Elevating

Elevating, Episode 1: What’s the Big Idea‽

December 22^nd, 2014—inhabitants of Grafton High have recently reported bizarre phenomena occurring at the local elevator. Several accounts describe unusual feelings of “weight shifts”, noting altered senses of weight while in transport. The reports have prompted unease in the community of scientifically-literate students who understand weight as being the gravitational force on any given object. A local group known only as the Super Six have attempted to explain the rumors, suggesting acceleration as a possible cause of these strange symptoms.

As a credible news source, we are obliged to tell you this image was retrieved here.

As the Super Six begins research, they realize that all their findings point to one culprit: their archvillain, AP Physics!

Elevating, Episode 2: Procedure

To investigate the correlation between perceived weight and the elevator’s acceleration, the Super Six return to their super-secret hideout to obtain the proper equipment to conduct their experiment: the Fantastic Force Plate and their truly secret weapon, the Vernier LabQuest. They rush to the elevator and, using their extraordinary Physics Powers, immediately configure the Fantastic Force Plate with the Vernier LabQuest to prepare for the real action.

For a second, silence. The enter the elevator cautiously, under the guise of civilians to avoid the compromise of their true identities. And, as a completely reputable news source, we have last-minute photographs capturing the Super Six in their attempts to fight crime and conquer AP Physics.

Two members of the Super Six—codenamed “Sam” and “Owen” apply their weight to the Fantastic Force Plate to measure the force they exert. Of course, being the amazing superhero team they are, the Super Six selected the members with the greatest deviation of masses to thwart AP Physics and minimize potential error. The elevator accelerates, but then—BAM!—AP Physics sneaks up on the entire Super Six! Weight-shifting ensues, as shown in our exclusive video clip below.

Clearly, the Super Six isn’t kidding around when it comes to justice, but AP Physics isn’t about to give up. Its anguish-inducing weight-shiftings torment them mercilessly! Upon (upwards) acceleration, they feel heavier, but as the elevator reaches its maximum velocity, the weight-shiftings stop, only to afflict them again upon deceleration, when they feel heavier. What will AP Physics do next‽ Will the Super Six survive this torture‽ Find out next time!

Elevating, Episode 3: Takeaways

Using their super secret weapon, the Vernier LabQuest, the Super Six escape the grasp of AP Physics just in the nick of time! They peruse their collected data, probing it for answers to the unexplained weight-shiftings.

Super Six Archive 98183447: Owen’s Data

Super Six Archive 76117103: Sam’s Data

Super Six Archive 57640556: Sam and Owen’s Data

“Aha!” someone exclaims. The Super Six finally notice that an increased force—caused by the upwards acceleration of the elevator—felt like an increase in weight, i.e. the purported “weight-shifting”. Likewise, a decreased force felt like a decrease in weight. Of course, they determine, these events occurred in a different order depending on the initial direction of the elevator. They realize AP Physics’ ploy all along—the sense of weight isn’t just affected by the gravitational force on an object, but the other forces as well! They return their results to the esteemed Dr. J. E., who succinctly details the specifics of the situation:

Courtesy of Dr. J. E.

The Super Six relate their conclusion back to the equation F = ma. The total force in the vertical direction is what is perceived as weight, regardless of the gravitational force. In fact, they realize, that the formula can be rewritten as F_G + F_E = m(a_G + a_E), where the superscript G denotes gravity and the superscript E denotes the elevator. When the elevator’s acceleration is downwards, the force is subtracted from the total force, making it seem like there is less weight, and more weight in the opposite case.

The Super Six finalize their conclusion, but then—SCREAMING! Horrible, ear-piercing cries for help. The Super Six hear a group of people shrieking from injustice, presumably AP Physics out on another weight-shifting spree. They pinpoint the sounds to the nearest amusement park, only imagining what wrongdoing their archvillain could cause on a ride with an intense downwards acceleration. “Weightlessness” is the word that comes to their minds as they sprint into the distance.

⁂

It’s nighttime. The Super Six have relinquished the rest of their energy, back at their super-secret hideout. Chinese food occupies the entire table, and all they do is eat. Oh wait—takeaways? Eh, oh well. Close enough.

