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/s2
, while the gravitational acceleration on Mars is 3.7 m/s2
. How much less force would the vacationer be applying to their joints when walking on Mars?

(1 point)
Responses

13.5 times less force
13.5 times less force

2.6 times less force
2.6 times less force

36.26 times less force
36.26 times less force

6.1 times less force
6.1 times less force

1 answer

To determine how much less force a person would apply to their joints when walking on Mars compared to Earth, we can calculate the ratio of gravitational accelerations.

The gravitational acceleration on Earth (g_E) is 9.8 m/s², and on Mars (g_M), it is 3.7 m/s².

The ratio of the gravitational forces can be calculated as follows:

\[ \text{Force on Earth} \propto g_E \ \text{Force on Mars} \propto g_M \]

The ratio of force exerted on Mars to that on Earth is given by:

\[ \frac{g_M}{g_E} = \frac{3.7}{9.8} \]

Calculating the ratio:

\[ \frac{3.7}{9.8} \approx 0.3786 \]

This means that on Mars, a person experiences about 37.86% of the force they would experience on Earth.

To find how much less force is applied, we take the inverse of this ratio:

\[ \text{Factor of reduction in force} = \frac{1}{0.3786} \approx 2.64 \]

Therefore, the force applied to joints when walking on Mars is approximately 2.6 times less than on Earth.

The correct response is: 2.6 times less force.