Centripetal force with motor

Purpose:  We must come up with a relation between theta and omega from an apparatus that swings a mass at the end of a string in a horizontal circle.

Process: 

1) To obtain the angle theta we can look at the right triangle that is formed by the string and the angle it makes with the origin. Using trigonometry we can obtain the angle.

2) To obtain omega we can time how long it takes for the stopper to make revolutions, or one complete circle, around the shaft device.

3) We can get the height from the floor to the mass by increasing the voltage to measure different heights which will give us different omegas also correspondingly.

4) We then record data of the omega and acceleration relations using logger pro. 

Conclusion: We can find the relation between the angle and omega by trigonometry and calculating other components such as velocity and tension. Different heights can be calculated and which will change the the angle and omega, experimenting with different trials and data to get different scenarios for different values.

Work-Kinetic Theorem

Purpose: We will measure the work that is done when we stretch a spring through a fixed or measured distance.

Process:
1) The first thing that we will do is collect data by a force that will be applied by a stretched spring. The graph will be a force vs distance graph. After we find this graph we will be able to calculate the work done by finding the area under the curve on the graph.

2) There will be a cart that will be pulled by a horizontal force on the surface of a ramp. Set up the motion detector, force probe and the spring attached to the cart. Now we must calibrate the force to be 4.9 newtons that will be applied to the cart.

3) Now we must begin graphing the force vs position graph by letting it move slowly towards the detector, which is the positive direction. You will get the graph until the spring is stretched about 1 m.We can find our spring constant by using hookes law.

4) Now we must measure the cart mass and enter a formula by going to data then new calculated column that will allow us to calculate the kinetic energy of the cart at any point. We then make sure that the cart is stretched out to 1 m from the unstretched point, let it go and and begin graphing.

5) Now we can find the change in kinetic energy from the initial release point to other final positions and the work done by the spring up to these positions. To find the area under the curve we divide the area into shapes we can take areas from, in this case a triangle and square. We calculate the areas of these and add them together to get the work done.

Conclusion:
We have learned how to find the work done by a spring and graph are results. It is important to make sure the graphing is done with nothing interfering with the motion detector and to accurately graph from the displacement along the track.

Magnetic Potential Energy

Purpose:
The goal of this lab is to verify that conservation of energy applies to the system of the cart with the fixed magnets. We will be using an air track with a glider on top of it with strong magnets attached to the end of the glider and the wall.

Procedure:
1) Our first step is to recognize that this is magnetic potential energy, not the usual gravitational potential energy or elastic potential energy. This means we must find an equation for the magnetic potential energy. The relationship that we will obtain the magnetic potential energy is the integral of the force with respect to r, integrated from infinity to r. r is the distance between the glider and the magnetic attached to the wall.

2) Next we will level the air track so that it creates a height h that will allow the magnetic repulsion force to be equal to the gravitational potential energy of the cart that is parallel to the air track. By tilting the air track we will have created an angle theta which we must calculate. We must tilt it at different angles so we can plot relationship between magnetic force and the separation distance.

3) We then plot a F vs r graph. The graph will be assumed to be a power law  F=Ar^n. In order to get the values of A and n we must apply a curve fit to the graph.




4) To verify conservation of energy, we attach an aluminum reflector to the top of the air track. We place the track near the magnet. We then run the motion detector and see the relationship of the distance the detector reads and the separation distance between the cart and magnet.   We can now measure the speed and separation between magnets at same time.

5) We can calculate the graphs of potential, kinetic and total energy of the system now by placing the track at the opposite end of magnetic, give it a gentle push and use logger pro to calculate the graphs.

Conclusion:
We have found how to calculate magnetic potential energy even though it was not straightforward as other types of potential energy. Energy was conserved at the end as expected and found the force function from the graphs we plotted and saw the relations between kinetic and potential energy from the experiment.

Trajectories

Purpose: 

The Purpose of this lab is to find the distance that a metal ball will fall on an inclined plane falling also from a higher height. 

How to do: 

1)We must first now take the ball and roll it off the incline on top of the table and mark where it hits on the floor. It should hit the same spot and be marked by a piece of carbon paper. 

2)Now the height must be determined when it is launched, and far it lands from the table. Once you get these values, you can calculate the speed of the ball as it is launched.

3) Then we must place a board inclined on the table, creating an angle theta. Then we must calculate the distance that the ball will fall on the lower incline after it rolls off the upper incline and the table.

4) Now we roll the ball again and put something heavy next to the inclined board so it will not fall and we attach carbon paper to the inclined plane where we think the ball will hit. Then we roll the ball five times to get the distance of where the ball lands on the inclined plane. Make sure the angle is calculated and the board is placed accordingly.

