When accelerating upward off a trampoline....

In summary, when accelerating upward off a trampoline, the acceleration-time graph would depict an initial acceleration that is greater than 9.8 m/s^2, as the force from the trampoline's elasticity overcomes the force of gravity. However, as the person reaches the highest point of the bounce, the force from the trampoline decreases and the force of gravity becomes greater, causing the acceleration to transition to downwards. The net force in this situation would be upwards, as the person is still in contact with the trampoline.
  • #1
Sebkarp0
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Homework Statement


When accelerating upward off a trampoline, how would you depict this on an acceleration-time graph? I know kinematics is the study of motion without a strict regard to the forces that are capable of changing motion, but according to Newton's 2nd law, an object accelerates in the direction of the net force. Thus, when you accelerate upward off the trampoline at the very beginning in a very small fraction of time, this force would have to overcome the person's force of weight right? So my question is this: would you display this initial acceleration as being greater than 9.8 m/s^2 or would you show the net acceleration on the acceleration-time graph (that is, would you put a number like 10 m/s^2 or 0.2 m/2^ respectively). I guess the same applies when you land back on the trampoline and accelerate in the positive direction to slow down... I would be grateful if someone could explain this to me. Thanks!

Homework Equations


F=ma and kinematic equations for free fall.

The Attempt at a Solution


I can't decide on the acceleration offhand...
 
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  • #2
What is "the very beginning" of the event? Is it when you are moving downward and your feet are just barely touching the trampoline? Is it when the dent your feet are making in the trampoline at its maximum depth and you have just come to a stop before starting back upward? Or is it when your feet are about to leave the trampoline?

Pick one and then figure out what forces apply at that event and what their relative magnitudes are.
 
  • #3
jbriggs444 said:
What is "the very beginning" of the event? Is it when you are moving downward and your feet are just barely touching the trampoline? Is it when the dent your feet are making in the trampoline at its maximum depth and you have just come to a stop before starting back upward? Or is it when your feet are about to leave the trampoline?

Pick one and then figure out what forces apply at that event and what their relative magnitudes are.
When your feet are about to leave the trampoline and you accelerate upward.
 
  • #4
Sebkarp0 said:
When your feet are about to leave the trampoline and you accelerate upward.
What force is causing you to accelerate upwards when you are about to lose contact with the trampoline?
 
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  • #5
This is very similar to what happens with a mass and spring in simple harmonic motion. Do you know how to analyze that situation? If so, when the mass is at its lowest point and has stopped moving downward, in terms of the spring constant k and the displacement x from the equilibrium position, what is the net force on the mass (and in what direction)? If m is the mass, what is its acceleration?
 
  • #6
haruspex said:
What force is causing you to accelerate upwards when you are about to lose contact with the trampoline?
Im not sure exactly what force, but I am guessing the elastic force of the trampoline when you push down initially. This is not a question that requires an exact acceleration, as it is meant to be a simple sketch of an approximation of what the graph should look like. I was just curious whether the acceleration you would put on the graph should be higher or less then the acceleration of gravity (i.e., the total acceleration without regard to gravity or the net acceleration). Sorry if this is a bad question, as it isn't really asked in the original question. I was just curious. I'm still in high school so my physics skills are not robust.
 
  • #7
When the trampoline and the person is at the lowest point, the acceleration can be 3 g upwards or more (so the force corresponds to 4+ g). When the person is just about to leave the surface of the trampoline, the upwards force from the trampoline is less than the force from gravity, so the acceleration transitions to downwards a bit before a person leaves the surface of a trampoline.
 
  • #8
Sebkarp0 said:
Im not sure exactly what force, but I am guessing the elastic force of the trampoline
If you are just about to lose contact with the trampoline, it is amost flat, so there will be hardly any force. Meanwhile, another force is acting in you. Which way would the net force be at this point?
 
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1. How does the force of the trampoline affect the acceleration when jumping upward?

The force of the trampoline is what allows you to accelerate upward. When you push off the trampoline, the surface of the trampoline exerts an equal and opposite force on your body, propelling you upward.

2. Is the acceleration when jumping upward off a trampoline always constant?

No, the acceleration when jumping upward off a trampoline is not always constant. It depends on various factors such as the elasticity of the trampoline, the amount of force you exert, and your body's weight and mass.

3. How does the angle of your body affect the acceleration when jumping upward off a trampoline?

The angle of your body can affect the acceleration when jumping upward off a trampoline. By keeping your body straight and pushing off the trampoline at a 90-degree angle, you can achieve maximum acceleration. However, if you lean forward or backward, your acceleration may be lessened.

4. Does the height of the trampoline affect the acceleration when jumping upward?

Yes, the height of the trampoline can affect the acceleration when jumping upward. The higher the trampoline, the more potential energy you have when you jump, which can result in a greater acceleration when you push off.

5. What role does air resistance play in the acceleration when jumping upward off a trampoline?

Air resistance can slightly affect the acceleration when jumping upward off a trampoline. The denser the air and the larger the surface area of your body, the more air resistance you will experience, which can slightly decrease your acceleration. However, for most trampoline jumping scenarios, air resistance is minimal.

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