A brief explanation on two of our conservation laws first of energy and then angular momentum.
Conservation of Energy
Energy can be defined as the capacity for doing work. It may exist in a variety of forms and may be transformed from one type of energy to another. However, these energy transformations are constrained by a fundamental principle, the Conservation of Energy principle. One way to state this principle is "Energy can neither be created nor destroyed". Another approach is to say that the total energy of an isolated system remains constant.
Conservation of Angular Momentum
The angular momentum of an isolated system remains constant in both magnitude and direction. The angular momentum is defined as the product of the moment of inertia "I" and the angular velocity.
The angular momentum is a vector quantity and the vector sum of the angular momenta of the parts of an isolated system is constant. This puts a strong constraint on the types of rotational motions which can occur in an isolated system. If one part of the system is given an angular momentum in a given direction, then some other part or parts of the system must simultaneously be given exactly the same angular momentum in the opposite direction. As far as we can tell, conservation of angular momentum is an absolute symmetry of nature. That is, we do not know of anything in nature that violates it.
Idea of the Experiment
The apparatus is a simple set up. We have a meter stick that has a hold drilled near the end of the stick. That will be our pivot point. We want the meter stick to be able to swing freely. On the other end of the meter stick will have tape with the sticky side out so that upon impact of the clay object it will help with an inelastic collision. The clay object will be stationary directly vertical with the stick.
The motion will be as followed from the above image.
Predicting Max Height
Before we start the experiment, we take measurements; mass of stick, mass of clay, length from the center of mass of stick to the pivot point and total length of the meter stick. Then predict the max height at which the stick and the clay reach from the ground before swinging back.
Big "M" is for the mass of the stick. Little "m" for the mass of the clay. Moment of inertia of the meter stick is twelve halves times mass of the stick times length squared.
We are going to approach this lab by calculating this problem into three parts. First at rest when the meter stick is horizontally up (held by someone) then released and the moment before the meter stick strikes the clay. Second the split second the stick is about the hit the clay and right after. Third part will be to calculate the max height.
Our origin is set on the horizontal at which the meter stick begins at rest.
First part we are going to use conservation of energy. We solve for angular velocity before impact.
Second part we utilize conservation of angular momentum. Plugging in angular velocity from part one into our initial angular velocity in part 2 will give us angular velocity upon impact.
Third part we use conservation of energy again. This time solving for our angle. The angle will lead to a value of predicting our max height off the ground.
We predicted our max height to be 0.29356 m
The Experiment
Now to obtain our value from logger pro we set up and camera level with the clay piece and far enough to record the height the stick goes after impact.
We set our idea into motion and record.
From the video capture we are able to set up parameters in which we will use the program to give us a max height.
Logger pro's max height is 0.2904 m
Calculating error from our value and logger pros.
Combining both conversation laws of energy, angular momentum and back to energy was quite the task. Key thing to note is setting the origin and going about using the origin in each little calculation correctly. Also using the appropriate masses for each piece in kinetic energy and moment of inertia. Kinetic energy for most all of the experiment were the rotational formula. While determining moments of inertia, the part of what lengths to use, were confusing at first. After many attempts of calculating using these principals, we obtained a satisfying error of about one percent. Errors that may apply to this experiment is the angle of the video capture. Friction on the pivot. Some energy may have also been lost upon impact from traveling through the stick onto the pivot. We have uncertainty from the meter stick, length wise. The meter stick is old and chipping. Uncertainty in weighing the masses on the scale.
No comments:
Post a Comment