In 1589, Galileo demonstrated that objects accelerate at the same rate regardless of their weight by dropping items of different masses from the Tower of Pisa. "The acceleration due to gravity at the surface of Earth is about 9.81 meters per second per second" (Faller 2014). On Earth, all objects have a downward force of gravity, this is known as an objects weight. An object's weight is proportional to the exertion of earth's mass on the object or the object's mass, but another factor comes into play. Another factor that can affect the speed at which objects fall is air friction. It can be said that the surrounding temperature of an object could affect the air friction of the object (Weisstein 2007). The temperature of the object could in turn affect the temperature of the air surrounding the object; therefore it could influence the air friction the object holds. Also, according to Perry's book, it says that air friction is influenced by the area of the object falling, but this factor will not affect our experiment because the objects being dropped will be the same shape and have the same area. Air density is decreased when temperature decreases, so air friction is decreased because the force needed to push the air out of the way is decreased. Lastly, according to NASA's website, objects will always fall at the same acceleration, and because of that, the speed of the object is able to be determined. A falling object will continue to accelerate to higher speeds until it encounters an amount of air resistance that is equal to its weight; this is known as an object's terminal velocity (Perry 1973). This experiment will look at the speeds objects fall at dependent on their temperatures.

Statement of the problem: Top

The purpose of this investigation is to find out if objects (ping pong balls) at different temperatures will fall at different velocities.

Hypothesis:

The velocities of each ping pong ball will stay the same no matter what the temperature is. The velocities will remain the same because the acceleration and weight of each object will remain the same between all the ping pong balls; also, due to the height the object will be dropped from, the air friction will have only a small effect on the object. Velocity is vector quantity that refers to "the rate at which an object changes its position." Temperature is defined as a measure of the average kinetic energy of the particles in a sample of matter, expressed in terms of units or degrees designated on a standard scale. The controlled variables of the experiment will be the height from which the ping pong ball is dropped, the shape/area of the object, temperature of the environment and using the same tools/instruments for each trial.

Method

Procedure: Top

In order to conduct the experiment of determining whether or not ping pong balls at different temperatures will fall at the same rate 50- 46 gram ping pong balls will be dropped through two photogates that are 67.31cm apart. For this to be possible the two photogates will be attached to a metal stand with a bucket at the bottom of the stand in order to catch the ping pong balls when they have fallen. The photogates then are connected to a computer that is running logger pro and will time when the ping pong ball will pass through each gate. There will be 5 groups of ping pong balls. The 1st group will be at at room temperature of 13 degrees Celsius. The 2nd group will be at the near freezing temperature of 1 degree Celsius. These ping pong balls are to be kept under ice using a cooler for a half an hour before being dropped. The 3rd group will be cool ping pong balls at 5 degrees Celsius. This group of ping pong balls will be kept under similar conditions as the 2nd group but only for 10 minutes. The 4th group will be heated ping pong balls at the temperature of 30 degrees Celsius. The ping pong balls will be heated up by being folded into a towel that was dampened and put into a microwave for 2 minutes. The ping pong balls must rest in the towel for 5 minutes. The 5th and final group will be doused in lighter fluid and lit on fire with a match. The temperature of these ping pong balls is 250 degrees Celsius. At the top of the stand a small metal clamp will be attached using duct tape. A level will be used to ensure that the clamp is parallel with photogates. This clamp will then hold each ping pong ball (except for the ones on fire) for the experiment. The ping pong balls will be released when the trigger on the clamp is pulled and after the timer on logger pro has been started. Once the ping pong ball has landed in the bucket and passed through the photogates stop the timer on logger pro and record the data. Repeat this process for every ping pong ball for the first 4 groups. For the final group that will be set on fire, the clamp must not be used. Instead one person must hold a pair of tongs that will hold the ping pong balls doused in lighter fluid. That person must steady their hand by setting their hand on the top of the stand, as to not effect the drop off the ball. Fill a third of the bucket underneath the stand with water. After the ball has been placed and the timer set, another person must take a match, light the match, and place the lit end of the match underneath the ping pong ball. When the ball ignites the person holding the tongs must let go of the ball and let it fall through the photogates and into the bucket of water; have a bucket of water ready in case of a free rolling ball of fire. Record data.

