}=\mathrm{ma} \\
& a=\frac{P-f_k}{m}
\end{aligned}
$
 

• Case 2:- Acceleration of a block sliding down over a rough inclined plane

• When the angle of the inclined plane is more than the angle of repose, the body placed on the inclined plane slides down with an acceleration a.

From the figure,

$
\begin{aligned}
& \mathrm{ma}=\mathrm{mg} \sin \theta-\mathrm{f}_{\mathrm{k}} \\
& \mathrm{ma}=\mathrm{mg} \sin \theta-\mu \mathrm{R} \\
& \mathrm{ma}=\mathrm{mg} \sin \theta-\mu \mathrm{mg} \cos \theta \\
& \mathrm{a}=\mathrm{g}[\sin \theta-\mu \cos \theta]
\end{aligned}
$

For $\mu=0 \quad \therefore \quad \mathrm{a}=\mathrm{g} \sin \theta$

• Case 3:- Retardation of a block sliding up over a rough inclined plane

• When the angle of the inclined plane is less than the angle of repose, then for the upward motion (with some initial velocity)

              $\begin{aligned} & \mathrm{ma}=\mathrm{mg} \sin \theta+\mathrm{f}_{\mathrm{k}} \\ & \mathrm{ma}=\mathrm{mg} \sin \theta+\mu \mathrm{mg} \cos \theta \\ & \mathrm{ma}=\mathrm{g}[\sin \theta+\mu \cos \theta] \\ & \mathrm{a}=\mathrm{g}[\sin \theta+\mu \cos \theta] \\ & \text { For } \mu=0 \\ & \mathrm{a}=\mathrm{g} \sin \theta\end{aligned}$