Question

The acceleration of system of two bodies over the wedge as shown in figure is : ​

Answer 1

mgsin53-T=ma. -(1)

T-mgsin37=ma. -(2)

solve for a

Answer 2

The acceleration of the system of two bodies over the wedge as shown in the figure is equal to 1 ms⁻².

Given:

The angle of inclination of the inclined plane of the left block = 37°

The angle of inclination of the inclined plane of the right block = 53°

To Find:

The acceleration of the system of two bodies over the wedge.

Solution:

→ According to Newton's second law of motion, the acceleration (a) of a body is directly proportional to the Net external force (F) applied and inversely proportional to the mass of the body (m). The direction of the acceleration is the same as the direction of the external force.

          $\therefore Acceleration\:of\:body(a)=\frac{Net\:External\:Force(F)}{Mass\:of\:body(m)}$

→ Hence we can say that the Net external force (F) is equal to the product of the acceleration (a) and mass of the body (m).

          $\therefore Net\:External\:Force(F)=Mass\:of\:Body(m)\times Acceleration(a)\\\\\therefore Net\: F_{external} =m\times a$

→ The above formula is valid only if the mass of the body remains constant.

Assume: Acceleration due to gravity (g) = 10 ms⁻²

Let the acceleration of the system be 'a'.

Let the tension in the rope be 'T'.

→ The tension 'T' in the ropes will try to pull the two blocks up along the inclined plane.

→ The component of gravity will try to pull the two blocks down along the inclined plane.

→ For the left block:

  → T - mgsin37° = ma        where [sin37° = 3/5]

  $\therefore T-\frac{3}{5}(m)(10) =ma\\\\\therefore T-6m=ma\\\\\therefore T=m(a+6)-Eq.(i)$

→ For the right block:

  → mgsin53° - T = ma         where [sin53° = 4/5]

  $\therefore \frac{4}{5}(m)(10)-T =ma\\\\\therefore 8m-T=ma\\\\\therefore T=m(8-a)-Eq.(ii)$

→ Equating equations (i) and (ii):

  $\therefore m(a+6)=m(8-a)\\\\\therefore a+6=8-a\\\\\therefore 2a = 2\\\\\therefore a =1\:ms^{-2}$

Therefore the acceleration of the system of two bodies over the wedge as shown in the figure is equal to 1 ms⁻².