Lab reasoning in conclusion. how and why did i get such error? or difference?

[pezzang]

I wrote a lab report for my physics class and i can't finish my conclusion. In conclusion, I have to write why the results i got was so off and so far i have only two weak reasonings. If any of you can see better or more reasonings, please leave me a comment and elaborate a little bit if you can. Thank you.
Here are my reasonings so far
a) the friction of the track in each experiment might have been differnt
b) in my lab, gravity(9.8m/s2) might not have been a theoretical value. So that's why the results were so off.

WHAT ELSE?



I. Purpose

This experiment consisted of two parts to compare the net force of a cart, driven by a fan. In the first part, we calculated the net force of the cart on a horizontally flat track by measuring the mass and acceleration of the cart. In the second part, we raised the end point of the track from the ground in order to make an upward slope for the cart. By finding the length of the track and the height of the raised endpoint from the ground, we calculated the net force of the cart. According to Newton¡¯s Second Law, a body accelerates if a net external force acts on the body. The direction of acceleration is the same as the direction of net force. The net force vector is equal to the mass of the body times the acceleration of the body. For the first experiment we can use the equation below to calculate the net force of the cart:
SF = m * a
(F = force in a vector form, m = mass of an object, a = acceleration in a vector form)
For the second part, we use a different equation since the track is no longer flat on the ground but rather has an angle:
SF = m * g (sin A)
(g = 9.8m/s2, A = the angle between the flat track and the ground)


II. Summary of Procedure

Before the start of experiment, we prepare a track, a cart, a motion sensor, a fan, a balance, a ruler and two batteries.
In the first part of the experiment, a track is placed on the horizontally flat surface of the table, and its length is measured using a ruler. A fan is attached on the top of the cart, and two batteries are put on. Using a balance, we measure the mass of the object, which consists of cart, fan and batteries. Then, a motion sensor is set up on the edge of starting point so that we can measure the velocity of the car once the cart starts moving. Then, the cart is put on at the starting position of the track, and we turn on the fan. While the cart accelerates, driven forward by the energy of the fan and moves toward the opposite end of the track, the motion sensor detects cart¡¯s acceleration. We repeat this procedure three times to derive an accurate result.
In the second part of the experiment, one end of the track is slightly raised so that the track has a slope. A car is put on the lowest part of the track, and its fan is turned on. The slope of the track is slowly raised so that the cart completely stops on the track with its final velocity equals zero. When the cart stops, the height from the upper end of the track to the table will be measured with the ruler. The same steps are repeated three times to get an accurate result.


III. Data/ Results
First Part:
Length of the track = 129cm
Mass of the o cart + fan + batteries = 0.724kg
Height of the raised track = 1) 4cm, 2) 4.1cm, 3) 4.4cm
Second Part:
Mass of the o cart + fan + batteries = 0.724kg
Acceleration of the object = 1) 0.1562m/s2, 2) 0.1769m/s2, 3) 0.1825m/s2

1) Calculation
First Part:
a) A = angle between the flat ground and the track = sin-1(4.0/129) = 1.78 degree
b) A = angle between the flat ground and the track = sin-1(4.1/129) = 1.82 degree
c) A = angle between the flat ground and the track = sin-1(4.4/129) = 1.95 degree
a) S Fx = m * g * (sin A) = (0.724kg) * (9.8m/s2) * (sin 1.78degree) = 0.220 N
b) S Fx = m * g * (sin A) = (0.724kg) * (9.8m/s2) * (sin 1.78degree) = 0.230 N
c) S Fx = m * g * (sin A) = (0.724kg) * (9.8m/s2) * (sin 1.78degree) = 0.242 N
Second Part:
a) First Trial: S Fx = m * a = (0.724kg)(0.1562m/s2) = 0.113 N
b) Second Trial: S Fx = m * a = (0.724kg)(0.1769m/s2) = 0.128 N
c) Third Trial: S Fx = m * a = (0.724kg)(0.1825m/s2) = 0.132 N

 

[Integral]

Your data and the discription of your lab do not match. Where is the data for the 3 runs on a flat track? From what I can gather from the purpose statement you should be taking data to deterimine the force generated by the fan. Then by tilting the track to find a stoping angle you should be able to duplicate the flat track values of the force.

Where are your flat track final velocities and time? With out these you have nothing to compare to.

I can see lots of possible errors in finding the stoping angle. If the heights you cite are the various stopping angles you had a significant amount of variation. Consider the methods used and if the car was actually holding in place or drifting slowly.

Computation hint. When using radian angle measure sin a = a for small angles. Your angles are quite small so if you compute 4/129 you will see that it is equal to the sin for as many digits as you need. Conversion to degrees is extra, and unnecessary computation.

 

[pezzang]

The experiment consisted of two parts and the results are clearly stated in the calculation part. And without the velocity and time you can stil figure out net force by using f = ma and f = mgsin(angle). Is there any problem with this equation? Here is my conclusion so far. You will understand better if you read this. But I still can't simply reason why the value of the net force of the fan was so different. Can you please help me reasoning?

In this experiment, we found the value of net force of the fan on the cart when the cart was run on the flat track and when the cart was run on the upward slope that decreases the velocity of the cart to zero. For the first part, we experimentally found out the mass of the object, height between the endpoint of the raised track and the ground and length of the track. Using sin-1(height/length), we figured out the angle between the flat ground and the track. Since we assumed g to be 9.8m/s2, we knew everything to find out the net force of the fan from the equation: S Fx = m * g * (sin A). m (mass of the object) was 0.724kg, g = and sin A = sin (1.78 degree,1.82 degree,1..95 degree) in three trials. The average of value of Fx came out to be . For the second part, we experimentally found out the mass and acceleration of moving object by using a scale and a motion detector. The m (mass) was 0.724kg and a (acceleration) came out to be 1562m/s2, 0.1769m/s2 and 0.1825m/s2 in three trials. Thus, using the Newton¡¯s Second Law (S Fx = m * a ), we calculated S Fx . Although value of the net force of the fan should have been theoretically the same or fairly close when we compare the average force of each experiment, the result came out to be very different. The net force in the first part came out to be 1.86 times larger than that in the second part.

 

[pezzang]

Also i did a calculatio using your method. I still get the exactly same number. It doesn't really make a difference if you use such calculators as texas instrument TI-83 Plus or TI-89. What else can be errors?

 

[Integral]

One other thing I see is that since you only have 2 digits on your measurement, you only used 2 digits of g. You cannot reasonalbly display more then 2 digits in your result.

Something else I notice is that the values of your force seem to be steally INCREASING, could it be that the output of your fan motor was not constant, perhaps as it warmed up it ran faster.

 

[Integral]

Originally posted by pezzang
Also i did a calculatio using your method. I still get the exactly same number. It doesn't really make a difference if you use such calculators as texas instrument TI-83 Plus or TI-89. What else can be errors?

Do not be a slave to your calculator, make it your slave. Use it when you need it but ALWAYS be looking for ways to avoid its use.

I did not say your results were incorrect, merely inefficient.

 

[jcsd]

I can't remeber exactly but I'm pretty sure that g on the Earth's surface varies by about 0.1 ms^-2, the maximum being at the poles and the minimum being at the top of some mountain on the equator, it's virtually impossible (unless you are posting from up a mountain in Venezuela) that the slight varibilty of g has an effect on your calculations esp. as you've used the very round figure of 9.8.

I haven't checked your equations, but it seems to me mostly likely that the error occurred in your measurment of the angles.