Question

PLEASE HELP ASAP. Best answer gets BRAINIEST:

a counter weight of 13.5kg is used to help a person of a mass 62.4kg do chin ups

1. Calculate the force applied by the person if he accelerates at 1.9m/s^2
2. calculate the magnitude of the tension in the wire.

Answer 1

Answer:

1. Force = -623.43 N

2.Tension = 106.65 N

Explanation:

Let us call the bigger mass $M$, and the smaller mass $m$.

Since the two masses are connected to each other, they must experience same acceleration (if they didn't, the unequal acceleration will cause the string to break. )

From the free body diagram, the forces acting on the mass $M$ are

$T - Mg-F_p$,

and according to Newton Second Law, this causes acceleration $a$; therefore,

(1).  $\boxed{ T-Mg-F_p=Ma}$.

Similarly, the forces acting on the mass $m$ are

$T -mg$,

which causes the acceleration $-a$ (upward); therefore,

$T-mg=-ma$

or

$\boxed{ mg-T = ma}$

From this equation we solve for $T$ and get:

$T = mg-ma \\\\T =m(g-a).$

We put this into equation (1) and get:

$m(g-a)-Mg-F_p=Ma$

$F_p = m(g-a)-M(g+a)$

putting in $M=62.4kg,m=13.5kg,$ and $a=1.9m/s^2$, we get:

$F_p=13.5(9.8-1.9)-62.4(9.8+1.9)\\\\\boxed{ F_p=-623.43N}$

The tension in the wire is

$T =m(g-a)\\\\T = 13.5(9.8-1.9)\\\\\boxed{ T= 106.65N}$