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Chapter 4: Problem 140

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

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

Step by step solution

01

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) = ?
02

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
03

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
04

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
05

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.

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Most popular questions from this chapter

In the physics laboratory, a glider is released from rest on a frictionless air track inclined at an angle. If the glider has gained a speed of $25.0 \mathrm{cm} / \mathrm{s}\( in traveling \)50.0 \mathrm{cm}$ from the starting point, what was the angle of inclination of the track? Draw a graph of \(v_{x}(t)\) when the positive \(x\) -axis points down the track.
A skydiver, who weighs \(650 \mathrm{N},\) is falling at a constant speed with his parachute open. Consider the apparatus that connects the parachute to the skydiver to be part of the parachute. The parachute pulls upward with a force of \(620 \mathrm{N} .\) (a) What is the force of the air resistance acting on the skydiver? (b) Identify the forces and the interaction partners of each force exerted on the skydiver. (c) Identify the forces and interaction partners of each force exerted on the parachute.
A hanging potted plant is suspended by a cord from a hook in the ceiling. Draw an FBD for each of these: (a) the system consisting of plant, soil, and pot; (b) the cord; (c) the hook; (d) the system consisting of plant, soil, pot, cord, and hook. Label each force arrow using subscripts (for example, \(\overrightarrow{\mathbf{F}}_{\mathrm{ch}}\) would represent the force exerted on the cord by the hook).
The coefficient of static friction between a block and a horizontal floor is \(0.40,\) while the coefficient of kinetic friction is \(0.15 .\) The mass of the block is \(5.0 \mathrm{kg} .\) A horizontal force is applied to the block and slowly increased. (a) What is the value of the applied horizontal force at the instant that the block starts to slide? (b) What is the net force on the block after it starts to slide?
A 2.0 -kg toy locomotive is pulling a 1.0 -kg caboose. The frictional force of the track on the caboose is \(0.50 \mathrm{N}\) backward along the track. If the train's acceleration forward is \(3.0 \mathrm{m} / \mathrm{s}^{2},\) what is the magnitude of the force exerted by the locomotive on the caboose?
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