Work & Energy

What’s the Big Idea‽

We know what work and energy per their colloquial definitions, but what do they mean in physics lingo? This lab explores the relationship between work and different forms of energy.

Procedure

This lab was like three mini-labs wrapped up into one big lab. So that means three mini-procedures!

Mini-Procedure #1

For the first of three mini-procedures, we will need:

• a 1.0-kg mass;
• a meterstick;
• a force probe;
• a Vernier LabQuest;
• a laptop.

Essentially, our objective was to do work on the mass and measure its energy. To do so, we attached the force probe to the top of the mass and lifted it approximately a meter, as performed in the following video:

We averaged the force recorded by the Vernier LabQuest and measured the mass’ displacement with the vertically placed meterstick.

Lifting a Mass
Trial	Mass	Average Force	Displacement	Work
1	1.0 kg	9.75 N	1.00 m	9.8 J
2		9.69 N	0.79 m	7.7 J
3		9.86 N	0.80 m	7.9 J

To calculate the amount of work for each trial, we used the formula W = Fcos(θ)d, where W is the work done on the mass, F is the average measured force, θ is angular difference of the displacement and the applied force, and d is the displacement.

We know that the mass goes from having no potential energy to having potential energy (PE) equal to mgh, where m is the mass of the mass, g is the acceleration to do gravity on Earth, and h is the height of the mass. This can also be described using the formula W = PE. Therefore, the work done should be equivalent to the potential energy the mass has after its displacement. In fact, it does! Notice how the average force is roughly equivalent to the acceleration due to gravity on Earth, which is 9.8 m/s². Calculating mgh results in the very same value.

Mini-Procedure #2

For the second of three mini-procedures, we will need:

• a spring;
• a meterstick;
• a force probe;
• a Vernier LabQuest;
• a laptop.

Similarly to the first mini-procedure, we needed to measure force and displacement. However, for this mini-procedure we stretched a spring instead of lifting a weight.

Fig. 1 The setup used to stretch the spring.

Once we had everything set up, we held the end of the spring and stretched it, using the Vernier LabQuest to measure the force and a meterstick to measure the spring’s change in length.

Stretching a Spring
Trial	Maximum Force	Displacement	Spring Constant	Work
1	4.58 N	0.010 m	458	0.023 J
2	7.25 N	0.015 m	483	0.054 J
3	9.96 N	0.020 m	498	0.100 J

Calculation of work was identical to the first mini-procedure, using the formula W = Fcos(θ)d. Also similarly, the spring goes from having no potential energy to having potential energy (PE), but this time it should be equal to 1/2 kx²., where k is the spring constant and x is the displacement. This situation can be expressed as W = PE or Fcos(θ)d = 1/2 kx², allowing us to calculate both the work done as well as the spring constant. Repeating our calculations with all three trials yields consistent results for the spring constant.

Mini-Procedure #3

Unfortunately, the third and final mini-procedure was never completed. However, if we has completed it, we would have needed:

• a dynamics cart;
• a track;
• a force probe;
• a Vernier LabQuest;
• a laptop.

And look too, there’s a lonely empty chart. We would have been able to accelerate the cart towards a force sensor and measure the amount of force it applied, but alas, we ran out of time.

Accelerating a Cart
Trial	Average Force	Displacement	Time	Acceleration	Work
1
2
3

However, we can still explain what we would have been able to do with the data. Again, we would be able to take the average force (one-half of the measured force) and multiply it by the cart’s displacement to get the work done, i.e. using W = Fcos(θ)d to do our bidding. But I think we’re kinder than that. Anyways, we know that the cart starts out with no energy but gains kinetic energy through the application of work, yielding the formula W = KE, which can be reincarnated as Fcos(θ)d = 1/2 mv². This would have allowed us to calculate the cart’s average acceleration and verify the relationship between the work done and the energy gained.

Takeaways

Even without the last mini-procedure, this lab allows us to answer the following Essential Questions:

1. How can you measure the work which is done?
2. How does the work in each case relate to the change in the energy of each system?
3. How can you measure the energy of each system so that it can be compared to the work that was done?

So, what did we learn?

1. The work which is done is equivalent to a force applied at a distance. Therefore, it can be measured by taking the product of the average force and the displacement caused by that force.
2. The change in work directly relates to a change of energy in each system. In the first two mini-procedures, we noticed that work caused an object with no energy to gain potential energy.
3. Since we can use the measurements of the force and displacement of an object, we must use a different method to measure the energy of each system. However, this varies for each system. Gravitational potential energy can be measured using the mass and height above the ground of an object, whereas elastic potential energy can be measured using the spring constant and change in length of the object being stretched. As for kinetic energy, it can be measured using the mass and velocity of the object. In a given system, the work should be equivalent to the change in energy, assuming the its conservation

Well, that’s all for now!