Question

A body hangs from a spring balance supported from the roof of an elevator. If the elevator has an upward acceleration of
3ms−2
and the balance reads 50 N, what is the true weight of the body?

Answer 1

Answer on Question #41194 – Physics – Mechanics | Kinematics | Dynamics

A body hangs from a spring balance supported from the roof of an elevator. If the elevator has an upward acceleration of 3ms⁻² and the balance reads 50 N, what is the true weight of the body?

Solution:

According to the Second Newton’s law:

$$\vec{F} = m \cdot \vec{a}$$

For vertical axis taking up as positive direction:

$$F = T - F_{gravity}$$

We are given:

$$T = 50 \, \text{N}$$

Force of gravity:

$$F_{gravity} = m \cdot g$$

Thus:

$$T - F_{gravity} = m \cdot a$$ $$T - m \cdot g = m \cdot a$$

For inertial system

$$W = F_{gravity} = m \cdot g$$

So:

$$m = \frac{T}{a + g}$$ $$W = \frac{gT}{a + g}$$

Calculating:

$$W = \frac{9.8 \cdot 50}{3 + 9.8} \approx 38.3 \, \text{N}$$

Answer: 38.3 N

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