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).