9/25/2014 Work and Energy

Purpose:
The purpose of this lab was to get physic students some needed sunshine. So we went out side to calculate the amount of work we use to walk up a flight of stairs and how much work we use to pull an object up the same distance. We will also calculate the power as well.

Experiment:
First thing we did in this lab is measure the height of one step. Then we counted the number of steps total. With the height of the steps and the number of steps we could calculate the height we would travel up the stairs.Then we had to walk up the stairs and time how long it took us to reach the top of the stairs. That was the first part of our experiment for data for work it will take to climb the stairs. Then the next part of the lab we bags with weights in them which we would hang on a pulley over a railing. One of our team members would time the other while they pull the bag up the same height as the stairs.

Here is a picture of the class out side performing collecting data for our experiments.

After all the data was collected when went back inside to calculate our results. First thing we did was take our known weight and convert it into kg. My weight converted into kg was 95kg. Then with this I plugged in the data to the formula for work which is work = force * distance. This formula will give the results for the bad and walking up the stairs.

4.29 m is the distance to the top of the balcony floor in the picture.

Stairs:

Work:

(95kg) (9,8m/s^2)(4.29m) = 3993.99 joules

Power:

work / 8.48 second = 251.19 watts

Bag on pulley:

(5kg)(9,8m/s^2)(4.29m) =  210.21 joules

Power:

work / 8.48 seconds = 24.78 watts

The amount of work or power to bring a bag up the stairs would be much easier using the pulley system, To burn calories the stairs is a better choice.

9/23/2014 Relationship of angular velocity and the angle of a conical pendulum

Purpose:
The purpose of this lab is to find a relation between angular velocity of a conical pendulum and the angle which the conical pendulum makes with is string and the ground.

Experiment:
To accomplish this lab we had a very large conical pendulum hooked up to a power source so our rotations where almost uniform. The first data we collected was the measurements of the concial pendulum which included the height, radius of the stick which spun around, the length of the string which held the weight, and later we measure the height on which the weight was above the ground during it rotations. Next we would calculate the period on which the pendulum was moving by timing a couple of rotations and finding the average of this time for one rotation. We repeated the task of increaseing the angular speed and find the the height of the weight from the ground during its rotation and the period of rotation for seven data collections.

Here is a picture of the setup:

Next we had to create a formula that is our predicton for the relationship betwewen the angle between the ground and the string with the angular velcotity. Here is our formula for the model of angular velocity and the the angle between the gournd and the wire. Here is the forumula.

Now with the height on which the weight would hit during its rotations we could use trigonometry to find the angle created with the ground in string. With this data we plugged in a table of possible useful data we would need to prove our relationship is correct shown below is our data table.

Now with this data was much more then we needed, but we decided to show our formula is correct by comparing it the formula of w = 2PI / T. We made a graph of our model for the model w = 2PI / T.

Even though our graph is not that great I think our model is still right and our collection of time is what make our data bad. The slope of this graph should be very close to one which our is and isn't.

Update: I re did the formula which is shown above and I realized our original formula was the one crossed out which is wrong. Which explains why our graph is so bad.

9/23/2014 Angular velocity and its relation with angular acceleration

Purpose:

The purpose of this lab was to use an accelerometer on a spinning table to some how show the relation ship between angular acceleration and angular velocity.

Experiment:
We first used the accelerometer to calculate the average acceleration of the sensor as it spun in a circle. As we found the acceleration we also timed the amount it would take for the table to spin two or 4 rotation and calculated the average time it one period or full rotation took. With the angular acceleration we can calculate the time of a rotation manually and with that data we will be able to find it angular velocity.

Here is a picture of the spinning table with the accelerometer:

Here is a picture of the raw data collected for time and angular acceleration:

Now we can use the formula w = 2PI / T to find angular velocity. Then with that data we can plug our data into logger pro and graph angular acceleration vs angular velocity squared to what I assume is radius in the equation a = rw^2 which should produce a linear graph of because the radius of the spinning table is constant which also show the relation between angular acceleration and angular velocity.

