#5 Projectile motion activity/lab

Projectile motion activity/lab

introduction:

Moving object have inertia. If the object do not any force except of the gravity on it, the object will do constant speed at the horizontal component. This lab we set up the apparatus as the figure. That we can have the same V0 every time I roll the ball. We have to calculate the first experiment we do then expect the second experiment result which add a board on the apparatus.

Material:

steel ball, aluminum V-channel, board, ring stand, clamp, carbon paper

carbon paper            aluminum V-channel

Thesis:

Measure the height and how far it hit the carbon paper. We can use those information to calculate the falling time and the V0. Then measure the angle can calculate where will the steel ball except to fall at the board. 

Process:

First, roll the steal ball and that it fall on the ground, and put the carbon paper at where it fall at last time that we can record the falling point.
Second, fall the ball 5 times to find the average falling point

Then set the broad and measure the angle.
Then, using the information we have to guess where will it fall on.

Calculate:

this is what we measure

This is how I calculate 

I find our initial velocity which is V0=1.4m/s 

Then find the distance it will fall on the board

Finally, I except the ball will traveled the board on distance= 46.073cm
We let the ball roll again and got 46cm for the result

Conclusion:

Our experiment compare with the expect can find
 an error is (46-46.073)/46.073=-0.158%
It means we are AWESOME! and really close to the experiment.
Beside, we can sure that the gravity cannot affect the horizontal component speed.

#4 Modeling the fall of an object falling with air resistance

Modeling the fall of an object falling with air resistance

introduction:

The free falling object on the earth usually cannot falling without any resistance. We knew that falling object have gravity accelerate but the experience we have tell us the result we get usually have an error on it. We have an error because the air resistance affect the object accelerate. In the lab we use different numbers of coffee filter to find the resistance when it is falling and find the relationship between the speed and the air resistance.






Thesis:

We said that air resistance equation is
Fresistance = kv^n
We do 1 to 5 coffee filter so that we have 5 date of it.
We expect that the coffee filter will speed up at first and turn into the constant speed then finally fall on the floor. Each date have different mass and slope n= constant speed
Collect the dates and use logger pro to make a fit for equation F=kv^n
find k and n


Experiment and date:

We want to the design technology building to take video. Try 1,2,3,4,and 5 coffee filter to get videos date.

By using logger pro, we put a dot on each 0.2s 

as the right hand figure

those are the date we have 

The first drop with one coffee filter. When the air resistance = the gravity, have constant speed 1.217 m/s^2 and F=0.01N

The second drop with two coffee filters. When the air resistance = the gravity, have constant speed 1.798 m/s^2 and F=0.02N

The third drop with three coffee filters. When the air resistance = the gravity, have constant speed 2.249 m/s^2   and F=0.03N

The fourth drop with four coffee filters. When the air resistance = the gravity, have constant speed 2.549 m/s^2 and  F=0.04N

   The fifth drop with five coffee filters. When the air resistance = the gravity, have constant speed 2.771 m/s^2  and F=0.05N

 this is the five dates we found

 Then we try to fit in the function F=kv^n

We got k=0.0054          n=2.147
Modeling the fall of an object including air resistance

We can see that point 2and 4 are close to the F=0.0054v^2.147
try those point in excel and see if speed would be constant
We do the drop with two coffee filter with Excel

 

This chart tell us the speed become constant and the speed is 1.823m/s^2
but experiment got 1.798
means we have an error (1.798-1.823)/1.823=-1.371%

conclusions: 

The relationship between air resistance and speed that we find is 
Fresistance = 0.0054v^2.147

It tell that speed do affect the air resistance. We can said that air resistance affect object accelerate a lot that generally free falling lab might have some error. Because each coffee filter could have different mass, the experiment of this lab and the expect would have an error.

#3 Non-constant Acceleration problem/Activity

Non-constant Acceleration problem/Activity

introduction:

In the activity, we try to find how far the elephant goes before coming rest.

solve:

Using the Newton's 2nd law F=ma, we can get the acceleration of the elephant.

a(t)=Fnet/m(t)= -8000N / 6500kg-20kg/s*t  =-400/325-t (m/s^2)

Then we can use integrate to find v(t) and x(t). However, the integrate way make the equation be so  complex that we can lots of work, so we are using the Excel to help us calculate.

