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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?

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boffeemadrid

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

[tex]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[/tex]

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

From Newton's Second Law

[tex]F=ma\\\Rightarrow F=80\times 16.06\\\Rightarrow F=1284\ N[/tex]

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

Lanuel

The magnitude of force which the tension in the rope must be pulling on the person so that the scale reads 500 Newton is 1284 Newton.

Given the following data:

  • Mass of person = 80 kg
  • Acceleration due to gravity = 9.80 [tex]m/s^2[/tex]
  • Weight of scale = 500 Newton

To determine the magnitude of force which the tension in the rope must be pulling on the person so that the scale reads 500 N:

First of all, we would determine the downward force applied by the person's weight:

[tex]F_P = mg[/tex]

Where:

  • [tex]F_P[/tex]is the person's weight.
  • m is the mass of the person.
  • g is acceleration due to gravity.

Substituting the given parameters into the formula, we have;

[tex]F_P = 80 \times 9.8\\\\F_P = 784 \; Newton[/tex]

Next, we would determine the tension in the rope:

[tex]Tension = F_P + F_S\\\\Tension = 784 + 500[/tex]

Tension = 1284 Newton.

Read more: https://brainly.com/question/18792908

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