Lab 6: Propagated Uncertainty

In this lab, we are going to measure the error that we get when we measure things.

For this lab, I had three identical cylinders. One was made of bronze, one silver, and one gold.

Because the scale could measure to a minimum of .1 grams, that is the propagated uncertainty for these three items

The density of bronze is supposedly 9.29.

However my calculations make it 9.69 cm^3 + or - .1 grams

 My calculation of the density silver was 3.54 cm^3 + or - .1which was severely wrong

as the density of silver should be 10.49

My calculation of gold is also extremely wrong as i received 10.86 cm^3 + or - .1 compared to 19.3

Using the equation on the bottom part of the image I get 

silver: dP/p = .015%

bronze: dP/p = .016%

gold: dP/p =  .016%

In the second part of the lab we have to find propagated uncertainty of a unknown mass

For this system the equation looks like 

Fy= mg- F1sin(x) - F2sin(y)

Fx=F1sin(x) = F2sin(y)

F1=3.5-4.5 N

F2 = 2.7-3.7 N

x = 47-49 deg

y = 37-39 deg

By using the y side of the equation we can move over mg

mg= F1sin(x) + F2sin(y)

to get m we then divide by g

m = (F1sin(x) - F2sin(y))/g

m = .505 + or - .015 N

For the first part of the experiment I must have accidentally used to wrong equation for silver and gold. I remember that I had to redo my calculations and was still redoing it while class was over. Unfortunately, I could not find the new sheet and just stuck with my old data. Besides the experimental densities being wrong, I think the rest of my lab is correct. 

Lab 8: Work on a spring

We are going to try to find the work that acts on a spring when a hanging mass is attached to the spring.

First we measure the length of the string stretched and the non-stretched. Using this data, we will calculate the constant of the spring. Afterwards we use the motion sensor to get GPE, EPE, KPE, and the total energy. 

the data of all our energies

this is the graph of the position of the spring vs time

This graphs is very unclear but shows all the energies that are in the system.

These are the calculations of how we derived which energies are going to be in the graph.

First we derived all the energies that were going to be in the lab and their respective equations. Then we calculated the spring constant by getting the position of the spring stretched vs non-stretched. We then used a motion sensor and logger pro and inserted all the equations we derived to get EPE, KPE, GPE, total energy. Our lab was for the most part successful as we were able to show all the energies present in the spring. Unfortunately, the total energy was quite a bit off.

lab 10: Centripetal Acceleration

This was a class lab where Professor Wolf wanted us to find the centripetal acceleration of a spinning disk. 

Unfortunately the apparatus is kind of blocked. However, it was basically a disk spinning on a tripod. 

Each group was supposed to find the time it took for the disk to rotate 4 cycles. 

We got the time by taking the average of each groups estimated time it took for four cycles. 

There were a lot of possible errors as people can have a different start and stop location. Everybody probably did not 100% accurately get the exact time it rotated 4 cycles. Although it is kind of blocked, in the first image we were able to get a graph that shows the relationship between angular speed and centripetal acceleration.

Lab 9: Angular Velocity

The purpose of this lab is to find the relationship between the angle at which the string spins at the speed at which it rotates around.

We checked at eight intervals for it to take ten revolutions and below is the result.

We then used excel to create a graph for the lab using the table below. 

This is a graph of omega vs theta. Our slope was .9877 when it was expected to be 1

After the eight intervals, we were able to solve for the equation that relates the angle and the speed. 

omega = (g*tan(theta)/d+l*sin(theta) )^(1/2)

Our experiment was a success as there was approximately a 1.3% error. 

Lab 4: Air Resistance

We went to the architecture and design building where we would drop coffee filters down from the second floor. We would first drop one coffee filter and add one more each at a time until there became five coffee filters all dropped at once.

The resisting force can be found with the equation, 

F = k*v^n

By taking the natural log of both sides, we derive the equation

ln(F)=ln(k) + nln(V)

where we have to find the value of F and the value of v.

List the mass and value of speed/velocity.

excel sheet of terminal velocities

The terminal velocities are listed below
1 filter: .922m/s
2 filters: 2.129 m/s
3 filters: 1.641 m/s
4 filters: 2.129 m/s
5 filters: 2.525 m/s 

Using the equation 

ln(F)=ln(k) + nln(V)

we derive this graph

We then use excel to calculate the terminal velocities once again.

The experimental values were a bit bigger than the actual values. But not by much. 

Overall it can be said this experiment was successful.

Lab 11: Power Lab

The purpose of the lab was to find the power needed to go up the stairs and pull a backpack up with a rope.

We had three bags to choose from. On the left was the heaviest, the middle and the second lightest or heaviest depending on how you want to look at it, and on the right was the lightest backpack.

This is the stair case which we had to walk up and then run up.

========================================================================There are 24 steps to the stairs and each step has a height of .156 m. 

By multiplying 24 to the height, we get the height of the stair case which is 3.24 m.

I walked up there in 13 seconds and I ran up the stairs in 8 seconds. 

Work is equal to force multiplied by the distance. The force is mass times acceleration and the distance was 3.24 m. 

90kg*3.24m*9.8 m/s^2 = 2857.68 Joules

Work divided by time gives power

2857.68 J/13 seconds = 219.82 watts (walk)

2857.68 Joules / 8 seconds = 357.21 watts (run)

I pulled the 6 kg backpack. 

The work for the backpack is 

6kg * 9.8m/s^2 * 3.24m = 190.5 Joules 

The power is 190.5 Joules / 9.65 seconds = 19.74 watts

In the experiment we would just find the work first. After finding the work, we would divide it by the time to get the power it takes to perform the action. I'm not sure if this is entirely accurate as I took two steps at a time when possible to make myself a bit faster. 

Lab 3: An Elephant on Roller Skates with a rocket attached

         As inhabitants of the earth, it is our job to protect it. When an elephant is rolling down a hill, we have to make sure the elephant does not fall off the edge and die in the process.

         We have to find the original speed of the elephant so that it does not fall off a cliff. A 5000-kg elephant on frictionless roller skates starts at 25 m/s going down a hill. When it hits a level plain, the rocket attached to the elephant then starts generating a constant 8000 N thrust against the direction the elephant is going down the hill. The mass of the rocket follows the equation m(t) = 1500kg - 20kg/s(t).

  From the equation F = ma. We derive a = f/m. 

In this case a(t)= 8000kg/((1500kg+5000kg)-20kg/s*t).

This equation will be simplified to:

a(t) = -400/(325-t) m/s^2

From our experiment the value we got was 248.69 meters which is to what you have calculated for us 248.7.

Ultimately the experiment was a success as the results were almost exactly the same.