Evaluate the least pull, through the center of wheel:

A uniform wheel having 600 mm diameter, weighing 5KN rests against rigid rectangular block of 150mm height as shown in the figure a. Find the least pull, through the center of wheel, required just to turn wheel over the corner A of the block. Also find reaction of the block. Consider the entire surface to be smooth.

Sol.: Let P = least pull required to turn the wheel

Least pull should be applied normal to AO. F.B.D of wheel is shown in the figure b, from the fig., sinθ = 150/300, = 30º

AB = {(300)² - (150)²}^1/2  = 260 mm

Now taking moment about point A, taking body is in equilibrium

P X 300 -5 X 260 = 0

P = 4.33 KN                                                            .......ANS

Calculation the reaction of block

Let R = Reaction of block

As the body is in equilibrium, by resolving all the force in horizontal direction and then equate to zero,

R cos 30º - P sin 30º = 0

R = 2.5KN                                                                                .......ANS