Question

Show whether energy is conserved for an object changing altitude. This could be anything from a object going down a ramp (with a minimum of friction), a pendulum, a object in freefall, or an object bouncing at the end of a spring. Take enough data points to show the type of function your different types of energy follows as the object moves. Include a graph (or several graphs) of energy (on the y axis) as the object progresses through the experiment (with an x axis of your choice), that shows the transfer of energy, and if total energy is conserved. You also need to find what percentage of initial energy was lost by the time the object came to the last data point. If you can account for some of the lost energy, then it would help. Include procedures, a data table (make sure you label your columns and rows for identification), correctly labeled graph(s), as well as summarize your procedures and the conclusions you obtained. There's no need to prove a complete conservation of energy to receive full credit, but design the experiment for a realistic scenario where you would expect the scenario to occur. Avoid any rotational motion.

Answer 1

A ball bouncing is a fun example.

Let the variable y represent the height.

Let the ball be initially at a height y=h (the ground is at y= 0).

The potential energy of an object is given by P.E = mgh

As the ball falls down, the amount of kinetic energy gained is

since h1 >h2 always (it is falling) the kinetic energy is GAINED (not lost).

Now, neglecting all the other forms of energy (example a charged ball getting repelled by the earth etc. or any other situation like that), we see that the kinetic energy and the potential energies are the only two energies and as one decreases, the other increases by the same magnitude.

Can this be proved? This is an experimental fact. Physics has to start somewhere getting it's facts from nature. In most books, the K.E change is equated to the negative change of the potential energy by considering the conservation of energy a priori.

Anyway , continuing with the experiment,

When the ball bounces, the realistic bounce is one in which some energy is lost. In an ideal world, the ball bounces perfectly and the moment it loses contact with the ground after the bounce, it has the exact same velocity that it had while coming down(just before itting the ground) but now pointed upwards. Neglecting air drag( in the idealised case), it goes all the way back to the original height.

In the real world, firstly, there is drag. So, the ball's velocity just before it hits the ground is less than . Then, when it collides and leaves the ground, the energy that it has is a fraction of the original energy. This fraction is called the coefficient of restitution.

So, the energy it has when leaving the ground is less than where gamma is less than 1 always.

Then, when it travels back up, the drag again acts on it and the ball reaches a height quite lesser than the original height h.

This process goes on and on, the ball bounces to a lesser height each time and finally settles down.