Here is the graph of the data:

9/18/2014 Modeling Friction Forces

Static Friction

Purpose:

On this lab we will measure the static force of an object which is the force created by friction when object is held in place by another from friction.

Experiment:

One of the items we needed was a wooden block which we measured it mass on a scale. Then we got a pulley which we put at the end of a table. With the a wire we attach the block to loop over the pulley down the table and hung a cup of for adding water as a mass. With this setup we added water until the block begin to move on the track. We then measured the mass of the cup of water. We repeated this experiment five times adding another wooden block on our original block. Here is a picture of our experiment:

Here is a picture of our recorded data after five tests:

I wasn't sure on this lab if our scale was weighing mass or weight so unfortunately this data is bad even though it comes out looking right.

With our data table we used Logger Pro to graph max static friction force vs normal force. With the graph we can find the coefficient of static by finding the slop of our graph. Here is our graph of  max static friction force vs normal force.

The value we have for the slope which is our coefficient of static is 0.3866 which I believe is inaccurate and we should have done another set of data.

Kinetic Friction:

Purpose:

The purpose of this portion of the lab is to measure kinetic friction which is the force created by friction of an object that is moving.

Experiment:
On this lab we used a force sensor which measure the amount of force created by pulling on the sensor or pushing on the sensor. To get good collection of data we first had to zero the force sensor on Logger Pro. Then we attached a string and a known objects mass to measure the force to make sure we had good data collection. Then we the same blocks we used on the static friction part of this lab we pulled the block across the table measuring the amount of force it took. Here is a picture of out setup:

Here is an example of a reading from the force sensor which we used to get an average force from a 

graphs slope of velocity vs time.

We did this experiment five times increasing the number of block on top of the original block four times. We measured the mass of the block and calculated the the normal force the block created with the table. We data reading from the force sensor we had a average kinetic friction force from Logger Pro. We took all this data and created a table as shown below.

With this data table we are now able to once again graph max kinetic friction force vs normal force of the block. Here is the graph showing are slope which is the coefficient of kinetic friction.

We now have a reading for our kinetic friction coefficient as 0.2887 which I think is a good collection of data and we have a good result for our kinetic friction coefficient.

Kinetic Friction and Static Friction on a slope:

Purpose:

On the last lab we once again measure static friction first then kinetic friction again, yet this time we did it on a track which was on a slope.

Experiment:

To find the static friction we set up our ramp to an angle where the block wood was just about to slide down the ramp. Then we measure the height and length of the ramp to calculate our angle. With that all we had to do was create a FBD with the forces and solve for us which ended up being the tangent of our angle. Here is the setup and our calculations.

As you can see from our FBD and equation we found the coefficient of static friction to be 0.3 which is not that far off from our first experiment.

For the static friction part we  raised the ramp to have the block slide down the ramp. We measured the angle again by using the height and distance of the track and we also got the mass of the block from a scale. Then we used a motion sensor to measure the velocity of the block which we graphed on Logger Pro to find the acceleration by graphing velocity vs time. With that data and our mass of the block we where able to create another FBD and solve our equation for the coefficient of kinetic friction. Here is our FBD and our equation.

As the picture shows our coefficient for kinetic friction is 0.386.

Results:

While measuring the static friction was simple it was not an effective way to get a measurement because the block we be moved by a smaller weight and then the same block would take almost twice the weight to move. So our mass of the object that made it move has a large range of error.

The measurement of the kinetic friction was easier to move the object but to move the object at a constant speed or acceleration was very hard to do. Out of all our measurements I think our last experiment produced the best result for reliable data.

9/16/2014 Determination of an unknown mass.

Purpose:
Purpose of this lab is to find the unknown mass of our object by using the tension of the strings holding the object up and calcuating the error.

Experiment:
The first thing we did was zero our spring scales to make sure we are getting a good reading. Then we attached the object to both string leaving the object hanging. We measured the angles the wire created on both sides of the poles holding up the object.

Here is a picture of our setup.

Results:
Once we had our measured angles and measurement for tension we calculated our results as shown below.