Conclusion: We have calculated how far the ball would fall both by deriving an expression and by performing the experiment multiple times to get an accurate answer.

Modeling fall of an object falling with air resistance

Purpose: The purpose of this lab is to determine the relationship between the air resistance force and speed of an object. We expect there to be determining factors in the the force resistance and graphs to show us relations.

Process: 

1)We studied this relation of air resistance and speed by using coffee filters as our objects that would drop from a second story balcony in a building. We found there to be factors in determining the air resistance force. These factors are generally the objects shape and speed. This equation is found to be  force of air resistance =kv^n. The k in this formula relates to the shape and area of the object. 

2) We used the video capture to capture 5 coffee filters dropping from the second balcony. We expect to find that each of these coffee filters reach terminal velocity eventually as they fall.  We then took the graphs that were recorded and attempted to linearize the curve we could obtain the terminal velocity. The slope is key to finding a velocity from the position versus time graph.

3) The next step was to take our data and then in excel create a table that would provide us with the terminal velocity. We created a table with columns. The time, change in velocity, velocity, acceleration, change in position, and position columns would eventually give us terminal velocity. We also added space for the k and n values of our equation. Smaller and smaller increments of time would give us a better result for our terminal velocity.

Conclusion: From the equipment we used and considering that excel is a good programming for acquiring this kind of data we our confident that our results are a good representation of terminal velocity.

Free Fall and Experiment Uncertainty

Purpose:
The purpose of this lab is to determine and examine the value of gravity when all other external forces are absent. We expect to find this value of acceleration to be 9.81, as the object is in free fall.

Process:
1)To perform this experiment we must set this apparatus up that will mark the falling object as it falls to the ground. The tape attached to the apparatus will mark the distance of the object as it falls in intervals that will give us two graphs. These two graphs are the position vs time graph and acceleration vs time graph, which will be able to allow the calculation of acceleration.There will be a series of dots on the paper that will correspond to the position of the mass as it falls for every 1/60th of a second.

2) We must then place a ruler next to the apparatus and line it up next to the tape, lining the two-meter stick with the 0-cm mark with the highest dot. We will record the position of the object as it falls through each dot respectively.

3) Open Microsoft Excel and then we will enter the data we took and also label our columns as Time, Distance, the change in distance and the change in time and the speed. From our data we will create a graph that will give us these graphs of distance and speed that we desire.

Analysis:
The uncertainty that we can find in our calculations can come from a misreading of the measurements from the tape, or even by our miscalculations of calculating data on excel . The graphs of position and velocity with respect to time can give us the acceleration due to gravity. In order to get the acceleration of these graphs, we must look at the slope of the graphs at a certain point or points. The slope will give us either a tangential value if specifically the slope at one point or the average value at two points. We expect to also find uncertainty to occur because nothing is ideally perfect, but the instruments we are using are expensive and the most accurate tools we can use. Two ways we can express this error is the absolute difference in our calculations, which is the result for acceleration that we got minus the actual acceleration that it is, or relative difference, where we take the value we got minus the actual divided by the actual multiplied 100, which will give us our percentage.

Conclusion:
The experiment led us to be able to use excel and calculate acceleration, along with plotting graphs and also being able to analyze data from graphs to obtain acceleration and realize nothing is ideal and prone to mistake. To make less mistakes is to replicate the experiment multiple times, which will give us a more stable answer.

3-March-2015: Finding a relationship between mass and period for inertial balance

Purpose:
The purpose of this lab is to find the relationship between a mass and its period using an inertial balance, which involves a power law equation that will show us the relation mathematically. We see how different masses and their respective periods behave on this device.

Process:
The inertial balance seen in the upper right hand of the paper, which will allow us to put masses on top of it and give us oscillations and a period of the mass.

The data that we took first was placing masses on top of the inertial balance. W started with 100 g, then proceeded to add more as we took the result for the period of each mass corresponding. We did this until we reached 800 grams, seeing 8 different results for the period and seeing a definite pattern. The period would increase as more mass was added to the inertial balance, which we then apply a force and see the resulting oscillations which we then cut off at a certain point to get the period. We also included two unknown masses.

We then proceeded to plot the equation T=A(m+Mtray) to the n power by taking the natural logarithm of each side and getting an equation very similar to the line equation y=mx+b. We must obtain the values of A, which is a constant, Mass of the tray and the exponent n.  The graph would not be perfectly straight line, but to obtain Mtray we would need to try different values until we obtain a relative straight line. Then linear fitting it would give us the straight line we were looking for as shown above.
 Conclusion: 
Overall we plotted data with varying mass values, obtained the periods of each mass and saw that plotting the power law equation with the right values of Mtray gives us the desired line.