Question

I'm wondering if one of you physics experts can help me with a practical application....I'm trying to determine when safety shoes are required for protection against the impact of a heavy item falling onto the foot. I used the calculator and learned that an 11kg object falling 1 m has a velocity of 4.43 m/s, kinetic energy before inpact 107.8 and the distance travelled after impact of 0.01m equals 10780 newtons. I'm having trouble understanding what a newton is and how many newtons will break a bone in the foot. I appreciate any help you can provide. Thank you very much.

Answer 1

The newton is the unit of force. 1 newton is force required to accelerate a mass of 1 kilogram by 1 m/s^2 i.e. \(F=ma\). One can gauge how large a force is by thinking of it in terms of weight. In the earths gravitational field, and object of mass 0.1 kg will have a weight of 9.8 N. So in your example, above, 10780 N would be the equivalent of about 1100 Kgs resting upon you.

Would this be enough to break bones? The issue here is not so much the force, but the pressure. Pressure is the force per unit area an object exerts upon another, i.e. \[P=\frac{F}{A}\]. A lady standing upon your hand with stiletto heels will exert a greater pressure (and hence localised damage) than a lady wearing flat, broad heels. It is the pressure that determines whether a bone will break or not, and hence it depends upon the shape of the object falling. Being hit on the foot with the spine of a hard back book will do more damage than being hit with the front cover of the book given the same impacting force. So when it comes to the 10780 Newtons, in your example, it would depend upon the area that it is spread over. I have no idea though on the amount of pressure a bone would take to break.

Answer 2

Its late at night, and i made an error in my statement. A mass of 1 Kg will have a weight of 9.8 N, not a mass of 0.1 kg (which would have a weight of 0.98 N). Apologies for any confusion I may have caused.