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? (1 point) Responses
A. 6.1 times less force
B. 2.6 times less force
C. 13.5 times less force
D. 36.26 times less force
To calculate the difference in force on Mars compared to Earth, we need to determine the ratio of the gravitational accelerations on the two planets.
The force experienced by an object due to gravity can be calculated using the formula:
force = mass x acceleration due to gravity
On Earth, the force would be:
force_earth = mass x 9.8 m/s^2
On Mars, the force would be:
force_mars = mass x 3.7 m/s^2
To find the ratio of the forces on Mars compared to Earth, we divide the force on Mars by the force on Earth:
force_ratio = force_mars / force_earth
force_ratio = (mass x 3.7 m/s^2) / (mass x 9.8 m/s^2)
mass cancels out:
force_ratio = 3.7 m/s^2 / 9.8 m/s^2
force_ratio = 0.3776
This means that on Mars, the vacationer would be applying approximately 0.3776 times less force to their joints when walking.
Therefore, the answer is:
B. 2.6 times less force