Materials: Top

50 ping pong balls

1 box of matches

2 bucket

2 photogates

1 pair of tongs

1 clamp

1 computer (with logger pro)

2 towels

water faucet

1 microwave

1 gallon cooler jug

1 gallon maximum of ice

1 tape measure

water

1 metal stand

1 roll of duct tape

1 level

1 thermometer

Top

Diagram: Top

Results

Data: Top

group 1	Time (sec) for 46 gram (g) ping pong ball to fall 67.31 cm (+/-0.05cm) at 13 C (+/-0.5C)
	Trial	Time through First laser gate (sec) (+/- 0.0005 s)	Time through second laser gate (sec) (+/- 0.0005 s)	Time (sec) (+/- 0.0005 s)	Velocity (cm/sec) (+/- 0.074 cm/s)
	1	4.139867	4.150909	0.011042	60.95815975
	2	3.502265	3.513619	0.011354	59.28307205
	3	1.704508	1.7162	0.011692	57.56927814
	4	3.377283	3.388905	0.011622	57.91602134
	5	3.041487	3.053057	0.01157	58.17631806
	6	1.527862	1.538986	0.011124	60.50880978
	7	2.009869	2.021241	0.011372	59.18923672
	8	2.168155	2.179521	0.011366	59.22048214
	9	1.404784	1.416422	0.011638	57.83639801
	10	4.617452	4.629175	0.011723	.5741704342
	Mean	2.749353	2.7608035	0.01145	.58784486


group 2	Time (sec) for 46 gram (g) ping pong ball to fall 67.31 cm (+/-0.05cm) at 1C (+/-0.5C)
	Trial	Time through First laser gate (sec) (+/- 0.0005 s)	Time through second laser gate (sec) (+/- 0.0005 s)	Time (sec) (+/- 0.0005 s)	Velocity (cm/s) (+/- 0.074 cm/s)
	1	2.13291	2.139055	0.006145	109.5362083
	2	5.012689	5.024331	0.011642	57.81652637
	3	1.407457	1.41991	0.012453	54.05123263
	4	2.753048	2.763689	0.010641	63.25533315
	5	3.005292	3.016933	0.011641	57.821493
	6	2.752316	2.76274	0.010424	64.57214121
	7	3.210739	3.221422	0.010683	63.00664607
	8	3.194816	3.201394	0.006578	102.3259349
	9	2.269305	2.280554	0.011249	59.8364299
	10	1.563315	1.571024	0.007709	87.31352964
	Mean	2.730189	2.7401052	0.0099165	67.87677104

group 3	Time (sec) for 46 gram (g) ping pong ball to fall 67.31 cm (+/-0.05cm) at 5.5C (+/-0.5C)
	Trial	Time through First laser gate (sec) (+/- 0.0005 s)	Time through second laser gate (sec) (+/- 0.0005 s)	Time (sec) (+/- 0.0005 s)	Velocity (cm/s) (+/- 0.074 cm/s)
	1	1.333238	1.34475	0.011512	58.46942321
	2	1.347044	1.35792	0.010876	61.88856197
	3	2.148901	2.160371	0.01147	58.68352223
	4	1.163705	1.171384	0.007679	87.65464253
	5	1.082288	1.093684	0.011396	59.06458406
	6	2.452607	2.46389	0.011283	59.65611983
	7	1.873009	1.884596	0.011587	58.09096401
	8	1.605408	1.616638	0.01123	59.93766696
	9	3.827219	3.83632	0.009101	73.95890561
	10	1.953901	1.965577	0.011676	57.64816718
	Mean	1.878732	1.889513	0.010781	63.50525576

group 4	Time (sec) for 46 gram (g) ping pong ball to fall 67.31 cm (+/-0.05cm) at 30C (+/-0.5C)
	Trial	Time through First laser gate (sec) (+/- 0.0005 s)	Time through second laser gate (sec) (+/- 0.0005 s)	Time (sec) (+/- 0.0005 s)	Velocity (cm/s)(+/- 0.074 cm/s)
	1	1.663178	1.674069	0.010891	61.80332385
	2	2.081614	2.09309	0.011476	58.65284071
	3	1.732441	1.7435	0.011059	60.86445429
	4	3.563236	3.575005	0.011769	57.19262469
	5	2.919088	2.929261	0.010173	66.16533962
	6	4.264568	4.275455	0.010887	61.82603105
	7	6.940593	6.950792	0.010199	65.99666634
	8	2.427892	2.439552	0.01166	57.72727273
	9	1.502151	1.513561	0.01141	58.99211218
	10	6.676268	6.686707	0.010439	64.47935626
	Mean	3.3771029	3.3880992	0.0109963	61.21149841

group 5	Time (sec) for 46 gram (g) ping pong ball to fall 67.31 cm (+/-0.05cm) at 250C (+/-0.5C)
	Trial	Time through First laser gate (sec) (+/- 0.0005 s)	Time through second laser gate (sec) (+/- 0.0005 s)	Time (sec) (+/- 0.0005 s)	Velocity (cm/s) (+/- 0.074 cm/s)
	1	11.5022556	11.670237	0.1679814	4.00699125
	2	12.487369	12.588013	0.100644	6.687929733
	3	3.727551	3.756545	0.028994	23.21514796
	4	8.245235	8.363522	0.118287	5.690397085
	5	5.595024	5.605968	0.010944	61.50402047
	6	4.740616	4.764538	0.023922	28.13727949
	7	3.299624	3.376127	0.076503	8.798347777
	8	3.272923	3.310057	0.037134	18.12624549
	9	0.679374	0.685761	0.006387	105.3859402
	10	5.112996	5.207297	0.094301	7.137782208
	Mean	5.86629676	5.9328065	0.06650974	26.86900817

