On Earth, a scale shows that you weigh 585 N. What is your mass? What would the scale read on the Moon? Use the results from Example Problem 3 to answer questions about a scale in... On Earth, a scale shows that you weigh 585 N. What is your mass? What would the scale read on the Moon? Use the results from Example Problem 3 to answer questions about a scale in an elevator on Earth. What force would be exerted by the scale on a person in the following situations? The elevator moves upward at constant speed. It slows at 2.0 m/s² while moving downward. It speeds up at 2.0 m/s² while moving downward. It moves downward at constant speed. In what direction is the net force as the elevator slows to a stop as it is moving down? Read more

Steps to Solve

1. Determine Mass from Weight To find your mass on Earth, use the formula that relates weight to mass:

$$ W = mg $$

where

• ( W ) is the weight (in Newtons),
• ( m ) is the mass (in kilograms),
• ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 ) on Earth).

Rearranging the formula gives:

$$ m = \frac{W}{g} $$

Substituting the given weight:

$$ m = \frac{585 , \text{N}}{9.81 , \text{m/s}^2} \approx 59.7 , \text{kg} $$

2. Calculate the Scale Reading on the Moon The acceleration due to gravity on the Moon is ( 1.60 , \text{m/s}^2 ). The weight on the Moon can also be calculated using the same formula:

$$ W_{moon} = mg_{moon} $$

Substituting the mass calculated earlier:

$$ W_{moon} = 59.7 , \text{kg} \times 1.60 , \text{m/s}^2 \approx 95.5 , \text{N} $$

3. Analyze the Elevator Scenarios We apply Newton's second law ( F = ma ) to find the net force exerted by the scale under different elevator conditions. The forces acting on the person include gravitational force and the net force from the elevator's acceleration.

• Scenario a: Moving up at constant speed means no net acceleration. The scale reads the weight:

  $$ F_{scale} = W = 585 , \text{N} $$

• Scenario b: Slowing down at ( 2.0 , \text{m/s}^2 ) (decelerating). The net force is:

  $$ F_{scale} = W - ma $$

  $$ F_{scale} = 585 , \text{N} - (59.7 , \text{kg} \times 2.0 , \text{m/s}^2) \approx 466.6 , \text{N} $$

• Scenario c: Speeding up at ( 2.0 , \text{m/s}^2 ). The net force is:

  $$ F_{scale} = W + ma $$

  $$ F_{scale} = 585 , \text{N} + (59.7 , \text{kg} \times 2.0 , \text{m/s}^2) \approx 703.4 , \text{N} $$

• Scenario d: Moving down at constant speed means no net acceleration.

  $$ F_{scale} = W = 585 , \text{N} $$

• Scenario e: When it slows to a stop while moving downward, we again calculate as in scenario b with a negative acceleration.

4. Determine Direction of the Net Force The net force direction depends on whether the elevator is accelerating upwards or downwards. When slowing downward, the force exerted on the scale is greater than just gravitational force.