Question

An 80-kg person stands at rest on a scale while pulling vertically downwards on a rope that is above them. Use g = 9.80 m/s2. With what magnitude force must the tension in the rope by pulling on the person so that the scale reads 500 N?

Answer 1

Answer:

1284 N

Explanation:

m = Mass of person = 80 kg

g = Acceleration due to gravity = -9.81 m/s² (negative as the elevator is going up)

Tension

$T=m(g+a)\\\Rightarrow 500=80(-9.8+a)\\\Rightarrow -9.81+a=\frac{500}{80}\\\Rightarrow a=6.25+9.8\\\Rightarrow a=16.05\ m/s^2$

The acceleration that the tension should provide is 16.05 m/s²

From Newton's Second Law

$F=ma\\\Rightarrow F=80\times 16.06\\\Rightarrow F=1284\ N$

Magnitude force must the tension in the rope by pulling on the person is 1284 N