5.Working With Spreadsheets

Purpose: To get familiar with electronic spreadsheets by using them in some simple applications.

Equipment: Computer with EXCEL software.

Part 1:

Create a simple spreadsheet that calculates the values of the following function:

f(x)=Asin(Bx+C)

Initially choose value for of A= 5, B= 3 and C= π/3 (1.047).

Create a column for values of x that run from zero to 10 radians in steps of 0.1 radians. Similarly, create in the next column the corresponding values of f(x) by copying the formula shown above down through the same number of rows (100 in roll).

Then copy and paste our data into the graphing program. Put appropriate labels on the horizontal and vertical axes of the graph. Use Curve Fit to find a function that best fit the data.

The best fit function: y= 5Sin(3x +1.05)-1.49×10^(-10)

Part 2:

Repeat the above process for a spreadsheet that calculates the position of a freely falling particle as a function of time. Start off with g= 9.8m/s^2, vo= 50m/s, xo= 1000m and △t= 0.2s.

The formula for free fall: f(t)= ro+vo△t+(1/2)a(△t)^2

We assuming the direction of vo positive.

(i)When g is positive:

f(t)=1000+ 50t+ (1/2)× 9.8t^2

Use Curve Fit to find a function that best fit the data:


The best fit function: f(t)= 4.9t^2+ 50t+ 1000

(ii)When g is positive:

f(t)=1000+ 50t+ (1/2)× (-9.8)t^2

Use Curve Fit to find a function that best fit the data:

 

The best fit function: f(t)= (-4.9)t^2+ 50t+ 1000

Question: How do data from part 1 and part 2 compare to the values we start with in our spreadsheet?

In part 1, we compare the data(A=5, B=3, C=1.05) from Curve Fit to the values(A=5, B=3, C=1.047) that we start with in our spreadsheet. In part 2, we do the same thing as initial values are "g= 9.8m/s^2, vo= 50m/s, xo= 1000m and △t= 0.2s". We find that the data from Curve fit are almost the same to the initial values.

Conclusion:
In this experiment we use excel spreadsheet to solve the problem.

We find that the data from Curve fit are almost the same to the initial values. This experiment helps us to have many data and efficiently do the formulas. 
 

4.Vector Addition of Forces

Purpose: To study vector addition by Graphical means and Using components.

Equipment: circular force table, masses, mass holders, string, protractor, and four pulleys.

Part 1.  Dr. Haag gave us 3 masses in grams which represent the magnitude of three forces and three angles.

	Magnitude	angle
A	100kg	0°
B	100kg	335°
C	100kg	270°

 

We made a vector diagram showing these forces, and find the resultant after adding the three vectors. There is two ways to calculate the resultant:

·         The head to tail vector. This involves lining up the head of one vector with the tail of the other.

·         The parallelogram method to calculate resultant vector. This method involves properties of parallelograms but, in the end boils down to a simple formula.

 

100 cos 0° + 100 cos 335° + 100 cos 270°= 190.631 = X

100 sin 0° + 100 sin 335° + 100 sin 270° = -142.262

Tanθ= 190.631/-142.262

θ= tan^-1 (142.262/190.63)= -36.733 + 180 = 143°

 

 

Conclusion:


When we place a mass on fourth holder equal to the magnitude of the resultant, the ring turns to equilibrium. That means the force of the fourth mass is equal to the resultant force of the first three masses. A vector is a quantity having a magnitude and a direction, and two vectors of the same type can be added.

The sources of error: Some magnitude of vectors are decimals, but we only have the masses with whole numbers.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.Acceleration of Gravity on an Inclined Plane

The purpose of these lab is to find the acceleration of gravity by studying  the motion of cart on an incline plan.                                                                                                                                         


We set up the track putting the wood friction block under the track support at approximately 50cm raising the end of the track.

To determine the inclination of anlge X we solve a for the triangle.

Since the force of friction acts with the force of gravity when the cart is going up the track and against the force of gravity when the cart is going down the track, we can average the slightly increased acceleration (when going up) with the slightly decreased acceleration (when going down) to obtain an acceleration that depends only on the force of gravity. If we call g the acceleration along the track is g sin θ  where theta is the angle of incline for the track.


g sin θ= (a1+a2)/2

a 1	a 2	g
-0.3316	0.2679	9.83232

There were 3 trials for the first angle 

 

 

For the second angle there were three trials as well.

 

 

 

 





Conclusion:
According to two experiments, we found when θ is larger, our experimental data are closer to actual data(0.5% diff compare to 8.2% diff). The reason is that when θ is larger, the motion of cart is closer to free fall, which is influenced less by the disturbance. The causes of error:  Air resistance also against the motion, Our table is not horizontal, so our θ is not precise enough and the error of the equipment and the error when we read the data.

In this lab, we learned acceleration along the track is gsinθ where θ is the angle of inline for the track. we can use this property to estimate the gravity. We also learned how to control the variable to get another group of data, then try to think abut what cause the difference.



a 1

a 2

g 

-0.3316

0.2679

9.83232

 



2.Falling Body Experiment - Acceleration of Gravity

The purpose of this lab is to determine the acceleration of gravity for a freely falling object and to gain experience using the computer as data collector.

We found the free fall acceleration of a rubber ball tossed into the air by collecting the ball position (x) vs time(t) data. Since the velocity of an object is equal to the slope of the x vs t, the computer also constructs the graph of v vs t because acceleration = ΔV/Δt. For this exercise we conducted 5 trials.

1.        We placed the motion detector in the floor with the basket for protection. Then we tossed the ball into the air until we got a position-time graph of a parabolic shape.

2.       We selected the data in the interval of the parabola we chose Analyze/curve fit and chose Quadratic.

3.       From the velocity vs time graph we found out the acceleration.

4.      Finally we calculate the percent difference for each of the trials.

 

Results from Falling Body Experiment
trial	g exp	% diff	g exp	% diff
1	-9.302		-9.785
2	-9.506		-9.61
3	-10.156		-10.62
4	-9.99		-10.06
5	-9.534		-10.1

 

Conclusion:

In this lab, we determine the gravity is close to 9.8m/s^2.
In order to get the most precise data, we did this experiment for many times and got the average data, which decrease the error accidental error. Our data is 3.18% varying from the actual, that mean this experiment can prove that the gravity for a freely falling object is close to 9.8m/s^2. Our errors are because of : Air resistance, The inevitable experimental error, because the equipment can't be exactly precise. The curve fit is an estimate, so our gravity is also an estimate value.

We also learned how to use Lab Pro interface, Logger Pro Software, motion detector and gained the experience using the computer as a data collector. We also worked as a team to gain and analysis the data. This experience may benefit us in the future.