	The Effect of Temperature (C) (+/-0.5 C) on Air Friction (measured by velocity) (cm/s)
		Temperature (C) (+/-0.5C)	Velocity (cm/s) (+/- 0.074 cm/s)	Uncertainty
	Frozen	1	67.8768	10.262
	Cold	5.5	63.5053	10.262
	Room Temp	13	58.7845	10.262
	Hot	30	61.2115	10.262
	On Fire	250	26.869	10.262

	General forms:		Mass of Ping pong Ball 46 g
	V= d/t	(F-32) x 5/9 = C
	TF-Ti=T	Δy/y = Δa/a + Δb/b
	Fd=-bv
	Results: According to the data, the ping pong ball at 1C fell the fastest at 67.88 cm/s while the pingpong ball at 290C fell the slowest at 26.87 cm/s. The median speed of the drops was 61.21 cm/s held by the ping pong ball at 30C.

Top

Graph:

Data file: text

Conclusion Top

The average velocities of each ping pong group varied significantly between the different temperatures. The average velocity for each group is as follows: group 1(room temperature balls) held an average speed of 58.7845 cm/s, the group 2 (frozen ping pong balls) held a velocity of 67.8768 cm/s, group 3 (cool ping pong balls) held an average velocity of 63.5053 cm/s, group 4 (warm ping pong balls) fell at an average velocity of 61.2115 cm/s, and finally group 5 (ping pong balls that were set on fire) held the average velocity of 26.869 cm/s. The fastest ping pong balls were the near freezing ones while the ping pong balls on fire were significantly slower than the other groups. The hypothesis was that the velocities of each ping pong ball would stay the same no matter what the temperature was. The assumption that velocities will remain the same because the acceleration and weight of each object will remain the same between all the ping pong balls was made; also, due to the height the object will be dropped from, the air friction will have only a small effect on the object was incorrect. The hypothesis was incorrect due to that each average velocity of each different group were different. The biggest difference was group 5 which had a much slower average velocity compared to the first 4 groups. While the other groups' velocities were within the range of 57 cm/s to 68 cm/s, group 5 had a average velocity of about 27 cm/s. The reason the data is so different than the expected result could be due to the environment the experiment was conducted in. Due to the danger present with the fire aspect of the experiment, it was conducted in an outdoor environment of 10C. The temperature of the surrounding environment was not taken into account in the experiment, but this could have had an effect on the experiment. Air friction is dependent on the viscosity of air, and the viscosity of air is dependent on temperature. Therefore the air friction was affected by the temperature of the surrounding air which could have caused the difference of the hypothesis and the actual results. Also, humidity was not taken into account in this experiment, which could affect the results of the experiment. Humid air is "lighter" or less viscous which is a factor in air friction; this could cause the results of the experiment to be skewed. There were sources of error in the experiment that could have also affected the experiment. The first source of error could be that the temperature of each ping pong ball could have been different. The temperature of only one ping pong ball was taken for each trial. Another source of error in this experiment was the inaccurate procedure of finding the temperature of the ping pong ball that was on fire. The temperature was taken with a surface temperature thermometer but could not exceed the temperature of 255 +/- 5.0 degrees Celsius, this could cause temperature to be negotiable. Another factor the could be a source of error could be that the weight of each ball was not taken. The average of 10 ping pong balls were taken and that number was used in the calculations. The last main source of error was that the loss of mass of the burning ping pong ball was not taken into account. Burning objects changes their chemical make-up and can result in some of the mass being lost to gases such as carbon dioxide. The procedure did have flaws that need to be improved. The first improvement would be to have the experiment conducted in a closed environment where humidity, pressure and temperature would be held constant. Another improvement would be to have the ball drop from a taller height, this would more likely give more accurate results because of the longer time the ball is in the air. Another improvement that can be made to the procedure would be to have a dropper that can withstand high temperatures so that each trial could be identical, no matter the temperature of the object being dropped. Another improvement to the experiment could be to take the measurement of the mass of each ball rather than just the average of 10 ping pong balls. The last improvement that can be made to this experiment would be to this experiment would be to use a refrigerator to keep the ping pong balls cool/frozen, and a warm water bath in order to keep the ping pong balls at a constant "warm" temperature (about 30C); this would have kept the ping pong balls at a more constant temperature and would have resulted in less error.