Energy Transformations in a Falling Ball

This assignment delves into the concept of energy transformations through the example of a falling ball. It begins by explaining the initial gravitational potential energy (GPE) possessed by the ball at rest. As the ball falls, GPE converts into kinetic energy (KE), which increases with velocity. Upon hitting a spring, the KE transforms into elastic potential energy (EPE), storing energy within the spring. This EPE is then released back into KE, propelling the ball upward until it reaches its maximum height and converts the KE back to GPE. The cycle repeats as the ball falls again. The assignment also provides a formula to calculate potential energy based on mass, gravity, and height, using a specific example with a 5 kg ball resting at 0.2 meters.

Engineering mathematics 1
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Engineering mathematics 2
The ball is placed at a height of 0.8 meters. First at this point is a not-zero point. The fact
that the ball is not at zero place makes it to have gravitational potential energy, EPE. At this
point, ball is resting and the kinetic energy is zero. When the ball is released, it acquires kinetic
energy as it gains velocity down. The amount is the kinetic energy is depended on the amount of
the speed which the ball gains (International Conference on Ubiquitous Information
Technologies & Applications & Han, 2013). As the ball fall on the spring, elastic potential
energy is experienced before it bounces back to a certain height. At this point, the Kinetic energy
is converted to elastic potential energy. Then the elastic potential energy will be converted to
kinetic energy and the ball gains some velocity moving upward. The ball will move to a height
when the velocity will be zero and unable to move further. The kinetic energy will transform to
gravitational potential energy, which is non-zero since the ball is at height. The ball will start
falling again and it acquires kinetic energy. The energy changes are GPE to KE to EPE then to
KE to GPE at top again (Tavakoli & Southern Methodist University, 2011). This experiment can
be based on the physical phenomenon when one is playing lawn tennis. The changes in energy
will be similar between these two instances. The tennis ball will start at GPE then move to KE
and when it hits the ground it gains EPE as it bounces, which is then transformed to KE.
The amount of potential energy, which the spring is storing at the time the ball comes to rest is
given by;
Potential energy = m* g* z
Where M = mass of the resting object
G = gravitational acceleration
Z = height at which the object lies

Engineering mathematics 3
In our case, the ball has a mass of 5 kg, at it rests at a height of 0.2 meter
Therefore potential energy is;
P.E = 5 * 0.2 * 9.81
= 9.81 kg.m2/s2

Engineering mathematics 4
References
International Conference on Ubiquitous Information Technologies & Applications, & Han, Y.-H.
(2013). Ubiquitous information technologies and applications: CUTE 2012. Dordrecht:
Springer.
Tavakoli, T. A., & Southern Methodist University. (2011). Gravity powered locomotion and
active control of a family tree of robotic mechanisms. (Dissertation Abstracts
International, 72-7.) Dallas, Tex: Southern Methodist University.