You are riding in an elevator holding a spring scale with a 1-kg mass suspended from it. You look at the scale and see that it reads 9.3 N. What does this tell you about the elevat... You are riding in an elevator holding a spring scale with a 1-kg mass suspended from it. You look at the scale and see that it reads 9.3 N. What does this tell you about the elevator's motion?
Understand the Problem
The question involves the scenario of being in an elevator while observing the reading on a scale. It asks what the reading of 9.3 N indicates about the motion of the elevator, likely relating to the concepts of weight, acceleration, or forces acting on the mass.
Answer
The elevator is accelerating downward.
Answer for screen readers
The elevator is accelerating downward.
Steps to Solve
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Calculate the Weight of the Mass
The weight ($W$) of the mass is calculated using the formula: $$ W = mg $$ where:
- $m = 1 , \text{kg}$ (mass)
- $g = 9.8 , \text{m/s}^2$ (acceleration due to gravity)
Thus, $$ W = 1 , \text{kg} \times 9.8 , \text{m/s}^2 = 9.8 , \text{N} $$
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Compare the Scale Reading with Weight
The scale shows a reading of $9.3 , \text{N}$.
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Determine the Motion of the Elevator
Since the scale reading ($9.3 , \text{N}$) is less than the actual weight ($9.8 , \text{N}$), it indicates that the elevator is accelerating downwards.
This can be concluded because the scale reading decreases when the elevator accelerates downward (force read on the scale decreases).
The elevator is accelerating downward.
More Information
The scale reading of $9.3 , \text{N}$ being less than the gravitational weight of $9.8 , \text{N}$ indicates that the upward force exerted by the scale is less than the gravitational pull, which suggests downward acceleration.
Tips
- Misinterpreting the scale reading as the actual weight. It reflects the apparent weight influenced by acceleration, not the true weight.
- Forgetting to use the gravitational constant correctly, which can lead to incorrect weight calculations.
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