Q: When something falls on your foot, how much force is involved?

Physicist: There’s a cute trick you can use here.  It a falling object starts at rest and ends at rest, then it gains all of its energy from gravity, and all of that energy is deposited in your unfortunate foot.

Kinetic energy is (average) force times distance; whether you’re winding a spring, starting a fire (with friction), firing projectiles, or crushing your foot.  The energy the object gains when falling is equal to its weight (the force of gravity) times the distance it falls.  The energy the object uses to bust metatarsals is equal to the distance it takes for it to come to a stop times the force that does that stopping.  S0, D_{fall}F_{fall} = E = D_{stop}F_{stop}.

The distance times the force that gets an object moving is equal to the distance times the force that brings that object to a halt.

The distance times the force that gets an object moving is equal to the distance times the force that brings that object to a halt.

Of course, the distance over which the object slows down is much smaller than the distance over which it sped up.  As a result, the stopping force required is proportionately larger.  This is one of the reasons why physicists flinch so much during unrealistic action movies (that, and loud noises make us skittish).  Something falling on your foot stops in about half a cm or a quarter inch, what with skin and bones that flex a little.  Give or take.

Bowling balls; keeping pediotrosts employed since.

Bowling balls: keeping podiatrists gainfully employed for 700 years.

So, if you drop a 10 pound ball 4 feet (48 inches), and it stops in a quarter inch, then the force at the bottom of the fall is F = \frac{48}{0.25}10lbs \approx 2,000lbs.  This is why padding is so important; if that distance was only an eighth of an inch (seems reasonable) then the force jumps to 4,000lbs, and if that distance is increased to half an inch then the force drops to 1,000 lbs.

The bowling ball picture is from here.

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25 Responses to Q: When something falls on your foot, how much force is involved?

  1. Dustin McPhate says:

    I think you meant 4000 lbs not 400. In fact 10(48/.125)=3840.

  2. Karl says:

    How do I metric system?

  3. The Physicist The Physicist says:

    @Karl
    There’s a subtlety there I was worried would distract from the point. “Pounds” are a measure of force, so they fit very naturally. “Kilograms” are a measure of mass, so when you talk about “weighing” a certain number of kg what you really mean is “the force experienced by X kg in Earth’s surface gravity”. X kg experiences 9.8X Newtons of force (9.8 meters per second squared is the acceleration of Earth’s gravity).
    However! If you just ignore all of that and think of kg as just being the weight of an object (instead of its mass), then everything works out in basically the same way. Nobody measures in Newtons anyway (for reference, 1000 N ≈ 225 Lbs).

  4. Raine says:

    I broke my foot dropping a 10 pound bowling ball on my foot. So wtf are you guys Saying?

  5. Ammar says:

    May I know how to calculate if a polycarbonate sheet rated to take 2 kg weight dropped from 1.5 meters can withstand a falling bullet exerting what is rated at 30 lb-ft impact force?
    My calculation from your D*W above says that the sheet can withstand about 22 lb-ft force, is this correct or am I missing something? I have no data on the “bounce” or travel of the sheet surface, i just know that the sheet takes that load dropped from that height.
    Many thanks

  6. Liz says:

    Well Raine it depends on how tall you are do properly determine how much pressure slammed onto your foot.

  7. Marilyn says:

    I am looking for the answer to this question:
    What is the impact of an 18 pound object falling, 12 inches, onto a 50 pound child who is 4’3″ tall?

  8. Spaace94 says:

    My friend dropped a stationary mortcycle wieging 700 punds by the owners manual . and well its swolen he can barley walk on it 1st day in from a tipsy last night lol its swolen middle of foot is where impact was but his toes are to ? Size 12 shoe …. Were gna just give it another 2 days or shld we make a splint

  9. ron says:

    how about 50 lbs of potatoes on top of your head? my neck and head were not strong enough to stop it though. Free fall about 8 feet

  10. Robert says:

    Scenario: I have a 700 lb motorcycle which was blown over by the wind. The motorcycle was previous leaning at about a 50 degree angle and was toppled in the opposite direction . This meant that it first had to blown past 90 degrees and then past the 90 degree tipping point.
    My first question is how much wind would it take to move 700 lb object? My second question is how much weight would have to be put on the opposite side in order to stabilize the motorcycle and prevent it from being blown over? The only part that may be difficult to compensate for is that the motorcycle had a cover on it which may have acted like a sail.

  11. Dana Esparza says:

    I flew off top a ladder from 35 feet on to my face on an asphalt curb infront of the home owner 20 feer away.And I was 225 lbs with 15 lbs of climbing gear on.Whats my impact.Or gforce if you may..

