Our challenge lab for our forces unit was partially cobbled together last minute–various other ideas we had weren’t going to work for practical reasons, or were going to be challenging for students in wrong ways, or involved mastery of material which had not been a focus of our time learning forces.

This is what we ended up doing:

- A plunger cart would be launched off an end stop (this produces a fairly reliable launch velocity with practice). Students had to measure the initial velocity. Some used photogates. Some used motion detectors. A typical launch speed is between 60 cm/s to 80 cm/s depending on which cart you use.
- Next, the plunger cart would be attached a string so it’s part of half-atwoods setup. That is the plunger cart would be pulled back a string that goes over a pulley. Once over the pulley hanging mass puts the string in tension.
- The goal for students was to predict the location of an obstacle on the track so that the cart would be stopped just before hitting the obstacle. Students could do this by either fixing the mass and predicting the distance; or choosing a distance and predicting the mass.

The rules were the following: students could take measurements of the starting velocity of the cart without the string attached. And students could take measurements with the string. But they couldn’t use the string and the endstop together until they were ready to make their predictions.

To determine the dynamics, students approached the problem a variety of ways:

(1) **Full theoretical treatment.** One groups took this approach. Choose a mass, apply Newton’s 2nd law to both the masses and solve analytically for the acceleration. Using the acceleration, determined the stopping distance.

(2) **Approximate theoretical treatment.** Two groups took an approach where, for a very light mass the tension in the straight should approximately be equal to weight of the hanging mass. One group who explicitly talked about how it was an approximation and why, I let them go with it. The other group needed some help to see this was on an approximation, so I made them actually calculate how different tension and weight would be (after the fact). They had a tension if about 0.2 N, and calculated that we’d expect a difference between tension and weight of about 0.07 N. So not terribly unreasonable. Both groups in this case picked the lightest mass you could hang off the edge (0.2 N).

(3) **Measure the Tension Directly:** Two groups decided to run the experiment with a force sensor mounted on the cart. Just measure how much tension force is exerted on the cart, and then apply Newton’s 2nd Law and kinematics to find the stopping distance.

(4)** Measure Tension Indirectly**: One group decided to just run the Atwood’s machine in order to speed up the cart (rather than have it slow it down), and measure the acceleration. From the acceleration, they could find the Net Force. Then assume that this same tension acts on the cart while slowing it down.

One group incorporated friction into their calculations, estimating that the rolling friction force was about 0.01 N. This changed their Net Force on the Cart from 0.18N to 0.19 N, which was enough of a difference to get a really good prediction.

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One of the interesting things about these challenges, is trying to meet students where they are at. For example, I had not intended to let students take an approximate theoretical treatment. But, I’ve learned it makes more sense to help students with their approach, then upheave them. I had also not expected students to measure tension indirectly–> because you really just measure the acceleration. But it made sense to students; “If I find the acceleration, and I measure the mass, I can get the net force acting on the object, by using Fnet = ma”.

Ultimately, this lab has a bit too much uncertainty to get great results. This is because the stopping forces required are pretty small. 0.2-0.5 N is what students typically needed. With forces this small, friction and measurement uncertainty is going to play a big role. That said, all but one group had pretty good results. Since the goal is to “NOT” hit the obstacle, students not taking into account friction places the obstacle further than needed. In talking with groups, students could make sense of why that might be the case. I think next time, if we keep this challenge lab, I would explicitly make it a bonus to explicitly consider friction.

Overall, the challenge lab was good in the sense that students had to wrestle with dynamics and kinematics; they took different approaches and used different equipment; everyone got pretty good results.

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