Question

a block of mass M is placed on a rough inclined plane which makes an angle of theta with the horizontal a force f is exerted on the block upward along the surface of a line plane which causes the block to accelerate in the direction of force

1) draw a diagram showing all the relevant forces acting on the block

2) taking u as the relevant coefficient of the friction obtain expression for the acceleration of the block ​

Answer 1

1. Diagram is attached in the photo.

2. The various forces are:

• Applied force = F

• Force due to component of gravity = $Mg\sin(\theta)$

• Friction = $\mu N$

Now, net force will be :

$\rm \: F_{net} = F - \{Mg \sin( \theta) + f \}$

$\rm \implies\: F_{net} = F - \{Mg \sin( \theta) + \mu N\}$

$\rm \implies\: F_{net} = F - \{Mg \sin( \theta) + \mu Mg \cos( \theta) \}$

$\rm \implies\: F_{net} = F - Mg \{ \sin( \theta) + \mu \cos( \theta) \}$

$\rm \implies\: Ma_{net} = F - Mg \{ \sin( \theta) + \mu \cos( \theta) \}$

$\rm \implies\: a_{net} = \dfrac{ F - Mg \{ \sin( \theta) + \mu \cos( \theta) \}}{M}$

So, final answer is:

$\boxed{\bold{\: a_{net} = \dfrac{ F - Mg \{ \sin( \theta) + \mu \cos( \theta) \}}{M}}}$