Question on pogo-stick physics

Hello,

I have no physics education at all, so this might come off a little vague.

The scenario: During a sustained jumping resonance, On a pogo-stick or trampoline, the user's downward mass is storing energy in the springs which eventually will try to force the user back up. But due to the dampening of gravity, the spring back up will not be as high as the one before. So the user has to press down at the right time to efficiently add force to the jump and thus achieve a sustained jumping resonance.

the Question: How much is this extra force? I guess I am interested in how much this extra force, at the most efficient time, is compared to the force from a stand-still, without the added momentum of the stored spring energy, to reach the same height?

would there be a big difference? would the well timed jump added to the spring force be that much more efficient than a jump from stand still?

Thanks for any help.

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Hi Shillbags,

You are correct that, as the spring compresses, energy is stored which is used to allow the mass to rebound, but it is actually gravity itself which is facilitating this. The user is pulled down by gravity, the spring compresses, and energy is stored in the spring.

The spring exerts a restoring force opposite its displacement,and in this case, opposite gravity. The restoring force increases as the compression increases. Eventually, you can imagine the spring force overcoming gravity, causing the mass to come to a halt and eventually rebound upward. You can picture the same thing when, say, a rubber ball bounces off the ground. The ball will deform a bit, and its elasticity will try to hold the ball together in its natural shape. This elasticity and deformation causes a spring force, which will rebound the ball off the ground.

Now, when you speak of dampening forces, gravity does not do this. Friction is what you're after, where things like air resistance and energy lost due to the mechanism of the spring reduces the overall amount of energy, and thus makes the rebounded height lower than the initial height. Back to the ball analogy, when you hear the ball bounce, that sound is energy lost due to the collision between the ball and ground.

When you talk about maintaining a constant bounce, and ask how much force should be applied, and when, it's a bit of a vague question. What causes this perpetual action is that, as the spring contracts, the user needs to assist the bounce by compressing the spring further than it naturally would, causing the spring to store extra energy, and thus push off the ground with more energy than an "unassisted" bounce where no extra action is taken by the user of the pogo stick.

The amount of extra push required would depend on how much energy is lost in the rebound process. This can be determined by observing an "unassisted" bounce, and comparing the maximum height of each bounce. The maximum height (ignoring air resistance) is a measure of the kinetic energy of the system right after the pogo stick leaves the ground. With a bit of kinematics number crunching, you can get an estimate of the amount of energy lost on each bounce, and thus the amount of additional energy required to sustain a constant bounce height.

Next, by studying the force applied by the pogo stick as you compress it, you can determine how much more the spring in the pogo stick must be compressed in order to provide this energy. The mass of the rider and pogo stick should be known.

rcgldr
Homework Helper
How much is this extra force?
As mentioned in the previous post the extra force has to be enough to overcome any losses that occur during each bounce.

most efficient time
In terms of extra force, there is no optimal time. In terms of minimal movement, the optimal time centers around the point of maximum compression and force. Work done equals force times distance, and if the work done is constant, then distance is smallest when the force is highest. In the case of a competition trampoline, you can lock up your legs and achieve fairly high bounces by just circling your arms with proper timing.

compared to the force from a stand-still
I don't know if maximum height can be acheived from a stand still on a pogo stick, but it's not humanly possible to do on a trampoline where the bounces can be over 15 feet (from feet to trampoline surface).