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

36.26 times less force
36.26 times less force

2.6 times less force
2.6 times less force

6.1 times less force
6.1 times less force

13.5 times less force
13.5 times less force
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1 answer

To determine how much less force a vacationer would be applying to their joints when walking on Mars compared to walking on Earth, we can compare the gravitational forces exerted on the body in both environments.

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

The force exerted by gravity (weight) can be calculated as:

  • Weight on Earth = mass × g_E
  • Weight on Mars = mass × g_M

To find the ratio of the force exerted on Mars to the force exerted on Earth, we can set up the following ratio for the same mass:

\[ \text{Force ratio} = \frac{g_M}{g_E} = \frac{3.7 , \text{m/s}^2}{9.8 , \text{m/s}^2} \approx 0.37857 \]

This means that a body would exert approximately 37.857% of the force on Mars compared to Earth.

To find how much less force this represents, we can calculate the reduction in force:

\[ \text{Reduced force factor} = 1 - \text{Force ratio} = 1 - 0.37857 \approx 0.62143 \]

In terms of how many times less force the vacationer is applying, we take the inverse of the force ratio, which tells us how many times the force is reduced:

\[ \frac{g_E}{g_M} = \frac{9.8}{3.7} \approx 2.64 \]

Thus, the correct answer is:

2.6 times less force.