a man is standing on a platform that is connected to a pulley arrangement, as the drawing shows. by pulling…

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 $vec{p}$ the man can raise the platform and himself. the total mass of the man plus the platform is 143 kg. what pulling force should the man apply to create an upward acceleration of 1.20 m/s²?

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 $vec{p}$ the man can raise the platform and himself. the total mass of the man plus the platform is 143 kg. what pulling force should the man apply to create an upward acceleration of 1.20 m/s²?

Answer

Explanation:

Step1: Identify forces and apply Newton's second - law

The total upward force is (2P) (two segments of the rope pulling up), and the total downward force is the weight (mg) where (m = 143\space kg) and (g=9.8\space m/s^{2}). According to Newton's second - law (F_{net}=ma), so (2P - mg=ma).

Step2: Rearrange the formula to solve for (P)

First, rewrite the equation (2P - mg=ma) as (2P=ma + mg). Then factor out (m): (2P=m(a + g)). Finally, solve for (P): (P=\frac{m(a + g)}{2}).

Step3: Substitute the given values

Substitute (m = 143\space kg), (a = 1.20\space m/s^{2}), and (g = 9.8\space m/s^{2}) into the formula (P=\frac{m(a + g)}{2}). [ \begin{align*} P&=\frac{143\times(1.20 + 9.8)}{2}\ &=\frac{143\times11}{2}\ &=\frac{1573}{2}\ & = 786.5\space N \end{align*} ]

Answer:

(786.5\space N)