Inclined planes

Authors Avatar by wannabefrenchfriesgmailcom (student)

Introduction- While riding a bicycle, I saw a downward sloping road, so I decided to go down that road but as I was starting to move down the road I did not move the pedals of the bicycle but my speed started to increase which was due to the gravitational force of the earth. Some other day I came across another downward slope which was at a less height from the ground level and I did the same thing as before but noticed that my speed was not increasing as fast as in the first slope and the time taken to cover that slope was also more but it could also be because both of the slopes had a different length but I was proven wrong when I looked up on google maps that their length was approximately the same, hence it was not enough to affect the value of time by a large amount. So, I decided to make an investigation on an incline plane by varying its height and seeing its effect on time taken to move down that slope with the research question being, To what extent does the time taken for a ball to roll down the ramp depend on the height of the ramp when distance along the ramp which the ball rolls and the acceleration of the ball are kept constant.

Background information- People have used inclined planes throughout history to build temples, aqueducts, and roads. Inclined planes have been used by people since prehistoric times to move heavy objects. Ancient Egyptians used inclined planes made of dirt when they built pyramids. These long ramps were built alongside the pyramids. The large stone blocks used to build the pyramid itself were pushed, pulled, or carted up the ramp. The sloping roads and causeways built by ancient civilizations such as the Romans are examples of early inclined planes that have survived, and show that they understood the value of this device for moving things uphill. It wasn't until the renaissance that the inclined plane was solved mathematically and classed with the other simple machines. The first correct analysis of the inclined plane appeared in the work of enigmatic 13th century author Jordanus de Nemore, however his solution was apparently not communicated to other philosophers of the time. Girolamo Cardano in 1570 proposed the incorrect solution that the input force is proportional to the angle of the plane. Then at the end of the 16th century, three correct solutions were published within ten years, by Michael Varro  in 1584, Simon Stevin in 1586, and Galileo Galilee  in 1592. Although it was not the first, the derivation of Flemish engineer Simon Stevin is the most well-known, because of its originality and use of a string of beads. In 1600, Italian scientist Galileo Galilei included the inclined plane in his analysis of simple machines in Le Meccaniche (On Mechanics), showing its underlying similarity to the other machines as a force amplifier. Galileo used balls rolling down ramps to study the relationship between time and distance travelled. However, without any knowledge of physics, it doesn't seem immediately obvious that the time-distance relationship of an object rolling down a ramp is the same as if it were free falling.

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Hypothesis- The distance which the ball travels along the ramp () is proportional to the square of time taken for the ball to travel (), so this can be explained by:

So, the formula for finding the distance (D) can be written as:

In the formula above  is the initial velocity of the ball which is 0 meters per second as the ball is kept on the top of the ramp before rolling. Then the equation simplifies to

The acceleration () for the ball is a constant so it does not change throughout the experiment and ...

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