Newton’s Third Law

What’s the Big Idea‽

N3L. Newton’s Third Law. Though we’re quite familiar with the idea that “For every action, there is an equal, but opposite reaction”, do we really know what it means? Time to investigate, to determine what Newton’s Third Law looks in a real, physical setting!

Procedure

For this lab, we used a Vernier LabQuest, a dynamics track, two (relatively) frictionless carts, two force sensors, and three different kinds of connectors. First we placed the track flat on the table and used the iPad to measure how level it was, adjusted its height as needed. We placed two dynamics carts on the track, each having a force sensor (one labelled Sensor A and the other Sensor B) on top of it, but facing towards each other. Next, we calibrated the force sensors as necessary and zeroed their values when they were experiencing minimal force. For one of the force sensors, we reversed the sign recorded values to account for the difference in direction.

In total, we performed 12 trials plus an extra trial just for the heck of it. The first four trials investigated two different methods of moving the carts and two different types of connectors. During the next four trials, we repeated these same steps but with an additional mass of 500g on the cart with Sensor A on it. The propreantepenultimate, preantepenultimate, antepenultimate, and penultimate trials primarily dealt with pushing the sensors towards each other in lieu of using a connector (bumpers were placed where the connector would have been). And finally, the very last trial had no major goal and used a spring as the connector between the carts. 

Above shows various setups for different trials. Counterclockwise from the top right: an additional mass on the cart; the carts attached by string; the Vernier LabQuest; the carts attached by a rubber band. Here’s a general overview of each trial:

Trial	Connector	Method	Additional Mass (Sensor A)
1	string	pull on Sensor A and Sensor B	0g
2	string	pull on Sensor A	0g
3	rubber band	pull on Sensor A and Sensor B	0g
4	rubber band	pull on Sensor A	0g
5	string	pull on Sensor A and Sensor B	500g
6	string	pull on Sensor A	500g
7	rubber band	pull on Sensor A and Sensor B	500g
8	rubber band	pull on Sensor A	500g
9	none	push Sensor A and Sensor B towards each other	0g
10	none	push Sensor A towards Sensor B	0g
11	none	push Sensor A and Sensor B towards each other	500g
12	none	push Sensor A towards Sensor B	500g
13	spring	none in particular	0g

The following images show the data for each trial sequentially.

Wow, that’s a lot of data. The thing is, it all boils down to the same conclusion!

Takeaways

The consistency among the thirteen trials, even the last one, is remarkable. To reiterate Newton’s Third Law, “For every action, there is an equal, but opposite reaction”. That shows itself quite clearly here—the data collected by the force sensors is is the same for each, just in the opposite direction! It didn’t matter if we changed the cart that was being pushed or pulled, the type of connector we used, or even the mass of one of the carts. Isn’t physics fantastic?

Atwood’s Machine

What’s the Big Idea‽

Ultimately, the goal of this lab is to answer three questions:

1. What are the variables that determine a system's state of motion (constant velocity vs. constant acceleration)?
2. What happens when the total mass of a system is kept constant, but the net force is varied?
3. What happens when the net force on a system is kept constant, but the total mass is varied?

Along the way, we’ll be discussing Newton’s laws of motion, inertia, equilibrium and disequilibrium, mass, velocity, acceleration, and force.  Luckily, we have the perfect tool to answer these questions: an Atwood’s Machine!

Procedure

However, before we can actually answer these questions, we need to make an Atwood’s machine. Turns out it wasn’t too difficult, at least this time. I can safely say that no major injuries were sustained*.

Fig. 1 Our beautiful Atwood’s machine.

Basically, we attached a photogate (at the top) to a metal rod, which supported the entire structure. In between the photogate’s sensors was a pulley with masses on both ends. To investigate equilibrium and disequilibrium, we could add and remove masses from each side.

Fig 2. Closeup of the pulley.

Fig. 3 Closeup of the masses.

But what would a lab be without Logger Pro? We used Logger Pro to take the data from the photogate and convert it into the velocity and acceleration of the pulley.

Fig. 4 QR code on Logger Pro used to log data on our iPads.

With everything set up, now to answer the first question!

