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?

Responses

2.6 times less force

6.1 times less force

36.26 times less force

13.5 times less force

1 answer

To determine how much less force a vacationer would be applying to their joints when walking on Mars compared to Earth, we can use the ratio of gravitational accelerations on the two planets.

  1. Gravitational acceleration on Earth (g_E) = 9.8 m/s²
  2. Gravitational acceleration on Mars (g_M) = 3.7 m/s²

The force exerted on the joints due to gravity is proportional to the gravitational acceleration. Thus, the ratio of the forces (and hence the impact on joints) can be calculated as follows:

\[ \text{Force Ratio} = \frac{g_E}{g_M} = \frac{9.8}{3.7} \]

Now, we can calculate this ratio:

\[ \text{Force Ratio} = 2.64864864865 \]

Rounding this to two decimal places gives approximately 2.65.

This means the vacationer would be applying about 2.65 times less force to their joints when walking on Mars compared to walking on Earth.

Based on the options provided, the closest option is:

2.6 times less force.