Then we took our uncertainties as +- for degrees of angle and 0.5 for tension of newtons and measured our propagated uncertainty.

Here is a picture of our calculated results.

9/16/2014 Measuring the Density of Metal Cylinders. Introduction to propagated error calculations.

Purpose:

This lab we show how to calculate the propagated error in each of our density measurements. We will first determine our measurements as an experiment then calculate a theoretical value.

Experiment:

The first measurement we took was the diameter of each cylinder and its height. When then measured the mass of each cylinder to calculate the density which is mass divided by volume. Volume is equal to PI * r^2 * h.

We logged all the data on a white board as a table. With the data we calculated our propagated error.

Here is a picture of the experimental phase of measuring and weighing the items.

Here is are table with are calculated errors. The formula we used for our data is:
Our values are dd = 0.1, dh = 0.1, dm = 0.1 which we found by our scales measurement of error.

9/11/2014 Trajectories

Purpose:

Unfortunately the purpose of this lab wasn't to just roll balls of the table.The real purpose of this lab is to use a calculate a balls initial velocity as it leaves and incline slope of the table to predict when it where it would hit another incline slope off the side of the table.


Steps we took:

We had to first setup the lab using  an aluminum v-channel for the balls slide which we attached to ring stand to have the channel on an incline slope. Then we took our steel ball and let it roll of the table to find the area it would hit the ground. With the general area of where the ball landed we put carbon paper on the a sheet of paper to mark where the ball has landed. We took about five marks of the ball falling and measured the distance from the end of the table to the spot the ball has landed. We then measured the distance the ball landed from the table and the height of the table where the ball left the table. With this we could use kinematic formulas to find out initial velocity the ball left the table.

Here is a picture of our set up lab.

Here is a picture of our calculations to find the initial velocity of the ball leaving the table.

Now that we have our initial velocity we attached an incline board end the bottom of the table going up towards where the ball is launched to predict where the ball will land on the inclined board.

Here is our calculations to predict when the ball will hit the board with the real distance and the predictions on the sheet.

Our theoretical value as shown in is 46 cm while our experimental value is 47 cm. The percent error is  (experimental - theoretical) / experimental  which is (47 - 46) / 47 =   0.02 which is  2%.

Conclusion:

The calculated value the ball would land is very close to our actual spot the ball landed. I think our biggest error calculation is the distance the ball landed from the table on our first test. The table is on wheels and our way of measuring the distance is not exact. Therefore I believe our theoretical calculations would have been correct if are initial measurement was correct.

9/9/2014 Modeling the fall of an object falling with air resistance

Purpose and attempt of our lab:

The purpose of our lab today was to determine the relationship between air resistance force and speed. Will attempt to find the relationship by gathering data of a falling coffee filters and graph this data to find a power fit for the air resistance formula F-resistance - kv^n. After graphing our data and finding the value for k and n we will use Excel to  compare our experiment graphs to our modeled graphs.


Collecting the data:

To collect our data we used a camera to film falling coffee filters. We first dropped one filer then two continuing until to our last drop of five coffee filters. The purpose of the camera is to have a known distance which we used a meter stick as a reference point in the video to calculate the number of pixels in the known distance. With this we can track the falling coffee filter on Logger Pro to find a terminal velocity (where the graph was linear) to get data of time and distance the object has fallen which in return calculates velocity. Unfortunately in the hype of experiment I forgot to take pictures of the falling objects in the room, yet here is a still from the video capture.

Here is the picture of the camera and laptop we used to capture the five falling objects.

Here is a picture of are table of data which did not all fit in the picture:

With Logger Pro we graphed all the falls time vs distance as shown below.

After that we used our data to calculate our power fit graph to find k and n. This shows a value for k as 0.008542 and a value for n as 1.794.

Modeling the data:

So with are experimental data now collected we used the values of k and n to make a model of a falling object including air resistance. We did this by using Excel  and using a time interval of 1/30 of a second. 

Here is a picture of a portion of our Excel data:

With this Excel model we find have a table of data we used to graph time vs distance for one coffee filter and five coffee filters.

