Stretch an elastic and then stop at a position. A quick release of your finger can cause the elastic to snap back to its original state but keeping your finger on it will leave it motionless; you're in full control of what the elastic does. Whether you wait a few seconds, a whole minute or longer, the elastic will always snap back. A storage of potential energy is what is being experienced by an elastic and is a similar situation to a ball in your hand that will always fall to the ground, whenever you decide to let go of it. Whether it's the ball or elastic, both objects have the potential to be displaced and consequently do work.
The formula for elastic potential energy is as follows:
The formula contains the same variables as those in Hooke's laws; k is the spring constant, measured in Newtons/meter, and x is the displacement, measured in meters.
We can predict the elastic potential energy gathered by stretching the arm of the projectile launcher. We must use the previously found spring constant of the bundle of elastic bands (109 N/m) and we also must find the displacement of the elastic bands when stretched as the arm is brought to 90 degrees. We also must calculate the cosine of each product since each elastic lies on an angle inward from 90 degrees.
When measured, the elastic slanting 34 degrees inward stretched to 21.0cm while the elastic slanting 10 degrees inward stretched to 20.5cm.
Displacement of elastic 1 (34 degrees) = 21.0cm - 6.0cm = 15.0cm
Displacement of elastic 2 (10 degrees) = 20.5cm - 5.5cm = 15.0cm
Conservation of Energy
The concept of conservation of energy is easier to understand in examples such as this one where potential energy is involved. Like we defined earlier, potential energy is a stored energy that can be released, in this case by letting go of the catapult arm. This trigger creates a thrusting force in which we see movement; when potential energy is released, it doesn't just disappear somewhere but it causes a consequent event. This consequent event involves a different type of energy that is converted from the previous stored potential energy. This scenario can be generalized with the law of conservation of energy.
Like the law of conservation of mass, this law specifies that energy cannot be created or destroyed but can be transferred between different types of energies. In this case involving elastic potential energy, we see that as the potential energy is released, the projectile is given movement and therefore, we can say that there's been a conversion of energy into kinetic energy. This law can be applied to different situations such as a breaking car in which kinetic energy is converted to heat energy which is dissipated through as friction occurs.
The transformation of energy doesn't happen all at once either. When we are still holding the elastic, we observe no kinetic energy because the projectile is not in motion yet and therefore can say only potential energy is present. As the elastic is released from its stretch displacement, it begins to revert back into its equilibrium position. The closer it gets to equilibrium, the more potential energy is converted into kinetic energy. By the time the elastic reaches equilibrium, all of the potential energy will have been converted into kinetic energy.
Using this law of conservation of energy, we can algebraically find the velocity of the projectile since kinetic energy = (1/2)mv^2 and is equal to the previously found value of elastic potential energy.
