Question

A 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 be pulling on the person so that the scale reads 25% of the persons weight?

Answer 1

The tension in the rope is 588 N

Step-by-step explanation:

I have attached a free body diagram of the problem.

First we calculate the force applied downwards by the person's weight:

`F_(weight) =m*a = 80 kg * 9.8 (m)/(s^(2)) = 784 N`

If the scale reads a 25% of the person' weight:

`F_(Scale) = F_(weight)*0.25=784N*0.25=196N`

which is the same value (but opposite) to the effective weight of the persons (
`F_(Person)=-F_(Scale)`)

The other 75% of the total weight is the force of the rope pulling the person upwards.

`F_(Pull)= F_(weight)*0.75=784N*0.75=588N`

To verify, we can use 1st Newton's law

∑F = 0

`F_(Rope)-F_(Pull)+F_(Person)-F_(Scale)=0 \\588N-588N+196N-196N=0`