Question

A 56 kg person stands on two bathroom scales. One scale reads 200 N. What does the second scale read?

Answer 1

348.8 N

Step-by-step explanation:

To address this problem, we need to understand how forces are distributed when a person stands on two scales. The key concept here is that the total weight of the person must be divided between the two scales.

We are given:

• m = 56 kg
• F₁ = 200 N

Let's first calculate the total weight of the person. Weight (w) can be calculated using the formula w = mg, where 'm' is mass and 'g' is the acceleration due to gravity (approximately 9.8 m/s² on Earth). For a 56 kg person, the weight is:

`\Longrightarrow \vec w =(56 \text{ kg})(9.8 \text{ m/s$^2$})\\\\\\\\\therefore \vec w = 548.8 \ N`

Since the total weight of the person is 548.8 N, and one of the scales reads 200 N, the force from the second scale must equal:

`\Longrightarrow \vec F_2 = \vec w - \vec F_1\\\\\\\\\Longrightarrow \vec F_2 = 548.8 \text{ N} - 200 \text{ N}\\\\\\\\\therefore \vec F _2= \boxed{348.8 \text{ N}}`

Thus, the second scale reads 348.8 N. This bigger number indicates the person is leaning more of their weight on the second scale.