Ball Bounce Efficiency Prac Report
Group: Tommy Chen, Felix Hall, Thasun Ranasinghe, Erica Stevens
By Tommy Chen
Research Question:
To what extent does adjusting the angle of a ramp affect the vertical bounce height of the tennis ball after it rolls off a ramp which lies on a constant height above the ground?
Rationale:
The science behind ball bouncing is actually quite complicated, it relates to how much energy
they have stored, their different aspects like shape and elasticity, as well as where the energy they have are transferred. The purpose of this experiment was to determine how the angle of the ramp affects the bounce height of a tennis ball. An experiment was conducted in class that measured the vertical magnitude of the tennis ball after it rolls of a ramp at different angles. The key factor of this experiment is the initial velocity of the tennis ball before rolling off, the kinetic energy builds up gradually as it accelerates on the ramp. Theoretically, all the tennis balls all dropped from the same height at the edge of the table, 87cm from the grounds. However, the more ramp angle is increased, the ramp height increases and the starting point of the tennis ball shifts. When the ball is higher, there is a larger amount of gravitational force which results in faster and stronger impact that leads to a higher bounce. The overall potential energy is also increased in this process. The potential energy is calculated by three different components, mass, height and gravity. In this case, the mass and gravity remains the same, 50grams and 9.8m/s2 respectivly, so the height position of the ball in this experiment must link to increase of energy as well as bounce height. It is likely that the rate of change is going to be exponential which means that the results will increase quicker and quicker as the angle increased become larger. The formula for an exponential growth(positive) is:
y = a(1 + r)x
Modification and justifications:
Original experiment
The original method was dropping tennis ball from different heights straight down and observe the change in bounce height and energy efficiency.
Modification
A ramp is added.
The method of the experiment was changed from dropping it vertically to rolling it off a ramp.
The ball bounced straight up and down before whereas it is now going forward.
One of the variables is now changed to angle of the ramp.
Justification
In the new experiment, the method of the experiment was changed from just dropping a tennis ball vertically to rolling the ball of a ramp and observe a different bounce height of the tennis ball and if it relates to the ramp angle. The ball now has two directional components, it is bouncing upwards as well as travelling forward at the same time. The independent variable is now changed to the angle of the ramp whereas in the original experiment, both the independent and dependent were height related-drop height and bounce height.
Risk assessment:
Constant Variables:
Results table:
Formulas:
Average=Sum of trials/ number of trials
Absolute error=Range/2
Percentage error=Absolute error/mean*100
Efficiency=Bounce height/drop height*100
Sample Calculations:
Discussion:
The aim of this experiment was to examine how changing the ramp angle affects the bounce
height of a tennis ball. It is expected that the results will display a positive trend as the ramp angle increases, the average bounce height of the tennis ball will increase as well in constant ratios. Constant ration means growing by common factors over equal intervals. The results proves the hypothesis and showed that as the ramp angle increases, the average bounce height of the tennis ball increased at a relatively steady rate. As shown in Graph1, the data displays a consistent rise in height in the bounce height of the tennis ball as the ramp angle ascended. However, as the ramp angle reaches 50°, there is a larger increase in the bounce height which changed the graph’s trend from a linear graph with steady rate of increase, to an exponential growth graph. In an exponential growth graph, the quantity increases slowly at first, and then very rapidly. Exponential growth is presented when the rate of change—the change per unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time. The reason behind this claim is because of the change in the potential energy of the tennis ball at different angles. When the angle increases, the horizontal distance between the ball and the edge of the table decreases and the balls dropping point becomes higher and higher. That is why most of the potential energy of the ball was transferred horizontally in travelling forward when there is less of an angle. When the angle increases, the ball is in a higher position and most of the energy is used in the vertical action of the ball. In this experiment, some of the errors could have come from the recordings we took wasn’t clear enough and some of the the roundings we did.
Our experiment altered the original experiment where you drop it from different heights and investigate change in bounce height and efficiency. We added a ramp to our experiment to see if it changes the bounce height of the tennis balls. Looking at the results table, every 10° increased, the ramp’s height is increase by roughly 14cm and the bounce height increased by 1~2cm. Some of the errors may be our recordings for the bounce, the numbers on the ruler wasn’t clear some of the times and we had to guess it. Another major issue is a few lessons after the experiment, we were told that our recordings must in the same decimal place and that changed our results up a lot, such as the average bounce height, efficiency and absolute uncertainty. The human error is definitely avoidable in any experiment when we dropped the ball. When we reached 50°, the results unexpectedly increased bounce height a lot more than usual. It is possible that the drag of the ramp decreased dramatically at that point but we had no way of knowing. Some of the limitations of this experiment includes the angle we tested to and the horizontal components of the bounce.
In this experiment, we only tested to 50° of the ramp’s inclination, we should have tested the tennis ball until 90° and see if there is big change when it is going straight down at that point. The horizontal distance, how far the ball travelled forward may be an important factor that will help us learn more about the transfer of energy. The law of conservation of energy states that energy always stays the same amount. At 90° of the ramp, how high it bounces should be as high as the ball could go, all the energy is transferred into the ground and reaction of the ground pushes it back up. If we measure both the horizontal distance and vertical height and add them together, we should be able to compare the total energy in the cycle and find out the liability of this experiment.
Conclusion
After observing the different in the tennis ball drop height when the angle of the ramp is changed, it is revealed that as the angle of the ramp increases, the bounce height increases too. The data from figure3 proves this point and the graph of figure4 further