Question

A 50.0 -kg crate is suspended between the floor and the ceiling using two spring scales, one attached to the ceiling and one to the floor. If the lower scale reads \(120 \mathrm{N},\) what is the reading of the upper scale? Ignore the weight of the scales.

Short answer

Answer: The reading of the upper scale is 370 N.

Step-by-step solution

Identify known and unknown variables

We know: - The mass of the crate (m) = 50.0 kg - The reading on the lower scale (F1) = 120 N - The reading on the upper scale (F2) = ?

Calculate the weight of the crate

The weight (W) of the crate can be calculated using the following formula: W = m * g where g is the acceleration due to gravity (approximately 9.8 m/s²) W = 50.0 kg * 9.8 m/s² = 490 N

Apply the concept of force equilibrium

Since the crate is in equilibrium, the sum of the forces acting on it must be zero. Therefore, the forces acting on the crate are: - The reading on the lower scale (F1), which pulls the crate upward - The reading on the upper scale (F2), which pulls the crate downward - The weight of the crate (W), which also pulls the crate downward In equilibrium, the upward forces should balance the downward forces, so: F1 = F2 + W

Calculate the reading on the upper scale (F2)

Substitute the known values into the equation from Step 3: 120 N = F2 + 490 N Solve for F2: F2 = 120 N - 490 N = -370 N

Interpret the result

Since we got a negative value for F2, it means that the direction of the force is opposite to what we initially assumed. In this case, it means that the upper scale is actually pulling the crate upward, not downward. So, the reading on the upper scale is 370 N (in the upward direction). The reading of the upper scale is 370 N.