UFPM Challenge Problem

UFPM Challenge Problem

     

     Our goal in this challenge problem was to use our learned knowledge and skills to land our weight from our Atwood machine on a cart moving at a constant velocity. However, we couldn't let the cart with our weight go, as this would've removed the 'challenge' component from our task. Below is a table with all of the variables that our group found: 

We took our data by measurements. We took our entire system (The Atwood machine) and set it on a scale to find our system mass of 1.14 kg. Our weight of the hanging force (our F pull) was very easy to find, as it told us on the actual weight. Because this was an Atwood machine, we decided to ignore friction as a factor. Using a motion sensor, we found the constant velocity of our cart, which turned out to be .31 m/s. Another thing to note is that the distance of our cart from the landing zone is actually supposed to read 1 meter, not .79 meters. The .79 meters is actually the distance of the hanging weight to our moving cart on the ground, because the distance to drop won't be to the ground; we had to include the cart's height. 

     Now that we collected all of the data we could without equations, all that was left to do was to find the acceleration of our system and the time the weight would take to hit the cart. We used the equation a = F net/ mass, plugging in .5 for F net and 1.14 for our mass. We ultimately came out with the acceleration of our system to be .438 m/s squared. Next, we wanted to use our acceleration we just found to find the time it would take for our weight to hit our moving cart. To do this, we plugged our acceleration into the equation (Change in) X = 1/2 a * (Change in) Time squared + v(initial)(change in Time). Here's our work:

.79 = 1/2 (.438)t^2 + 0

1.58 = .438t^2

t^2 = 3.607

t = 1.899 seconds or t = 1.9 seconds

With this information, we now found the time it took our buggy cart to reach our drop point. It made it in 3.2 Seconds from 1 meter away. Because these two times didn't match, our group realized that we would have to change the distance from which to start our buggy cart to match our drop time of 1.9 seconds. Once we had our correct distance, we dropped our weight and started our cart at the same time. This led to a perfect test drop, with our weight landing directly on target (We have video evidence of our drop test, but due to complications I'm not able to put it up on this blog). Thanks to our group's knowledge of everything we've learned so far this year, we were able to put it all together to solve a challenge problem such as this one. I'm looking forward to utilizing even more of my physics skills this year!