Question

A 172-cm-tall person lies on a light (though impractical, but assume massless) board, which is supported by two scales, one under the top of her head and one beneath the bottom of her feet. The two scales read, respectively, 35.1 and 31.6 kg. What distance is the center of gravity of this person from the bottom of her feet

Answer 1

The center of gravity of the person is calculated to be approximately 90.4 cm from the bottom of their feet by using the concept of moments and the scale readings provided.

Step-by-step explanation:

The question presented involves finding the center of gravity of a person lying on a massless board supported by two scales. The scales are positioned at the opposite ends of the board, one beneath the head and one beneath the feet. The top scale reads 35.1 kg, and the bottom scale reads 31.6 kg. To find the distance of the center of gravity from the bottom of the person's feet, we will use the concept of moments (also known as torques).

Firstly, we establish the total weight of the person which is the sum of the readings from both scales:
Total weight = Top scale reading + Bottom scale reading = 35.1 kg + 31.6 kg = 66.7 kg

Next, we consider moments around the bottom scale (as the pivot). Let d be the distance from the bottom of the feet to the center of gravity. Since the board is assumed massless, we can ignore its weight. The moment produced by the total weight around the bottom scale will be equal to the moment produced by the top scale reading:

Top scale reading * Total length of the board = Total weight * d

35.1 kg * 172 cm = 66.7 kg * d

Solving for d, we get:

d = (35.1 kg * 172 cm) / 66.7 kg

Upon calculation:

d ≈ 90.4 cm

Therefore, the center of gravity of the person is approximately 90.4 cm from the bottom of their feet.