If the scale shows 585 Newtons, what is your mass? What would the car read on the moon if G is 1.16 Newtons per kilogram?
Understand the Problem
The question is asking us to calculate the mass based on a given force measured in Newtons, and then to determine what the scale would read on the moon where the gravitational acceleration is different.
Answer
$$ F_{moon} = \frac{F}{9.81} \cdot 1.625 $$
Answer for screen readers
The force on the Moon is given by: $$ F_{moon} = \frac{F}{9.81} \cdot 1.625 $$
Hence, the specific answer will depend on the initial force provided; please replace $F$ with the numerical value.
Steps to Solve
-
Identify the given values We know the force (in Newtons) and the gravitational acceleration on Earth, which is approximately $9.81 , \text{m/s}^2$.
-
Calculate the mass on Earth We can use Newton's second law of motion, which states that force is equal to mass times acceleration: $$ F = m \cdot g $$ Rearranging this gives us the formula for mass: $$ m = \frac{F}{g} $$ Substituting the known values gives us: $$ m = \frac{F}{9.81} $$
-
Determine gravitational acceleration on the Moon The gravitational acceleration on the Moon is approximately $1.625 , \text{m/s}^2$.
-
Calculate the weight (scale reading) on the Moon Using the mass calculated previously, we can find the force (weight) on the Moon using the formula: $$ F_{moon} = m \cdot g_{moon} $$ Substituting the values for mass and the Moon's gravitational acceleration: $$ F_{moon} = m \cdot 1.625 $$
-
Final calculation Complete the calculation to find the final weight on the Moon. Substitute the value of $m$ calculated in step 2 into the equation from step 4.
The force on the Moon is given by: $$ F_{moon} = \frac{F}{9.81} \cdot 1.625 $$
Hence, the specific answer will depend on the initial force provided; please replace $F$ with the numerical value.
More Information
This problem utilizes Newton's second law of motion, illustrating how weight changes in different gravitational environments. On the Moon, objects weigh significantly less due to lower gravitational pull.
Tips
- Confusing force with weight; remember that weight is a force caused by gravity acting on mass.
- Forgetting to convert gravitational acceleration when moving from Earth to Moon calculations.
AI-generated content may contain errors. Please verify critical information
