Forces Table Lab Report Essay

Name: Madison Campbell Partner George Tauber
Title: Forces Table
Introduction:
The purpose of this week’s lab, titled “Forces Table”, was to look at vectors in two dimensions. The lab was also used to help up understand how to sum up forces and the decomposition. In our experiment, we had to estimate a third force that would balance out our other two. This would then make the sum of the forces zero. To calculate our forces we used Newton’s Second Law below: (1)
In the above equation, the ƩF represents the sum of all of the forces in Newton’s. The m is the mass of our object in kg, and the a is the acceleration in m/s^2. As stated above, we are trying the get the ƩF to equal 0 by having no acceleration. We can also draw a “free-body diagram” to show what we did, and how the forces affected the lab.
Experimental Procedure:
To begin the lab, we first move our m_1 mass to 17ͦ and added weights so that the total mass was 100g. Next we put our m_2 mass at 67ͦ and added weights so that
the total mass was 150g. Each of the masses were connected with a string to a ring that went around a central pole. Next we began to find the component of the third force. Our goal was to find an angle and weight such that the center ring didn’t touch the pole. Once we found this angle and weight, we recorded our values. To check our work we calculated our third vector. Lastly, we drew a top view of our experiment with a ruler and protractor.
Equipment Used: Weights Weight Hanger Force Table Ruler Protractor Ring String
Data and Error
In this lab, we considered the error in our hanging masses as well as our angle measures.
To find the uncertainties associated with this lab we used the direct method. For the mass, we took our smallest weight that we added and used half of that as our uncertainty. That means that our mass had an uncertainty of ±1g. Our angle uncertainty was half of a tick mark or ±0.50ͦ.
Calculations
Figure 1: Free-body Diagram
Figure 2: Force Diagram
To find the third force we use the equation 1 or Newton’s Second Law. Since we are working with two dimensions, we need to do calculations for both the x and y components.
(2)
(3)
(4)
(5)
ƩF_x represents the sum of all of the forces in the x-direction, while ƩF_y is the sum of all of the forces in the y-direction. The |ƩF| represents the magnitude of the sum of the vectors. The x ⃗ and y ⃗ represent the vector components. Since the acceleration is 0
then
(6)
F_1,F_2,and F_3 are all vectors of the forces, and the F_3 is the only unknown variable. For each force ,we now use Newton’s Second Law. We use g or gravity for each acceleration. For F_1 and F_2 we find the following:
(7)
(8)
Next we need to use trigonometry and vectors to find the x and y components of the forces.
(9)
(10)
The next step is to plug the two vectors into our equation (6) as follows and solve for F_3:
(11)
(12)
Using equation (5) we can turn our vector back into a magnitude:
(13)
If we manipulate equation (2) we can get our θ_3:
(14)
(15)
We can check our angle measurement by looking at what quadrant the angle would be in on a graph. By doing this we can confirm that this is the right angle.
This means that our theoretical values are |F_3 |= 2.231N and θ_3=227.33ͦ. Our values that we obtained through the experiment were slightly different. We can calculate our experimental |F_3 | by using equation (1):
(16)
We found that our experimental mass was 222g or 0.222kg. To find our uncertainty of our |F_3ex | we can use the Error Analysis Reference handout equation (6):
(17)
Therefore, our |F_3ex | with uncertainty is
We also needed to calculate the uncertainty in our data. To do this, we used equation (10) from the Error Analysis Reference handout. Once we calculate our z values, we will know if our data is consistent. If our value is under two then it is.
(18)
(19)
(20)