Question

A body of mass 2 kg slides down with an acceleration 3 metre square per second on a rough inclined plane

Answer 1

The question is incomplete. You can find complete question in below.

Question

A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of 30∘. The external force required to take the same body up the plane with the same acceleration will be : (g=10 m/s2)

Answer

First of all, we have to find the frictional force(f) of the plane.

by using Newton's second law(F = ma) for 2kg in downward direction,

                    F = ma

mg Sin (30) - f = ma

     20*(1/2) - f = 2*3

              10 - f = 6

                     f = 4 N (frictional force)

Then we can use F=ma in upward direction,

                        F = ma

F - mg Sin (30) - f = ma

     F - 20*(1/2) - 4 = 2*3

              F - 10 - 4 = 6

                        F = 20 N

Answer : External force = 20 N

Answer 2

"Case i)

$\quad f\quad =\quad \mu N$

$N\quad =\quad mg\cos { \theta}$

$N\quad =\quad \frac { 20\sqrt { 3 } }{ 2 }$

$N\quad =\quad 10\sqrt { 3 }$

$mg\sin { \theta} -f\quad =\quad ma$

$20\sin { \theta} -\mu 10\sqrt { 3 } \quad =\quad 2\times 3$

$10-\mu 10\sqrt { 3 } =\quad 6$

$1-\sqrt { 3 } \mu \quad =\quad 0\cdot 6$

By simplifying we get,

$\mu \quad =\quad \frac { 1\quad -\quad 0\cdot 6 }{ \sqrt { 3 }  } \quad =\quad 10-6\quad =\quad 4N$

Case ii)

$\quad F-\left( f+mg\sin { \theta} \right) \quad =\quad ma$

$F-(4+10)=2\times3$

$F=6+14=20N$"