Lab #3: Non-Constant accelertaion problem

Purpose: This lab is meant for people to see that sometimes solving a problem using calculations and calculus is not the way to go. Because things can get complicated really fast.

For example this problem:

If a person were asked to solve for how far the elephant would go before coming to rest, it would a nightmare. The calculus to solve this problem is not impossible but difficult and time consuming.

However, there is another way to find the distance and time the elephant goes. That would be by using Excel and solving with numerical integration. By choosing an interval like 0.1 to set the time at and calculating the acceleration, average acceleration, change of velocity, velocity, average velocity, change in position and distance we will be able to find the time and position if we extend the graph far enough.

By extending the graph all the way down until the velocity almost reaches zero we can see the approximate time and distance found the elephant has traveled.

We were able to test other time intervals to see how close the approximation can get or how far estimate will be.
                                         0.05 sec:

                                        0.2 sec:

                                        1 sec:

As you can see all of the graphs had relatively the same time and distance gathered. Some being closer to the calculated actual then others.

26-Feb-2015 Lab #2:Free Fall, determination of gravity

Purpose: This lab is meant to prove the acceleration of a falling object without any external forces besides gravity is 9.8m/s^2.

The way we prove this is by using an a free fall body that is connected to an electromagnet. When the free fall body is released it will fall along side a strip of carbon paper and leave little marks indicating a certain distance it fell during a certain time.
 

 
















Once the spark generator has fallen the 1.5m distance, we take the piece of tape and measure the distances between the dots on the paper.

 The dots were hard to see so we darkened them with a pen and wrote the distances measured from zero. We are only meant to measure 11 dots because any more then that would be a little too much.

Once all of the distances were gathered we had to chart them on Excel along with a column for time, the change in distance, mid interval time and mid interval speed.

Then once that is gathered we were meant to create a graph of the mid-int speed vs the mid int time. By graphing this data we were able to gather our acceleration in cm/s^2.

After gathering our own acceleration, the whole class put all of there accelerations in a chart in order to figure out the deviation between us.

However, since our g value turned out to be really high a majority of the class took it out of their calculation. With our g value being so high it increased the average deviation significantly.

23-Feb-2015 Lab #1: Mass on an Inertial Balance

The purpose of this experiment is to determine the mass of the tray in order to find the period of the balance itself.

We used a stand and a c-clamps to attach the photogate at the same level as the balance. The balance is attached to a table using a clamp as well. There is also a piece of tape attached to the balance that is meant to sway between the photogate. The photogate is meant to record the period of the passing of the tape.

With this setup we had to add 100 grams to the balance and record the period.We continued all the way until we reached 800 grams. We also measured the periods of two unknown objects.
Unknown #1: phone
actual mass: 143g
0.370 sec
Unknown #2: motion sensor
actual mass: 191g
0.398 sec



 The graph below shows the increase in the period as more weight was added to the balance.

The formula we used to determine the mass of the tray was T=A(m+Mtray)^n. However, before we can actually use it we make the formula look like the linear equation by natural logging both sides.
By doing that our formula transformed into ln T = n * ln (m + M_tray) + ln A.

 Before we can make the line graph we have to create separate columns with the ln(period) and ln(m+Mtray).

So once the columns were developed we are able to create the best fit line. However, since we do not know the actual mass we have to guess until the correlation is 0.9999. We must find the highest the mass can be and the lowest the mass can be. We came up with a range of 311g to 282g. With the masses we came up with we plugged the values found into T=A(m+Mtray)^n and solved for m (which represents the unknown objects).

 The actual masses of the unknown objects are suppose to be at least within the values that are calculated.

Unknown #1: phone
actual-143g
lowest-145.3g
highest-146.8g

Unknown #2: motion sensor
actual-191g
lowest-195.6g
highest-197.9g

Since the values calculated are off by 2 or 3 grams for both objects there must have been some problems that may have accord during the actual lab.