Energy of a Tossed Ball

What’s the Big Idea‽

When is energy conserved? When is energy not conserved? And how can we measure that energy? This lab explores these questions by investigating what happens to the energy of a tossed ball.

Procedure

First, we gathered the materials for the lab, which included a Vernier LabQuest and laptop, as usual, but also included a motion detector and a ball (for tossing purposes).

The completed setup.

Once everything was connected, we placed the motion detector flat on the table, tossed the ball directly upwards, and recorded the corresponding data.

The raw data from the LabQuest.

A much clearer readout of the above data.

Oh, and we also measured the ball’s mass with a scale:

mass

0.403 kg

The following table is a synthesis of three recorded points (one corresponding to after the release, one at the top of the path, and one before the catch), yielding data for the time, height, and velocity. This then allowed us to calculate the potential energy (using the formula PE = mgh), kinetic energy (KE  = ½mv²), and mechanical energy (ME = PE + KE).

position	time	height	velocity	PE	KE	ME
after release	1.299 s	0.375 m	2.580 m/s	1.482 J	1.341 J	2.823 J
top of path	1.598 s	0.805 m	0.002 m/s	3.182 J	0.000 J	3.182 J
before catch	1.865 s	0.464 m	-2.580 m/s	1.834 J	1.341 J	3.175 J

If the tossed ball demonstrates conservation of energy, only conservative forces (e.g. gravity) are acting on the system. Otherwise, a combination of conservative (again, e.g. gravity) and nonconservative forces (e.g. friction) are acting on the system. The calculated change in mechanical energy suggests conservation of energy, however, I think that the recorded point directly after release is incorrect. The change from 2.823 J to 3.182 J would only occur if an upward force was temporarily acting on the ball (such as a hand), therefore, this point is unsupportive of our conclusions. (However, in a way, it does show that the hand pushing up on the ball is somewhat like a nonconservative force, because it only acts in one direction.)

Ignoring the first data point, the change in mechanical energy from 3.182 J to 3.175 J makes much more sense. For the most part, the total energy of the system remains constant, suggesting that the most significant forces acting on the system are conservative. I presume the slight decline in energy can be attributed to friction in the form of air resistance (a nonconservative force) acting on the ball.

Takeaways

In this lab, we learned about conservative and nonconservative forces. Basically, as I just described, we can determine whether or not a system demonstrates conservation of energy by measuring its change in energy over a period of time during which forces are acting on it. If the change in energy is minimal, work that displaces an object is done by conservative forces. Contrastingly, if the change in energy is significant, this displacement is partially being done by nonconservative forces.