On Earth, a scale shows that you weigh 585 N. a. What is your mass? b. What would the scale read on the Moon? c. Use the results from Example Problems to answer questions about a p... On Earth, a scale shows that you weigh 585 N. a. What is your mass? b. What would the scale read on the Moon? c. Use the results from Example Problems to answer questions about a person in the following situations: The elevator moves upward at constant speed. The elevator slows at 2.0 m/s² while moving downward. It speeds up at 2.0 m/s² while moving upward. It moves downward at constant speed. In what direction is the net force as the elevator is moving down?
Understand the Problem
The question involves physics concepts related to weight measurements on a scale in different scenarios including gravitational variations, such as on the Moon. It requires using forces and acceleration calculations to understand the readings from the scale in various situations within an elevator.
Answer
Your mass is approximately \( 59.84 \, \text{kg} \) and weight on the Moon is about \( 95.74 \, \text{N} \).
Answer for screen readers
- Your mass is approximately ( 59.84 , \text{kg} ).
- Weight on the Moon would read approximately ( 95.74 , \text{N} ).
Steps to Solve
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Determine Your Mass from Weight
On Earth, weight is given by the equation: $$ W = mg $$ where ( W ) is weight, ( m ) is mass, and ( g ) is the acceleration due to gravity (approximately ( 9.8 , \text{m/s}^2 )).
We can rearrange the equation to solve for mass: $$ m = \frac{W}{g} $$ Plugging in the weight ( W = 585 , \text{N} ): $$ m = \frac{585}{9.8} \approx 59.84 , \text{kg} $$
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Calculate Weight on the Moon
The acceleration due to gravity on the Moon is approximately ( 1.6 , \text{N/kg} ). Using the mass we just calculated: $$ W_{\text{moon}} = m \cdot g_{\text{moon}} = 59.84 \times 1.6 $$ Calculate the weight: $$ W_{\text{moon}} \approx 95.74 , \text{N} $$
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Evaluate the Scale in Various Elevator Situations
In each scenario, we'll need to account for the forces acting on the person in the elevator:
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For upward movement with acceleration ( a ), the apparent weight is: $$ W_{\text{apparent}} = m(g + a) $$
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For downward movement with acceleration ( a ): $$ W_{\text{apparent}} = m(g - a) $$
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Summarize Each Situation
- Elevator moves upward at constant speed: No change in weight.
- Elevator slows to a stop: Apparent weight increases.
- Elevator speeds up while moving downward: Apparent weight decreases.
- Elevator moves downward at constant speed: No change in weight.
- Your mass is approximately ( 59.84 , \text{kg} ).
- Weight on the Moon would read approximately ( 95.74 , \text{N} ).
More Information
The weight readings on different celestial bodies vary due to differences in gravity. Understanding these dynamics helps in comprehending how forces act on objects in motion, especially in elevators or spacecraft.
Tips
- Forgetting to convert units when applying formulas.
- Confusing weight with mass; remember weight changes with gravity, while mass remains constant.
- Miscalculating the apparent weight by not considering the direction and magnitude of acceleration.
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