1. What are the variables that determine a system's state of motion (constant velocity vs. constant acceleration)?

To answer this question, we experimented with directly applying force to one side (by tapping it) versus constantly applying a force (by adding a mass). For a nice visual, the latter looks something like this:

Fig. 5 Placing a 2g mass.

We completed three trials using this method. The first trial consisted of pushing one side of the Atwood’s machine, whereas the other two trials consisted of placing additional weight on it.

	total m	net m	side 1 m	side 1 Δm	side 2 m	side 2 Δm
Trial 1	100g	0g	50g	n/a	50g	n/a
Trial 2	102g	2g	52g	2g	50g	0g
Trial 3	105g	5g	55g	3g	50g	0g

Below shows Logger Pro’s output of the three trials, analyzed in the takeaways.

Fig. 6 Trial 1

Fig. 7 Trial 2

Fig. 8 Trial 3

On to the second question!

2. What happens when the total mass of a system is kept constant, but the net force is varied?

This question can be answered using the same strategy as the first, but with alterations. The video below shows what I’m talking about.

Fig. 9 Explosion of masses optional.

We performed three trials similar to the above, augmenting the mass by ±10g each trial.

	total m	net m	side 1 m	side 1 Δm	side 2 m	side 2 Δm
Trial 1	150g	50g	100g	n/a	50g	n/a
Trial 2	150g	30g	90g	10g	60g	10g
Trial 3	150g	10g	80g	10g	70g	10g

Each trial yielded telling results, once again, analyzed in the takeaways.

Fig. 10 Trial 1

Fig. 11 Trial 2

Fig. 12 Trial 3

Hark! Question 3 awaits!

3. What happens when the net force on a system is kept constant, but the total mass is varied?

This question is very similar to the last, so it only requires minor variations in the masses placed on each side. The difference in the masses of each side remained the same, but we consistently increased the amount of mass each trial.

	total m	net m	side 1 m	side 1 Δm	side 2 m	side 2 Δm
Trial 1	150g	50g	100g	n/a	50g	n/a
Trial 2	190g	50g	120g	20g	70g	20g
Trial 3	230g	50g	140g	20g	90g	20g

Fig. 13 Trial 1

Fig. 14 Trial 2

Fig. 15 Trial 3

Alright, so that’s the last of the data, time to delve into it!

Takeaways

As a refresher, below are the questions we attempted to answer with our three experiments of three trials each.

1. What are the variables that determine a system's state of motion (constant velocity vs. constant acceleration)?
2. What happens when the total mass of a system is kept constant, but the net force is varied?
3. What happens when the net force on a system is kept constant, but the total mass is varied?

Let’s look at the first one. This question directly relates to Newton’s first law of motion, which states:

“An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force” (Retrieved from the Physics Classroom).

Turns out, our first question was discussing inertia: the tendency of an object to remain in the same state of motion. We noticed that, when the two sides were in equilibrium (i.e. they had the same amount of mass), they remained at rest. However, upon applying a one-time force (such as a push), the two sides moved at a constant velocity (see Fig. 6). Since the forces were still balanced (after the initial push), we noticed that it continued at the same, consistent velocity. But upon applying a constant force that would unbalance the entire system, we observed different results (see Fig. 7 and Fig. 8). A difference in mass of the two sides causes one side to accelerate downwards and the other side to accelerate upwards. Weight is effectively the force of an object due to gravitation, and since the masses were unequal, the entire system was in disequilibrium. And, when the weight difference was greater, so was the acceleration.

As for the second and third questions, we’re looking at Newton’s second law of motion, which essentially states that force is equal to the mass of an object times its acceleration. In designing an experiment to answer the last two questions, we were able to explore this. When the total mass of a system is kept constant, but the net force was varied, we noticed that different trials (see Fig. 10, Fig. 11, and Fig. 12) yielded different accelerations, suggesting that there is a direct correlation between mass and force as well as between acceleration and force. When the net mass or the acceleration increases, so does the net force  (see Fig. 13, Fig. 14, and Fig. 15). When the net force is kept constant, but the total mass is varied, the trials still show a change in acceleration, due to the increased mass of the entire system.

*I just put that asterisk there to make it sound like injuries actually were sustained. But no, there weren’t any (at least that I was aware of).