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

Answer:

The tension in the rope is 588 N

Explanation:

I have attached a free body diagram of the problem.

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

$F_{weight} =m*a = 80 kg * 9.8 \frac{m}{s^{2}} = 784 N$

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

$F_{Rope}-F_{Pull}+F_{Person}-F_{Scale}=0 \\588N-588N+196N-196N=0$