Scott Lutes

April 4, 2013

Dr. Haag

Newton's Second Law

Purpose:

To study and measure the effect that forces have on the motion of a cart on a horizontal track.

Equipment:

Computer with Logger Pro software, lab pro interface, motion detector, horizontal track, cart, low friction pulley, string, paper clip weight hanger, regular weight hanger, slotted weights, triple beam balance, carpenter level, two mass bars, Microsoft Excel Software

Procedure:

1. First set everything up. Lay out the track and make sure it is leveled with the carpenter's scale. Attach the pulley system at the end of the track. Place the motion detector on the end of the track and connect it to the lab pro interface, turn on the computer and start the Logger Pro software and open it on the graphlab file. Find the combined weight of the cart and the two mass bars using the triple-beam balance.
2. Next discover the friction by placing the cart (with the two mass bars) on the track directly in front of the motion detector. Attach the string to the cart and place the other end on the low-friction pulley so it hangs off the end of the track. Than use the paper clip hanger and attach it to the end of the string at the end of the track. Add enough weight to the paper clip so when you give the cart a gentle push, it will move with a constant velocity meaning no acceleration. Record the results on Logger pro with graph lab. Once you determine that there was no acceleration in your trial, than you calculate for the friction with the equation: (mass)(gravity) – friction = (little mass +big mass)acceleration.
3. Now you will test the acceleration with different weights. Remove the paper clip hanger and attach the 50gram weight hanger to the string. Than put on an additional 50 grams (totaling to 100grams) on the hanger. Release the cart and study the results on Logger Pro. Use the quadratic fit on Logger pro in order to determine the acceleration of the cart. Repeat for a total of 5 trials, record the results on an Excel spreadsheet.
4. Than use the equation in part 1: mg – f = (m + M)a, or a = (mg – f)/(m +M) to determine your own calculated acceleration. Compare your calculated acceleration with the experimental acceleration and find the percent difference.
5. Repeat steps 3 and 4 with different masses: 150g, 200g and 250g.

Data:

Friction = (mass) * (acceleration)

F = (.00565 kg) * (9.8 m/s/s)

F = .055 N

Prediction 1 100grams	Prediction 2 150 grams	Prediction 3 200 grams	Prediction 4 250 grams
a = (mg – F) / (M+m) a = ((.1)(9.8) - .055) / (1.493 + .1) a = 0.581m/s/s	a = (mg – F) / (M+m) a = ((.15)(9.8) - .055) / (1.493 + .15) a = 0.861 m/s/s	a = (mg – F) / (M+m) a = ((.2)(9.8) - .055) / (1.493 + .2) a = 1.125 m/s/s	a = (mg – F) / (M+m) a = ((.25)(9.8) - .055) / (1.493 + .25) a = 1.374 m/s/s

Conclusions:

We ended up with some minor percent error's that was most likely due to a slight miscalculation in the friction. The most difficult part of the experiment was to find the friction. It is difficult to find an exact mass for the cart to have a constant velocity. If we used a slightly different weight, our calculation for friction would be off, since the friction is used on all of the calculations to discover the acceleration, One minor mistake in determining our friction would result in a miss-estimate to find a predicted acceleration. Our percentage difference included a maximum of 13% and a minimum of 3%, resulting in a total average of 8.2% error. I believe this was mostly due to our calculation error rather than the experimental error because the most difficult part was left to us to find the friction, and the experimental results were mostly taken from the machine tools we used including the motion detector and logger pro, and though these tools are not perfect, they will most likely conclude a better result than we can to find an appropriate weight to calculate friction. I did notice that the more weight we we added in the experiment the lower our percent difference was. We started off with 100g and and got a 13% difference in the predicted and experimental results. We ended with 300g and received a 3% difference between the two results. I have concluded that there is less room for error as the weight becomes more significant because our results become more exact as the weight increases. For instance it is easier to calibrate a scale with a 100g weight than it is with a 0.1g feather.

In our experiment we over-estimated our acceleration each trial. I have come to realize that if you over estimate the friction, you will under-estimate the acceleration. In our case we under-estimated the friction so our acceleration was over-estimated. This is discovered by simply looking at the equation: a = (mg – f)/(m +M), the higher the friction, the lower the numerator will become thus the lower the acceleration becomes.

In conclusion, we should have taken more time determining the friction in step number two. We should have carefully evaluated the friction between a spectrum of different weights in order to find the one resulting in the least amount of acceleration. Though we did study several different weights, we could have been even more precise up to the last fraction of a gram.