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------------------------------------------------ What is the magnitude of the net force [tex]\(\sum F\)[/tex] on a 1.0 kg bathroom scale when a 66 kg person stands on it?

[tex]\(\sum F = \square\)[/tex] N

To solve the problem of finding the magnitude of the net force on a 1.0 kg bathroom scale when a 66 kg person stands on it, we need to consider the weight of the person. The key here is understanding that the weight of a person is the force due to gravity acting on their mass.

Here's how you calculate it:

1. Know the Formula for Weight:
The weight of an object can be calculated using the formula:
[tex]\[
F = m \times g
\][/tex]
where:
- [tex]\( F \)[/tex] is the force in newtons (N),
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity.

2. Values Given:
- Mass of the person ([tex]\( m \)[/tex]) = 66 kg
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.81 m/s²

3. Calculate the Force:
By substituting the values into the formula, we get:
[tex]\[
F = 66 \, \text{kg} \times 9.81 \, \text{m/s}^2
\][/tex]

4. Result:
Upon performing the multiplication, the magnitude of the net force (the weight of the person) is found to be approximately:
[tex]\[
F \approx 647.46 \, \text{N}
\][/tex]

So, the magnitude of the net force on the scale when the 66 kg person stands on it is 647.46 N.