You are going up in an elevator that is accelerating upward on Earth and your apparent weight is measured to be 120% of your weight on Earth. Suppose you were to go in an elevator with the same acceleration on Mars, where acceleration due to gravity is 3.71 m/s². What will be your apparent weight comparing to your weight on Earth? A) 37.1% B) 100% C) 120% D) 57.8% E) 44.5%

Question

Quizplus · Accepted Answer

The apparent weight is the force perceived by a person as a result of the contact force with a surface. This force can be calculated as:

Apparent weight = (mass)(acceleration)

On Earth, the acceleration due to gravity is 9.81 m/s^2. If the apparent weight is 120% of the weight on Earth, then the acceleration must be:

(1.2)(weight on Earth) = (mass)(9.81 m/s^2 + acceleration)

Solving for acceleration:

acceleration = 0.2(wight on Earth) / mass

On Mars, the acceleration due to gravity is 3.71 m/s^2. We can use the same equation to calculate the apparent weight on Mars:

(apparent weight on Mars) = (mass)(3.71 m/s^2 + acceleration)

Substituting the expression for acceleration that we found earlier:

(apparent weight on Mars) = (mass)(3.71 m/s^2 + 0.2(weight on Earth) / mass)

The mass cancels out, and we are left with:

(apparent weight on Mars) = 3.71 m/s^2 + 0.2(weight on Earth)

Dividing by the weight on Earth and multiplying by 100% gives us the percentage of the weight on Earth that corresponds to the apparent weight on Mars:

(apparent weight on Mars) / (weight on Earth) x 100% = (3.71 m/s^2 + 0.2(weight on Earth)) / (weight on Earth) x 100%

Simplifying:

(apparent weight on Mars) / (weight on Earth) x 100% = 3.71 / 9.81 + 0.2 x 100%

(apparent weight on Mars) / (weight on Earth) x 100% = 0.378

(apparent weight on Mars) = 0.378 x (weight on Earth)

(apparent weight on Mars) = 0.378 x 100%

(apparent weight on Mars) = 37.8%

Therefore, the answer is D) 57.8%.

You Are Going Up in an Elevator That Is Accelerating