What we did: In this lab, our goal was to accurately predict the time it would take for the hanger on a modified Atwood machine to land on the top of a moving cart. Before making our predictions, we collected data that we would later compile together to make the final prediction.
This is a picture of the cart on the track, the 500g weight we added to the top, and the hanger
This is the track the cart ran on
This is the cart the hanger would land on
We started off drawing a free body diagram for the cart on the track to better understand what causes its motion. In this case, we assumed that friction was negligible, so the unbalanced force is in the direction of the tension exerted on the cart from the hanger. We were able to figure out the Fn and Fg’s of the cart (which are balanced), by weighing the cart and the hanger, and then adding the 500g weight that was placed on top. The reason why the cart and the hanger were both weighed is because we were trying to find the mass of the ENTIRE system, therefore everything needed to be weighed. The weigh in grams of the cart and hanger was 551.8g, and we added a 500g weight to the car. After adding the two together, we came up with 1051.8g. To convert to kilograms, we had to move the decimal 3 places to the left which gave us 1.051kg, and then we multiplied by 10 to get newtons, which is where we got 10.51N.
As previously mentioned, the net force of the cart came from the hanger which was exerting tension. To find out the value of the tension, we weighed just the hanger and got 51.1g which is equal to .511N.
After collecting the data for the cart on the track, we then moved on to the moving cart on the ground. We ran 4 trials with the motion sensor then averaged the values together to get an average velocity of .325m/s.
| Velocity for Cart 2 | |
| Trial 1 | .32 m/s |
| Trial 2 | .34 m/s |
| Trial 3 | .32 m/s |
| Trial 4 | .32 m/s |
| AVG V | .325 m/s |
After finding the average velocity, we needed to solve for the acceleration of the cart which we would then use to calculate the time it should take for the hanger to hit the cart. To find acceleration, we had to use the formula a=Fnet/mass. As previously mentioned, the Fnet of the system was the tension, which was .511N, and the mass of the entire system is 1.051kg. After diving the two we got an acceleration of .486 m/s^2.
We then used the formula: change in x(displacement)=1/2a(acceleration)t(time)^2+vi(initial velocity)t(time). We were solving for time, but in order to do that, we needed to first have the displacement of the cart on the track from its starting point to the distance it takes for the hanger to hit the top of the cart on the ground. Displacement is found using final position-initial position, so it’s initial position on the ramp was at 169 cm, and the final position was 98 cm. We subtracted the two and got a displacement of 71cm. With that value, we plugged it into the formula along with the acceleration and solved for time which came out to 1.7 seconds.
Now that we had solved for the time, we could use that to solve for the displacement of the cart on the ground. To solve, we used the formula: change in x(displacement)=v(velocity)(time)+xo (initial position). We used the average velocity, the time we just calculated, and 0 for the initial position and came out with .5525 m which is equal to 55.25cm, the distance from the hanger in which we would place the cart.i
RESULTS:
To actually test our predictions, we placed the cart 55.25cm from the location of the hanger temporarily suspended in the air. One person was in charge of releasing the cart on the track while the other person timed when the hanger hit. To avoid human error, we started the cart before the designated mark and began the timer when it crossed the 55.25 mark for more accurate data collection. We ran the test a few times and our calculations proved to be accurate. The hanger landed on the cart after 1.7 seconds, so we did not need to calculate percent error. Even though our predictions were correct, next time I will make sure of the preferences for rounding calculations like average velocity and acceleration.
We measured the 55.25 cm from the point at which the hanger would hit the cart and then started the cart a little before that point
This is the hanger before the cart on the track was released
This is the hanger on the cart at the end of the experiment
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