Lab 9
Purpose: the purpose of this lab is to find the relationship between angular speed W and the angular θ.
Apparatus:
Set up:
As show in picture, here is the equipment and set up.
To find the relationship between W and θ, we are using this equipment to set the function between them.
Here is the force diagram and the function.
We can see the relationship between W and θ from the picture. what the lab need to do is to make sure that's true or not by experiments and then we can say that's the relationship.
(One thing we need to know is the
radius is not just r, it's r + R
, so we got)
this function we can see as the linear
function y = kx. so the slope of this
function should be 1 or around 1, and we can say our experiments is prove the relationship between W and θ.
Therefore, Our job is simply collect many sets of W and θ by using our equipment we just set up, then input our data into computer, linear fit the line, and see if the slope is very close to 1 or not.
How to find out the W and θ.
and W = 2PI / T
We can see H, R, and L are very easy to measure. That's the data we know.
What we need to do is to start with a slow spin at the beginning, we can measure the period by passing one specific point and get the T, then we measure the h.
By period T we can get the angular speed W,
By knowing the h we can find the angle θ.
Then we try with different speed, and spin the object, and then we collect the T and h.
After many tries. we got those data.
Next, we input our data in to computer, and linear fit the line.
we can see from picture, after we linear fit the data W^2 and x (which we know from above.)
We got y = 0.9827 x, so our data just prove that the relationship between W and θ is
Uncertainty:
Of course, for every experiments we all made mistakes or errors that we cannot avoid. Our data from the experiments all have uncertainty. such that the period T
We measured or the h we got. What if our T and h are bigger, the angle will be smaller, and W will be bigger.
Conclusion:
By trying so many times experiments, we find out the relationship between W and θ is really what we got from the function. Even though our experiments have some uncertain facts, but we can roughly say we did a very good job. For the uncertainty of this experiment, I assume that this whole experiment has no air resistance at all , and each time the small object hit on the paper, it will change the speed and direction of object. Also, the measurments I did on this experiment, such that angle, length of string or height of the paper. If I say made the whole angle I got from the experiment, W will bigger than before, or say reduce the length of string, the W will become smaller.
没有评论:
发表评论