A person doing a chin-up weighs 660 N, exclusive of the arms. During the first 22.0 cm of the lift, each arm exerts an upward force of 355 N on the torso. If the upward movement starts from rest, what is the person's velocity at this point

Respuesta :

Answer:

0.57183 m/s

Explanation:

g = Acceleration due to gravity = 9.81 m/s²

a = Acceleration

u = Initial velocity

v = Final velocity

s = Displacement

Mass of person

[tex]m=\frac{W}{g}\\\Rightarrow m=\frac{660}{9.81}\\\Rightarrow m=67.27828\ kg[/tex]

As the forces are conserved

[tex]\text{Upward forces - Downward forces}=ma\\\Rightarrow \text{Force of both arms - Force of gravity}=ma\\\Rightarrow 355+355-660=67.27828a\\\Rightarrow 50=67.27828a\\\Rightarrow a=\frac{50}{67.27828}\\\Rightarrow a=0.74318\ m/s^2[/tex]

From equation of motion

[tex]v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 0.74318\times 0.22+0^2}\\\Rightarrow v=0.57183\ m/s[/tex]

The person's velocity at the point is 0.57183 m/s