When interplanetary space travel becomes viable, doctors may suggest to people with arthritis that they vacation on a planet with lower gravitational attraction and do more walking.
The gravitational acceleration on Earth is 9.8 m/s^2, while the gravitational acceleration on Mars is 3.7 m/s^2. How much less force would the vacationer be applying to their joints when walking on Mars?
6.1 times less force
2.6 times less force
36.26 times less force
13.5 times less force
To determine the difference in force applied to the joints when walking on Mars compared to Earth, you can use the concept of weight. The force exerted by an object is equal to its mass multiplied by the gravitational acceleration.
First, you need to calculate the ratio of gravitational accelerations between Earth and Mars:
Ratio = gravitational acceleration on Mars / gravitational acceleration on Earth
= 3.7 m/s^2 / 9.8 m/s^2
≈ 0.3776
This ratio represents the difference in gravitational accelerations between the two planets.
Next, you can calculate the ratio of forces applied to the joints:
Ratio of forces = (mass of the vacationer)x(gravitational acceleration on Mars) / (mass of the vacationer)x(gravitational acceleration on Earth)
= (gravitational acceleration on Mars) / (gravitational acceleration on Earth)
≈ 0.3776
Therefore, the vacationer would be applying approximately 0.3776 times less force to their joints when walking on Mars compared to Earth.
So, the answer is approximately:
0.3776 times less force
or
2.6 times less force
Hence, the correct answer is 2.6 times less force.