What law will be used in this experiment?

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The experiment investigates how varying air pressure in a soccer ball affects its travel distance upon impact. The hypothesis posits that increased air pressure will result in a greater distance traveled. Five specific air pressure levels will be tested using a Playmaker Soccer Ball Machine for consistent launching and a measuring tape for distance. The discussion highlights the relevance of the law of conservation of energy and the kinetic theory of gases in understanding the energy dynamics involved. Key questions focus on the relationship between internal pressure, energy transfer, and the mechanics of the launching device.
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The research question of this experiment stated "What is the effect of changing the air pressure (kPa) inside a soccer ball on the distance (m) that the ball will travel (when it first hits the ground) as measured by using the AG500 digital air pressure gauge (to 0.01 kPa) and a field measuring tape to 0.22m (roughly the diameter of a soccer ball)?"

The hypothesis of this experiment stated that as the air pressure inside the soccer ball increases, the average distance traveled when it first hits the ground will also increase.

The experiment will be done by using a range of 5 different air pressure—58.00kPa, 68.00kPa, 78.00kPa, 98.00kPa, and 108.00kPa—while using a Playmaker Soccer Ball Machine to launch the soccer ball and field tape measure to measure the distance it'll travel.
 
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Well, what do YOU think ?
 
I believe that this experiment applies to the law of conservation of energy since energy does transform into from one to another. However, I think that the internal changes inside the soccer ball seem applies to other law. I believe that the law applied to the gas is the Kinetic theory of gases, particularly the average kinetic energy of the gas molecules.
 
EelAnes said:
I believe that this experiment applies to the law of conservation of energy since energy does transform into from one to another.
a). How does the pressure inside the ball translate to energy of the ball?
b). How does the energy of the ball translate to distance travelled?
c). Are the quantities referred to as "energy of the ball" the same in a) and b)?
d). How does a Playmaker Soccer Ball Machine work? What is held constant when balls of various inflation are propelled by it?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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