Please I need step by step solution F 518 Determine P and x

F 5-18 Determine P and x 09 m 100 mm 100 mm 100 mm 6 kN Solution P 2.00 kN x 0.333 m

Solution

The beam is balanced means the forces at A and B are such that the moments about any point are equal.

The length AB = 1.0 m from geometry since the radius of the pulley is 100 mm, A is displaced left by 100 mm from top centre, and B is directly below right top pulley centre, so distance = .9 +.1 =1m

The system of pulleys shown will have a mechanical advantage of two, hence the force trasmitted to A is 2P. You can work it out from statics or assume it. The force at B is P since the first pulley is fixed to the beam at B.

So you have a beam with load 2P at A and P at B with a load inbetween of 6KN

For moments to balance about any point ( take the point where the load is attached), the distance x must satisfy    2P.x = P (1-x)

solve for x, cacel out P

2x = 1-x ==> 3x=1 ==> x=1/3 =0.333 m

Taking vertical forces in equilibrium on the beam,

2P +P ( forces at A and B ) = Weight down = 6 KN

3P = 6 KN

P = 2 KN

Best!