Terminal Velocity Lab 5h1y30

Terminal Velocity Lab The relationship between an object’s mass and its terminal velocity Report by Victor Jeung, Terry Tong, Cathy Liu, Jason Feng Special thanks for entire class for collection of data. 2011 October 8

1 Terminal Velocity

Abstract The lab that our class has conducted observes and verifies the relationship that exists between an object’s mass and its terminal velocity during free fall, while keeping the surface area that is perpendicular to the ground constant.

Introduction Hypothesis Through the theoretical equation (1) that we have solved, we conclude with the hypothesis that the reason an object reaches a terminal velocity is that the drag force resisting motion is proportional its velocity by an N factor.

Theory Variables The variables used in this experiment included the mass of the object, the fluid density of the room, the drag coefficient, surface area that is perpendicular to the ground, initial height, initial velocity, and time. The controlled variables are initial height from the ground (2.871m) and initial velocity ( ). This eliminates the initial velocity from the equations. The drag coefficient will be determined by the shape of the object which has a with air; so we tried not to change the shape of the coffee filter during the trials.

Equations √

Ρ: Fluid density (air for our case)

(Equation1)

A: Projected area of the object : Terminal velocity

Cd : Drag coefficient

All of these variables listed don’t affect the final result of the lab because they are kept constant. The relationship between the mass and the terminal velocity is: Equation (2)

Equation of the drag coefficient

Equation (3)

Forces acting upon object during terminal

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Linearizing the formula Substituting equations (1) & (2) in to (3) we get (

(

) ( )

( )

(

)

)

( )

(

( )

(

) )

Equation(4)

The equation in which above is stating that velocity will be changing due to a slope of 0.5 to the mass.

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Experiment Apparatus  

6 coffee filters 2 stop watches



1 metre stick

Figure 1 As shown here this is the setup of our apparatus which includes a person holding the coffee filter at ceiling height and letting it free fall back down to the ground while our timer and recorder takes down the time.

Conducting the Experiment The experiment was conducted by having one person stand on a table and holding a coffee filter faced downwards (flat side down) close to the ceiling and letting the coffee filter fall back down to earth. Time was measured by the timers to see how long it would take for the coffee filter to reach the ground. To collect a uniform result, the experiment was done carefully by taking the following precautions: limited movement around the area where the projectile is let go to limit turbulence in the air making 4 Terminal Velocity

data unfeasible and by not dragging our hands under the coffee filter when letting the coffee filters freefall from the ceiling causing a mini vortex which can also render the data unfeasible.

Analysis of Data The data below shows the average speed and the average time to the number of filters. The data shows that the average free fall time decreases as the number of coffee filters increase which is expected as the mass is increasing the speed at which it reaches terminal increases as well. The speed is derived from the distance from the ceiling divided by the average free fall time, which would give an approximate value of the speed. We are assuming because of how light the coffee filters are, they hit terminal velocity almost instantly when they are dropped from the ceiling. This could be a great source of error as to ask what if the coffee filter didn’t hit terminal within the time taken down, as the heavier filters fell much quicker than the lighter ones. Filters 1

Average F-Fall Time (s) 2.70s

Average Speed (m/s) 1.028813

2 3 4 5 6

2.01s 1.65s 1.52s 1.28s 1.20s

1.378797 1.675708 1.827445 2.159223 2.307054

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Hundreds

Speed Shown in Meters Per Second on a scale of log to the base of 10

logarithmic graph of Number of Filters VS Speed 0.005

0.004

0.003

0.002

0.001

0 -0.2

0

0.2

-0.001

0.4

0.6

0.8

1

Number of Filters

Figure 2 Graph showing the comparison of Number of filters to Speed in m/s all to the log base of 10. With a linear regression that yields y = 0.4732x + 0.0034.

Graphical Analysis From the graph that is shown above which shows the log base of ten for both the average speed of the filters in meters/ second and the number of filters. The graph in which has an approximate slope of 0.5 which is conclusive with the equation that we have derived which shows that 0.5 is the slope of the graph and the equation

( )

( )

(

) . The 0.5 slope of the log means that the

relationship between the speed and the mass is a square root relation. The mass of course cannot equal zero as the filters always has weight. The y intercept in this case will represent the minimum speed that a coffee filter with zero mass (impossible) can go through in this density of fluid.

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Conclusion We conclude that our hypothesis was correct, to which the time it took to free fall back to earth did decrease at a close to an equally proportional rate. Our equation (4) proved to show that the relationship between the mass and the terminal velocity is a square root based on our equation (4) which shows the slope of log to equal 0.5. There were some random and systematic errors in our experiment. These were:      

The systematic error of the coffee filters getting bigger as more trials were completed. This resulted in the gradual increase in time as more trials were completed. The systematic error of the timer’s reaction time. The random error adding initial velocity when releasing the coffee filter. This resulted in a faster time to reach the ground compared to no initial velocity. The random error of inconsistent air currents in the room such as draft wind. This effected how long it took for the coffee filters to reach the ground. The systematic error of 6 different groups conducting trials for each number of coffee filters. Initial velocities and reaction times vary for each group. The different height that groups could have started with, so there is possible error for different heights.

If we were to complete the terminal velocity lab again, here are some things that we would change:   

Get the same people to perform the lab for the 6 different trials to ensure that initial velocities and reactions times are constant. Try to eliminate the air current movement by limiting actions such as the motion of people moving around. Determine how air resistance depends on mass, shape or area of the object.

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