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?
a. 6.1 times less force
b. 2.6 times less force
c. 36.26 times less force
d. 13.5 times less force
The force applied to a person's joints when walking is directly proportional to the gravitational acceleration. Therefore, if the gravitational acceleration on Mars is 3.7 m/s^2 (lower than that on Earth), the force applied to the joints would be less.
To calculate the difference in force, we can take the ratio of the gravitational accelerations on Earth and Mars:
Force on Mars / Force on Earth = Gravitational acceleration on Mars / Gravitational acceleration on Earth
Now substituting the given values:
Force on Mars / Force on Earth = 3.7 m/s^2 / 9.8 m/s^2
Simplifying the equation:
Force on Mars / Force on Earth ≈ 0.3776
Therefore, the vacationer would be applying approximately 0.3776 times less force to their joints when walking on Mars.
Rounded to one decimal place, this is approximately 0.4 times less force. Hence, the answer is not among the provided options.