Question

Express in terms of θ, β and W the force T necessary to hold the weight in equilibrium as shown in fig, Also derive an expression for the reaction of the plane on W. No friction is assumed between the weight and the plane.

Answer 1

Since block is put on the inclined plane, so plane give a vertical reaction on the block say ‘R’. Also resolved the force ‘T’ and ‘W’ in perpendicular and parallel to plane, now

For equilibrium of the block,

Sum of components parallel to plane 

= 0, i.e., ∑ H = 0

T cos β – W sinθ = 0 .......(i)

Or T = W sinθ/cosβ

Sum of components perpendicular to plane = 0, i.e., 

∑V = 0 R + T sinβ – W cosθ = 0 

Or R = W cosθ – T sinβ ...(ii)

Putting the value of T in equation(ii), We get

R = W{cosθ – sinθ.tanβ}

Hence reaction of the plane 

= R = W{cosθ – sinθ.tanθβ}