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.