Momentum and Force: Solving Problem with Springs

[Bengo]

I've come across a few problems where it seems like momentum is acting like a force. For instance take a man wearing springs on his shoes who jumps high in the air and lands. The force down is mg and as he compresses the springs the force up is kx. At some point mg=kx but how can the man continue to compress the springs? Where does this force come from? Does this have to do with momentum or am I way off here? Thank you

 

[DrewD]

Force is the rate of change of momentum with respect to time ($\frac{dp}{dt}$ if you've had calc). In the (semi)static case $(p=0)\ \ mg=kx$ would be the farthest the person compresses the spring. When the person has gained momentum while falling, this is only the point where the (magnitude of the) momentum starts to decrease. When $mg=kx$, the net force is zero. As the spring is compressed more, the net force becomes an upward force which begins to decrease the downward momentum. The important thing to remember is that zero force does not mean zero motion (and thus momentmum). Zero force means that the momentum is not changing. Does that clear things up?

 

[Bengo]

Force is the rate of change of momentum with respect to time ($\frac{dp}{dt}$ if you've had calc). In the (semi)static case $(p=0)\ \ mg=kx$ would be the farthest the person compresses the spring. When the person has gained momentum while falling, this is only the point where the (magnitude of the) momentum starts to decrease. When $mg=kx$, the net force is zero. As the spring is compressed more, the net force becomes an upward force which begins to decrease the downward momentum. The important thing to remember is that zero force does not mean zero motion (and thus momentmum). Zero force means that the momentum is not changing. Does that clear things up?

That does clear things up. Thank you very much