Question

Determine the force $P$ applied at ${30}^o$ to the horizontal just necessary to start a roller having radius $50cm$ over a obstruction $12cm$ high. If roller is of mass $100kg$ as shown in figure also find the magnitude and direction of $P$ when it is minimum.

Answer 1

To start the roller over the obstruction,

P should balance the anti - clockwise moment of W

about point A with an equal clockwise moment.

The maximum distance between the point A and line of action of P is AC.

Therefore, to create a given moment about A,

the force P will be minimal when it acts at right angle to AC as shown in Figure

Then the $P_{min}$ will make an angle

$\alpha ={40.54}^0$ .

$\alpha +\theta =90°;$

$\alpha$ + 49.49 = 90 °

$\alpha ={40.54}^0$

$\Sigma M_A$ = 0

$100\times 9.81\times 32.5-P_{min}\times 50=0$

$P_{min}=637.63$ N