Question

All surfaces are smooth. wedge is placed on smooth surface. rod is placed perpendicular on inclined face of wedge. find the acceleration of wedge ​

Answer 1

Given,

All surfaces are smooth. wedge is placed on smooth surface. rod is placed perpendicular on inclined face of wedge.

To find,

The acceleration of wedge.

here angle of inclination is θ.

let acceleration of rod is a₁ and acceleration of wedge is a₂.

from free body diagram of rod,

mgcosθ - N = ma₁ .......(1)

from free body diagram of wedge,

Nsinθ = 2ma₂..........(2)

from constraint relation,

a₁ = a₂sinθ ..........(3)

from equations (1), (2) and (3) we get,

mgcosθ - 2ma₂/sinθ = ma₂sinθ

⇒mgcosθ.sinθ= ma₂ [2 + sin²θ]

⇒a₂ = gsinθ.cosθ/(2 + sin²θ)

Therefore acceleration of wedge is gsinθ.cosθ/(2 + sin²θ)

Answer 2

Answer:

Explanation:

let acceleration of wedge = a

acceleration of rod = asintheta

equation for wedge

2ma = nsin theta

equation of rod

mgcostheta - n = masin theta

mgcosthetasintheta - nsintheta = masin^2 theta

mgcosthetasintheta  -2ma = masin^2 theta

mgcosthetasintheta / 2m+msin^2theta = a