O Physics:How does jumping work?

[rantermanter]

I've been thinking about impulse, jumping, and related problems. Here is an example:

You have two Masses A, and B connected by a loose inelastic massless string. Mass A is on the ground and you throw mass B straight up. Mass B will have velocity v_bi at the moment the string becomes tight. What velocity, v_bi is required to make the two masses lift off the ground?

[Note: I've been considering the moment the string becomes tight as an inelastic* collision between mass A and B]

I keep trying to solve the problem different ways but I keep coming to the conclusion that the system lifts off the ground for any v_bi greater than zero and this does not make intuitive sense.



*I had previously accidentally said elastic

 

[NateTG]

Well, the moment the string becomes taut is probably closer to a perfectly inelastic collision, but that's not likely to change your result.

It might be instructive to determine the peak tension on the string.

 

[Hootenanny]

I'm not sure but one could possibly consider energy here? Correct me if I'm wrong but the we could write an equation as;

$$V_{bi} > \sqrt{2gl}$$

Where l is the length of the string.

~H

 

[rantermanter]

Nate:
The peak tension on the string would be a force. The impulse applied on Mass A from the collision is this force times an infinitely small time interval. This means that for an instant the upward acceleration is infinite. I'm having trouble dealing with infinite accerlations during infinitely small periods of time.

Hootenanny:
The length of the string does not matter. It only matters that the two masses "collide" at some time (when the string is taut)

 

[Andrew Mason]

Nate:
The peak tension on the string would be a force. The impulse applied on Mass A from the collision is this force times an infinitely small time interval. This means that for an instant the upward acceleration is infinite. I'm having trouble dealing with infinite accerlations during infinitely small periods of time.

Hootenanny:
The length of the string does not matter. It only matters that the two masses "collide" at some time (when the string is taut)

The force is not arbitrarily large. It is limited by the weight and acceleration provided by the string to A.

The string supplies an impulse to B which transfers some of B's momentum to A. If you have a completely inelastic string, the force will be enough to exceed the weight of A. This will start to lift A, so the force will be $F = m_Aa + mg$. It will only last long enough to stop B.

AM