23-Sept-2014 Angular Velocity and the angle of a conical pendulum Lab #9

Purpose:
The purpose of this lab is to find the angle of the pendulum as it rotates at different speeds.

This photo shows how the conical pendulum is labeled to find theta.

Here are the intervals of time in which the pendulum were measured. Each is according to 10 rotations.




Once our data is collected we were able to input it into logger pro using the formula we were required to derive. After we had to graph it along with a trend line.

 

Which was relatively straight beside a few minor dots.

18-Sept-2014 Modeling Friction Forces Lab #7

Purpose:
This lab was designed for us students to figure out the value of the static force of an object held against another object.

Materials:

• 1 wooden block with felt
• 3 wooden blocks
• Styrofoam cup with string attatched
• water
• "frictionless" pulley

 The basic set up of this lab is the pulley locked on the table with a string connecting the block and foam cup going through the pulley.

The way we do this lab is pour water into the cup little by little until the block moves slightly. Once it moves we measure the cup for mass. This way we can calculate the normal force and static friction.

 This part is with two blocks. (Be careful with spills)

Then three blocks. We do this one more time with four blocks.

With this table you can see all the masses of water and blocks along with there normal forces and max static friction.

By putting the max friction and the normal force on logger pro we were able to graph and create the best fit line. The best fit lines slope is our static friction (0.3019).

Purpose:
Next is to find the kinetic friction of the blocks stacked on top of each other and dragging it across the table using a sensor.

We did this four different times with different am amounts of blocks.

This is the data we collected along with the recorded values from logger pro.

This last graph shows the kinetic relation between all of the trial and with the slope of the trend line we are able to determine its kinetic friction (0.3957).

Purpose:
The last part of this lab we have to determine kinetic and static but at a high slope.

The first step is to find the slope in which the block barely starts to move. Once that is done we measure the angle (ours being 30.5).

23-Sept-2014 Angular Velocity and Angular Acceleration Lab #8

For this lab we had to use an accelerometer on a spinning circle in order to calculate the average acceleration.

We timed each interval then recorded them as a class to get the average. We did this for several different speeds.

They were timed between two to four rotations depending on the speed going at the time. The formula for angular velocity is w=(2pi)/t. Once all the data was calculated we were able to input it into logger pro along with our angular acceleration (a=rw^2) to create a graph that will show us their relation to each other.

25-Sept-2014 Work and Energy Lab #10

Purpose:
The purpose of this lab is to have us calculate how much work is needed for me to walk up a flight of stairs and pull up an object a certain distance.

This is not me in the picture but I did do the samething.

 First we had to measure the height of the stairs in order for us to figure out the height of the flight, which turned out to be 4.30m.

Once this I had to time myself going up the stairs at a slow pace(15.12) then once again at a faster pace(9.56sec).

Then came the pulley. For this one we had to time how fast till we pulled the object all the way to the top. My time being 10.62 seconds for 6kg.

After this is accomplished we had to calculate the work and power of each.

Work: mass*gravity*distance
86kg*9.81m/s^2*4.30=3619.3 Joules

Power: work/time

slow walk: 239.4 watts
fast walk:378.6watts
pulley:23.8watts

16-Sept-2014 Density of Metal Cylinders Lab #6 part 1

During this lab we had to figure out the densities plus or minus there uncertainties of three different metal cylinders by measuring there height, diameter and mass.

Materials:

• Caliper (height and diameter)
• Scale (mass)

Our three chosen metals were aluminum, copper and steel.

SteelAluminum

Copper

The above photo shows all the measurements of diameter and height in centimeters and grams for the mass.

After this is done we had to figure out there densities and plus or minus uncertainties.

Density Aluminum:

Density Steel:

Density Copper:

16-Sept-2014 Unknown Mass Lab #6 part 2

Purpose:
The purpose of this lab is to determine the unknown mass of unknown mass #5.

Materials/Setup:

• 2 spring scales 10N
• unknown mass
• two clamps
• string

Use the clamps to attach the spring scales to the rods. Then use the string attached to the unknown mass and connect then to the spring force.

Once the setup is finished we had to measure the angles and write them down along with the forces in our diagram.

 With the angles and tensions gathered I was able to determine the masses and uncertainty of unknown mass.

mass=.501kg +/- 0.04kg

11-Sept-2014 Trajectories Lab #5

The purpose of this lab is for us to understand projectile motion and to learn how to predict the point of impact of a ball on a inclined plane.

Materials:

• 2 aluminum v channels
• a steel ball
• board
• ring stand
• clamp
• paper and carbon paper
• tape

 This is the general set up of the apparatus. The two v channels were taped together in order to create and angle for the ball drop. The ring stand, pole and clamp were placed to hold the v channels up.