  12. Pingback: Ways a Messy Garage Can be Dangerous

  13. don gregg says:

    Please help me I’m very worried about my 37 year old son he was on the rocks next to the pier fe sliped on seaweed while walking modertly fast feet flew out from under him his body was paralell to the large.flat rocks he landed on the back of his head first main brunt of impact on about a area the size of a 50 cent coin. He was knocked out does not know how long some guys helped him up walked him to his car like an idiot he drove home. He called and I told him I live 1200 miles from him if he didnt go to emergency I would call 911 in his area for a ambulance so he went dr said severe concussion no brain bleed or swelling set him home said if head hurts In morn back to hospital..what I want to know is how hard his head heat that 6″ thick rock.force of impact.i can do it but im so upset I cant think straight.
    .

  14. paul says:

    ok so I have a 50 lb object falling one foot. that equals 50 ft lbs. if it is now at 3 feet, how many foot pounds is it? or do I just multiply by three.

  15. The Riddler says:

    Ok, now the real question. The Undertaker choke slams Mankind on top of the hell in a cell cage. The force was enough to break through the fencing of the cage causing him to fall the remainder of the distance onto the mat. How much force was there when he hit the fence, and how much on the ground. Let’s guess that Mankind was 300 lbs. and the chokeslam was a fall from about 4 ft. to the fence. The cage was another 16 ft roughly? Help me out here.. How is this man alive?

  16. Steve says:

    I had a 24lb steel hitch drop onto my bare head from a height of 10ft. How much force did I experience?

    Gave me a concussion, but I’m wondering how much trauma may be undetected.

  17. Linda says:

    A 44.5 lb. microwave slid down a 9 step ladder that stood at approximately 11 feet high ( top of the rails), the microwave didn’t free fall, but, slid down the rails at a diagonal angle of 60 degrees and hit me in the face. The lowest point of the rails was approximately 4 feet.

  18. Paul says:

    I am trying to figure out which rating do I need for a bullet proof vest: Knife Resistant Level 1 or Knife Resistant Level 2 . here are the energy (joules) ratings: Energy (joules) 24 36 33 50.

    How do I determine which rating I need?
    I know 17.7 foot-pounds = ~24 Joules, but what is that in real world physical examples?

    Thanks

    Paul

  19. Ryan Buikema says:

    I fell 9 feet with a collapsing stairway, landed on the now pointed upward unfinished steps, which then contacted approximately 6 square inches of my 250 lb body.

  20. Paul F. says:

    I weigh 360 pounds and am 6’2″ tall. Walking on concrete my feet slipped out from under me and my butt being 3 feet from the ground slammed into the concrete. How much weight is that like? A week later I fell again only I went up about half a foot before crashing down to concrete. A total fall of 42 inches of 360 pounds. How much weight is that like?
    Need this info to get my doctor to understand it was no small fall.
    Thanks, Me no math wiz.

  21. Frank says:

    So if I’m dropping 9,5o0 lbs from 48″ and the pile goes down 2″ is
    9500(48/2) correct?

  22. Jay says:

    Ok simple laymans terms. I want to build a power hammer it will have a 25 pound steel bar attached to the handle. It will drop from 24 inches to a stricking anvil. What is the force in pounds I can expect with each hit.

  23. Zork says:

    Tomorrow, I will be having a 200 pound woman stand on a chair 2 feet high and jumping on to my stomach. How much weight is that?

  24. RK says:

    I broke my head trying to sort out these calculations in the imperial system (and I’m an American).

  25. Paul F. says:

    Physicist; It’s nice to have an equation to work with. However I have no way to express this because I do not know how to type a fraction. Look above and you will see my query.
    Wanting to know how much force is exerted on my back from two falls.
    My butt being half the distance of my height from the ground would be 36 inches. The weight of the object ( me ) 360 pounds. The ground is 36 inches away from the contact point on my body, my hips.
    The surface I hit was nogive concrete. So you say above the stopping distance in your example is 0.25. Mine was 36 inches falling and immediate stop.
    Less than a week later I fell on my lower back after slipping on loose gravel where my thrust was up first then down on concrete. I estimate 6 inches more on that fall so 42 inches with an immediate stop of 360 pounds.
    I was just trying to estimate how much weight would it take to simulate that if I were lying on the ground? 360 pounds or would it be like more weight. OH well I guess there are just some equations even physicists can’t figure out.
    Thanks anyway.

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