One coffee filter:

Two coffee filters:

Now that we have a graph the data from our model and our experiment we combined both graphs to compare our experimental data and our model data.

Conclusion of data:

With any experiment in physics are data is only as good as our equipment and using cheap cameras to get our data is not a reliable source. The first set of data is much better then our second even though both graphs are very similar when comparing the slope. Overall I think our model data is much better then our experimental table because of the our inexperience using the camera to collect data and the amount of work needed to get reliable data from a camera.

9/4/2014 Non-Constant acceleration problem / activity

On this lab we went over a problem on non constant acceleration analytically and then used a computer to solve the same problem numerically. Here is the problem we solved:

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.

Analytically:

To solve this problem analytically we first had to use Newton's 2nd law to find the acceleration of the elephant plus the rocket system as a function of time. Here is the formula:

Then we integrated the acceleration from 0 to  t to find ▲v to derive an equation for v(t) as follows:

Next we integrated the velocity from 0 to t to find ▲x and then derive an equation fro x(t) as follows:

Solving v(t) to find the time at which v = 0 allows us to use that time to plug into the equation to solve for the distance of how far the elephant goes. Solving the equation analytically gives a distance of  248.7 m.

Numerically:

After we solved the problem analytically we used Excel to solve the problem numerically.

• We first created a row of time which incremented by 0.1 seconds for about 300 rows. 
• With the next column we input the formula to calculate acceleration at any time.
• In the third column we calculate the average velocity.
• The fourth row calculates the change in velocity
• The fifth row calculate the instance Velocity.
• The sixth row calculates change in distance.
• The last row calculate the instance distance.
• With all the columns going down to about 300 rows.

Here is a picture of a portion of the excel table:

 Here is the portion of the table where time is near 0 and as you can see we find a instance distance of about 248.69 m.

Conclusions:

1) To solve each problem takes a decent amount of time, yet if we needed to change any data it would be easier to find new results numerically. The results are almost the same even though the data on excel is not as close to zero as we could get we could always change the information to find a better result.

2) If you wanted to check if the time interval numerically is close enough to get a good result you could always change the interval of seconds on the first table to see how much the distance changes in out answer. We tested in class by decreasing the increment to see how much the answer would change and it did not change at all. If we did it the other way around and increased the time interval and noticed no new answer we can assume the time interval is sufficient

8/28/2014 Free Fall Lab

This free fall lab purpose is to measure the constant acceleration of gravity and learn how to use Excel with our data. Gravity should be 9.8 m/s^2 yet any physic lab experiment I have done

The gravity measuring apparatus we used has a metal device connected to electricity of 60 hz which when in free fall rubs up against a paper making burn marks every 1/60 of a second. Here is a picture of the apparatus.

After using the apparatus we took the paper which was burned every 1/60th of a second and measure every mark in cm from an the same initial mark. Here is a picture of us measuring the marks on the paper.

Here is the raw data we collected and put into a table of our time and distance of the marks. We took a total of 10 marks.

We entered this data in a table on Excel to get a table with time, distance, and delta distance by taking the distance minus the last distance. We then found the mid interval time and mid interval speed of each row. Then we graphed mid interval time vs mid interval speed. Here is our data and the graphs.

Questions and Analysis:

1.  With constant acceleration the velocity in the middle of time interval is the same as the average velocity for the time interval because the graph of the velocity is linear so the middle time interval velocity is exactly the same as the average because it is the average.

2. You can get the acceleration due to gravity from the velocity vs time graph by finding the slope of the line created with the data points on the computer or if you had the formula of the line you could take the derivative.

3. You can get the acceleration of gravity with the positive time graph by finding the slope of the line.

Although are data seemed correct there is a good amount of error from the apparatus we used from friction of the metal on the wires and from the metal on the paper. To understand this more we next used Excel to calculate the deviation from the average and the deviation squared. With this data we can now see the amount of standard deviation from the mean are data should be. Even with the deviation are data is very low from where is should be.

Here is our Excel data of deviation: