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PROBLEMAS RESUELTOS DE FÍSICA DEL CBC
(Leyes de Newton, vínculos)

26- A man weighting 50 kg jumps up with a take-off acceleration of 20 m/s².

a) What is the magnitude of the force that the floor exerts on the man?

b) How many times his weight is this force?

This exercise is super interesting for beginners. If you have already solved more than 30 dynamic problems you might find it boring and very simple. However, I will solve it whit a lot of detail and discussion thinking on beginners. If you are one of the others, make it on your own and come back to check the answer.

The essential, as in every dynamic problem, is the FBD (free body diagram). This consists of drawing each one of the bodies separately (a FBD for each) and indicating on each of them, with vectors, all the forces that act on it (Not the ones it makes on others… just the ones it receives!)In this case there is only one body we are interested at, and that’s the dude who hops. Here it goes:

 Only two forces act on the guy. His own weight, P, that is the gravitational force with which he is attracted to the Earth which is always vertical down. Also the contact force with the ground, C, that is generally normal (meaning perpendicular) to the ground and is usually called normal by popular masses, but they are wrong in adopting that name, it generates confusion. C, the contact force, will disappear instantly after the guy’s feet lose contact with the ground and the dude starts his free flight. As you might know, he will have an acceleration pointing down of 10 m/s², that is g. All of this is irrelevant for the author of the problem that is referring to the act of jumping… This movement of leg extension is done thanks to the contact with the ground and accelerates the man up, in this case at 20 m/s².

This problem confuses the inexperienced a lot, owning to the fact that they intuitively think that the guy jumps thanks to the force that he is doing with his own quadriceps (his legs, come on). But they are wrong! Nobody jumps or moves only by their own means. We always need another body pushing or stopping us, or whatever, in order to change our velocity.

In this case this body is the ground, that pushes us up with a force that we have called C. But this creates a conflict: why do we train our legs in order to achieve higher jumps every time… if the miserable floor is the one boosting us instead of our legs?

So as to answer this crucial question I will ask another one before: Which are the action and reaction force pairs acting on the man?

 Here you go, interacting bodies and pairs of interaction forces. W´ is the force with which the man attracts the Earth. C´ is the force exerted by the man on the floor, as wanting to sink it. Each one of them acts on a different body, which dynamics-in this case- we are not interested at. In both cases P and P´ are constant forces that don’t change with what the man does (unless he were doing a special diet, which we won’t know until the exercises´ guide is edited again).

However, C and C' are variable forces that depend on the attitude of the guy. If the dude stays quiet C will be the same as W. Yet, if the man decides to crush a cockroach (or jump)… then C will increase pretty much.

At this point we have already understood the mechanic of the jump: the man exert a huge force with his legs on the floor. The floor (as every other body in the Universe) is bound by a principle of action and reaction to return an equal and contrary force to the man. Conclusion: the floor doesn’t accelerates down because of being too massive, but the man is accelerated up and jumps in joy.

nd now the equation (stated with a frame of reference pointing up):

C — P = m a

C = m a + P

C = m a + m g

C = m (a + g) = 50 kg . 30 m/s²

 C = 1.500 N

Como P = m g = 500 N
 C/P = 3

CHALLENGE: What acceleration is this problem talking about if the feet are always in contact with the ground? What height does the dude reaches after launching?

 Todos los derechos reservados (no es que sean tímidos, callados, y los izquierdos extrovertidos... es que si transgredís esta norma te acuchillo). Eso sí... se permite su reproducción citando la fuente. Traducción gentileza de Celina Nassello. Última actualización ago-21. Buenos Aires, Argentina.