# Investigate impulse and rebound height

Experiment Report – Planning (b), Data Analysis Investigate impulse and rebound height Planning (a): To investigate the relationship between impulse and rebounce height.

Planning (b): In order to measure rebounce height, we first have to select an apparatus which has a considerable rebounce. This also means something which undergoes a highly elastic collision. Tennis ball seems to be a good object to use since it rebounces at a considerable and measurable height. Measuring the height is a problem.Since the tennis ball reaches its highest rebounce height and stays there for not more that a second, it is very difficult, if not impossible, to measure this height at this split second.

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From literature formula, we have the followings: s = ut + 1/2at2 where s= displacement, u = initial velocity, a = acceleration, t = time Since the initial velocity is zero from rest, u becomes zero which gives us: s = 1/2at2 where s= displacement, a = acceleration, t = time From this, displacement can be calculated and does not have to be measured.This can increase our accuracy because using a stopwatch has a smaller percentage error than using a meter ruler. Using computer to calculate can also eliminate our random error. So using a stopwatch is preferred. Variables that I control Variables that I cannot control Variables that remains constant Variables that I measure Dropping height Air friction Acceleration due to gravity Time for tennis ball to go from initial height to rest Angle of incidence to the ground Mass of tennis ballThe initial falling height of the tennis ball might seem to be important. But from the formula, it is very clear that the dropping height is not important. As long as we start measuring when the tennis ball first hit the ground, our results will not be affected.

Stopwatch seems to be the most suitable apparatus for measuring time. We can start and stop measuring time when we see the ball hitting the ground. Although using our hands will generate a high percentage error, it is still preferred.Time gate is another time measuring equipment in the laboratory.

But this is not appropriate. It is due to the fact that time gates are too precise in time. It cannot measure a long period of time nor can it measure a long length. Due to the fact that the time is the time it takes to complete the whole displacement, which is double of the height. So we divide time by two to get the time it takes to complete the displacement from the highest point to the ground.

From the graph, we can see there is a relationship between the different rebounces.This is due to the fact that as the ball first hit the gorund, much energy is lost to overcome the significant air resistance and some kinetic energy is changed into heat energy and transferred into the ground. So the rebound heights are not as high as the first one, and they have a decreasing trend. The rate of decreasing rebound height slows down as the number of rebounces increases. This is because at a smaller height, air resistance is not as significant as before. So less kinetic energy is lost to overcome air resistance.

Also, the ball hits the ground with a smaller velocity thus transfer less energy as heat to the ground.