 

As for the paper and carbon paper that was placed on the floor by testing the ball drop to see were it will land. Then we put the papers around that area. With this setup we have to determine the initial velocity of the entire system drop.

After this is set up we measured all of the distances with a meter stick and placed them on this diagram.

Height of launch being 93cm, distance of launch being 47.2 cm away from bottom of table.

With the measurements we were able to do our calculation to find the initial velocity, which turned out to be 1.08 m/s.

 Then once that is figured out we had to figure out a formula that will help us determine the distance that the ball would strike a board if it was inclined against the table.

This formula will help us determine the theoretical distance while the actual measured distance after the laugh is 38 cm (.38 m).

With the theta measured at 45 degrees we were able to determine the theoretical distance at .33m meaning .05 meters from the actual.

Conclusion:
Our percent error=(experimental-theoretical)/theoretical*100%=15%.
Some uncertainties maybe the drops of the ball not being exact every time. We had to estimate the distance measured of x which may mess with some calculations.

4-Sept-2014 Non-Constant Acceleration Lab #3

For this activity we were given this scenario:

A 5000-kg elephant on frictionless roller skates is going 25 m/s when it gets to the bottom of a
hill and arrives on level ground. At that point a rocket mounted on the elephant’s back generates
a constant 8000 N thrust opposite the elephant’s direction of motion.
The mass of the rocket changes with time (due to burning the fuel at a rate of 20 kg/s) so that the
m(t) = 1500 kg – 20 kg/s·t.

Find how far the elephant goes before coming to rest.

We were given some suggestions to help us solve this equation:

1) Newtons second law gives us the acceleration of the elephant plus the rocket system as a function of time:

2) You can integrate from 0 to 1 to find delta v and then derive an equation for v(t):

3) You can integrate the velocity from 0 to 1t to find delta x and then derive an equation for x(t):

4)You can solve v(t) to find the time at which v=0
5)Then you can use the time you derived above in 4 and plug that into your expression for x(t) to find how far the elephant goes.

Here are all of the calculations done to get the distance 248.7m

Then once that is determined we had try to determine it through excel (numerically).

1. We first created a row of time which incremented by 0.1 seconds for 258 rows. 
2. With the next column we input the formula to calculate acceleration at any time.
3. In the third column we calculate the average velocity.
4. The fourth row calculates the change in velocity
5. The fifth row calculate the instance Velocity.
6. The sixth row calculates change in distance.
7. The last row calculate the instance distance.
8. With all the columns going down to the 258 row
   

This table is continued on until the 258th row.

To figure out the distance numerically we have to find the velocity right before it turns negative in the table. Then once we have this we change the time interval in the tables to 1 sec and 0.05sec in order to compare the differences.

1 second interval

0.05 second interval

Conclusion:

1) The information gathered doing the problem analytically and numerically are relatively the same. It is probably off by .3 or less.
2) The way I knew that the results were small enough was that the distance was pretty close to what I calculated. I knew when to stop when the velocity was close to zero before turning negative.

28-Aug-2014 Free Fall Lab #2

This Lab is designed for students to figure out the value of g (gravity) through the measurement of a falling object on an apparatus.

 This apparatus has a falling distance of 1.5 meters. The way that the measurements are recorded is through a spark generator. As the object falls it will release a spark marking the paper that is hanging along the pole at approximately 1/60th of a second intervals on its way down.

 

With these marks we will have to measure the distance from the first dot to every other dot after. We measured for 23 dots after and plotted them on excel.

Once the distances were recorded for 1/60th of a second we had to find the distance (delta x) by subtracting the first distance from second, then the second from the third and so on. Then we find the mid interval time by grabbing the first time interval then adding 1/120 so that we can get the middle of each 1/60th second. As for the mid interval speed we grab the delta x and divide by the 1/60th of a second. Once that is finished we graph the mid interval with the mid interval speed.

By graphing the mid speed and mid times and inputting a trend line we are able to determine the acceleration in cm/s^2 by using the slope gathered Which turned out to be 9.40 m/s^2 when converted. After this we graph columns t(s) and distance in centimeters.

When graphing the distance and time column, instead of choosing a linear trend line (black line through points) we graphed a polynomial column. The way we find acceleration is to find the slope and multiple by 2.

Conclusion

Once finished with with our graphs we had to figure out the places in which can cause error in our data. Nothing is absolute when experimenting. Other factors can come into play like friction in the apparatus or the paper that it is stamping can cause a slowness in the dropping of the object. With the table above we are able to calculate the error that has occurred according to the whole class. Ours being #6.

Then there was the relative difference that was calculated by getting the experimental value (9.40m/s^2) and subtracting the accepted value (9.81m/s^2) and dividing it by the accepted value then multiplying this by 100 to get the percentage error. Our error being -4.18%.