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.
- The gravitational acceleration on Earth (g_E) = 9.8 m/s²
- 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.
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