Question

A block of mass 2Kg is pushed against rough vertical wall with a force of 40N, Coefficient of static fiction being 0.5. Another horizontal force of 15N, is applied on the block in a direction parallel to the wall. Will Block Move ?
If yes, in which direction and with what minimum acceleration? If no, find the frictional force exerted by the wall on the block . G = 10 ms^-2​

Answer 1

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Answer 2

Given that,

Mass = 2 kg

Vertical force  = 40 N

Coefficient of static friction = 0.5

Horizontal force = 15 N

We need to calculate the resultant force

Using formula of resultant force

$F=\sqrt{F_{x}^2+F_{y}^2}$

Put the value into the formula

$F=\sqrt{15^2+20^2}$

$F=25\ N$

We need to calculate the direction of force

Using formula of direction

$\tan\theta=\dfrac{F_{y}}{F_{x}}$

$\theta=\tan^{-1}(\dfrac{F_{y}}{F_{x}})$

Put the value into the formula

$\theta=\tan^{-1}(\dfrac{15}{20})$

$\theta=\tan^{-1}(\dfrac{3}{4})$

$\theta=37^{\circ}$

We need to calculate the resisting force

Using formula of force

$F=\mu N$

Put the value into the formula

$F=0.5\times\times40$

$F=20\ N$

As driving force is greater than maximum resisting force,

So, the block will move and friction will be kinetic nature

$f_{r}=20\ N$

The direction of friction force will be opposite to the direction of net force.

We need to calculate the acceleration

Using formula of acceleration

$a=\dfrac{f_{net}-f_{r}}{m}$

Put the value into the formula

$a=\dfrac{25-20}{2}$

$a=\dfrac{5}{2}$

$a=2.5\ m/s^2$

Hence, The block will move  and the acceleration is 2.5 m/s².