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Name: Jessica
Status: other
Grade: 12+
Location: KY
Country: USA
Date: Summer, 2011

If you kick a 10 kg rock on the moon, would the force exerted by the rock on your foot be substantially different from the force you feel when you kick the same 10 kg rock on Earth? I am mainly interested in the force exerted by foot, but also in the general answer.

Hi Shadrack,

Assuming you were kicking the rock horizontally (not punting it) the forces will be the same on the moon as on earth. All of the equations that apply to kicking the rock involve mass and a rock's mass,(or yours for that matter) does not change with gravity.

Because gravity is a force acting towards the center of an object (in this case, the moon) only motion in that direction, up or down, is affected by the moon's 1/6 gravity.

R. W. "Mr. A." Avakian Instructor Arts and Sciences/LRC Oklahoma State Univ. Inst. of Technology

Nope, the rock would resist acceleration by your foot the same on Earth, on the Moon, in orbit, or anywhere else. The rock would be easier to lift on the Moon than on Earth, but kicking it would be the same.

Why is that? To lift something, you have to work against gravity. Gravity varies from place to place, so lifting requires the greatest force where the gravitational field is strongest. To kick a rock sideways, however, simply involves the interaction between your foot and the rock. Gravity, since it does not act sideways, is not a factor.

That is true to a first approximation. If the rock is resting on something, such as the ground or the floor, kicking the rock will involve pushing it against friction, which will be roughly proportional to gravity. To the extent that friction is a factor, it will take more force to kick the rock, and the rock will push harder against your foot, where the gravitational field is greater.

Richard E. Barrans Jr., Ph.D., M.Ed. Department of Physics and Astronomy University of Wyoming

Jessica -

If your foot was going as fast as it would on earth, the impact force would be the same, and given same force and momentum, the rock would start traveling just as fast, and then it might fly farther in the lower gravity.

But, in lower gravity one is standing on the ground with less force, and maybe that makes it biomechanically difficult to do the same robust swinging kick, and then the force and transferred momentum would be less.

But then, the space suit would make your "foot" more massive, so maybe that would help....

Oh, your question is what the foot experiences. And I assume that padding by the space-suit boot is not supposed to be the issue. Yes, if you (stupidly) kicked a 10kg rock just as fast as you could on earth, only you did it on the moon, it would do the same forces damage, and pain. Inertia and yield (elastic or inelastic) are the only issues there, and they do not change depending on the local gravity field.

I guess on earth the rock has higher friction of sliding on the ground which will add to the inertial force it applies against your foot. I am thinking the friction force is small compared to the inertial force in any short sharp impact. But if there was a great deal of springy padding around your foot to lengthen the time of the impact, then the inertial force would be lower and longer (equal integral or product) and maybe then the friction force would become a significant portion of the total force, and then there would be a noticeable difference, but still not as big a difference as the 6:1 gravity ratio.

On earth a big rock might be half-embedded in firm dirt. You can imagine that would sometimes increase its impact-resisting forces greatly. The dust covering the moon would rarely be as firm, and the low gravity probably makes it explode out of the way very easily I'd guess..

Jim Swenson

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