A man is standing on a platform that is connected to a pulley arrangement, as the drawing shows. By pulling upward on the rope with a force, P, the man can raise the platform and himself. The total mass of the man plus the platform is 102 kg. What pulling force should the man apply to create an upward acceleration of 1.20 m/s2?
I can not see the drawing, so, I will explain what I believe is happening!
The man is pulling up on the rope, and the platform moves up. The simplest pulley arrangement is 2 pulleys. The rope goes from the man’s hand, down, under, and around the bottom pulley, up and over the top pulley, and down to the top of the bottom pulley. This end of the rope is attached to the top of the bottom pulley.
Draw a horizontal line above the bottom pulley. To determine the mechanical advantage of the pulley system, you count the number of ropes lifting the bottom pulley. All three ropes are lifting up on the bottom pulley, so the mechanical advantage = 3 : 1.
A 3: 1 mechanical advantage means the pulls 3 meters of rope up, and the platform moves 1 meter up.
A 3: 1 mechanical advantage means the man only has to exert ⅓ of the force that will create an upward acceleration of 1.20 m/s^2.
To create an upward acceleration of 1.20 m/s^2, the net force upward must equal 102 * 1.2 = 122.4 N
Net force up = Total force of 3 ropes pulling up – weight of platform and man pulling down.
Weight of platform and man = 102 * 9.8 = 999.6 N
122.4 = Total force of 3 ropes pulling up – 999.6
Total force of 3 ropes pulling up = 122.4 + 999.6 = 1122 N
Force of 1 rope = 1122 ÷ 3 = 374 N