To find v, we give time interval 0.1(s) to find the average acceleration then we calculate the change in velocity and get the speed at the end of each time interval. v/t=x so that we find the distance.

this is what we do in Excel

between 19.1 to 19.2 v=0

In our chart, we find when time close to 19.7s elephant speed reach 0m/s and travel a little bit more than 248.69804m

conclusions:
1. The result we got from analytically is

19.7s when speed=0 distance =248.7
It means that the analytically and numericallys' answer are the same

2. I try to put time interval= 0.2 and the result is when 19.6 ,v=0.1189  when 19.8, v= -0.1431
that result v range is about +or -0.1 means not quite close to 0 .
Back to time interval 0.1 when t= 19.7 ,v=-0.0121 , means the error is small that we can ignore 

#2 Free Fall Lab

Free Fall Lab- determination of g

introduction:

Generally, object on the earth have gravity, and a free falling object will accelerate at 9.8m/_s²downward. We learn that knowledge in high school and now we try to find by ourselves.

setting:

free fall apparatus
from(http://web.alfredstate.edu/quagliato/lab/lab.htm)

  1. put the long paper in the free falling apparatus

  2. set the sparker box on the very top and turn on the
electromagnet make it hold.

  3. let it start sparking at 60 hz and turn off the electromagnet

  4. sparker box will leave dots on the paper while it falling down

  5. measure the distance








thesis:

Our purpose is to find the accelerate if it close to the gravity accelerate 9.8m/_s².
We use the free falling apparatus to collect the dot which the sparker box leave when it falling down. Then we can use the distance between every 1/60 s which is ∆X=X_n  -X_{n-1  to find mid-interval speed.}
 ∆X/(1/60)=V(mid-interval speed)    and  ∆V= V_n -Vn-1  ,∆V/(1/60)= accelerate then compare with accelerate of gravity.

date and calculation:

 paper with dots . This is our date from. We measure the distance from 0 cm mark, then type it in the Microsoft Excel.

 here is the excel date we did in class

using the ∆V to find the average accelerate and average it can get a=969.23(cm/_s²) =9.69239(m/_s²) which is really close to g=9.8(m/_s²) but the air resistance affect the lab result.

we use excel to make this graph. it shows that slope =970.02(cm/_s²)
d/dt v(t)=a(t)=970.02(cm/_s²) =9.7002(m/_s²)







 This is the date from other group. there are 9 groups, ours is 4

Conclusion:

Except and experiment are different our experiment is that each result have different accelerate.
According to the standard deviation of the mean theory 68% of us get 9.57+or-0.18 in the standard deviation from the mean value.
our group get 9.696 we can find our error is (9.696-9.8)/9.8=-1%

#1 Finding a relationship between mass and period for an inertial balance

Finding a relationship between mass and period for an inertial balance

Introduction:
 We know that object mass measurement affect inertia, then object inertia might affect the period of inertial balance. By changing mass, we can find that mass influence the period of an inertial balance. In the lab, we tried to use the inertial balance and photo gate to find relationship between mass and period. 

   Setting:  

                 Put the paper in front of the inertial balance between the photo gate that the photo gate read the period easier.

Thesis: 

      We said that the relationship between mass and period would be 

                              period             mass

                                 T      = A(Mtray+ m )^n   

      

  

y=nx+ b

            lnT=lnA + n ln(Mtay + m)                                                    y=lnT=n ln(mtray+m) + lnA                     

The job is to use the different mass to find each period by using Logger Pro to calculate the slope n and lnA.

Our date; 

We used mass from 0 to 800 adding 100grams each time then find each period with photo gate

We let   lnT=n ln(mtray+m) + lnA  

become    y     =  n  *    x    +b 

which mean using those collect point to graph can find 

slope n and the b which is lnA.

  

calculation:

     Those are two graph we use Logger Pro to draw. The closest correlation we can find is 0.9998.

Mtary=0.328 ,We found that biggest slope n= 0.7133 , and b= lnA=-0.4479
which A= e^(-0.4479)=0.639

Mtary=0.315 ,We found the smallest slope n=0.6524, and b=lnA=-0.4168
which A=e^(-0.4168)=0.659

Conclusion:

      Collect the calculation date, we get the relationship between mass and period for an inertial balance.

T= (0.649±0.010) (m+Mtary)^( 0.68285±0.05015)

The equation tell us the when our total mass is larger, the period also be larger. This is the relationship between mass and period in inertial balance.