Acceleration vs Time Bungee Graph

[ZCV99]

Homework Statement

https://bb9.waukesha.k12.wi.us/bbcswebdav/pid-692070-dt-content-rid-2436419_1/xid-2436419_1

The graph above was made from acelerometers placed on a person while experiencing a bungee jump. The graphed data is not smooth because it is real data. The positive direction is up. While answering the following questions look at the overall shape of the graph and filter out the momentary spikes.

1. Study the graph of the acceleration during an actual bungee jump.. Identify the time corresponding to the lowest position during the jump.
2. What was the acceleration at that point? Was the direction of the acceleration up or down?
3. Identify the time when the jumper reached the highest position after the first bounce.
4. What was the magnitude of the acceleration at that time? Was the direction of the acceleration up or down?
5. What was the maximum speed of the jumper?
6. What was the impulse on the jumper during the first bounce?

Homework Equations

p=mvf-mvi

The Attempt at a Solution

2. The lowest point of the bungee jumper is at 6 seconds because this is when his acceleration from the stretched bungee cord is at its highest, assuming that the previous spikes at 4.5 seconds and 5.5 seconds are inaccuracies in the accelerometer. 3. Following the general shape of this curve, the acceleration of the bungee jumper should be 20m/s^2 upwards at the lowest point of his jump.4. The time when the jumper reached his highest point should be about halfway through the free fall section, or 9 seconds, because during this free fall section, the negative, downwards force of gravity is providing the only acceleration experienced by the jumper, but he continues to have a positive upwards velocity from the positive acceleration he had previously experienced due to force provided by the bungee cord beforehand. This velocity doesn’t become negative again until just before halfway through the free fall when velocity is zero and the jumper reaches his highest point.5. The acceleration is 9.8m/s^2 downwards.6. The maximum speed of the jumper can be found by estimating the area under the acceleration vs time graph between 5 and 7 seconds, when the bungee jumper is experiencing positive acceleration from the force of the bungee cord acting on it. Assuming that the maximum acceleration from the bungee cord is 20m/s^2 and a roughly triangular shape for the area between the graph and the 0m/s^2 a value, the maximum speed is calculated as: 0.5*2*20=20m/s.7. The impulse is equal to the change in momentum during the first bounce, which can be found by the equation mvf-mvi. vf=20m/s because that is the maximum speed of the bungee jumper calculated before. vi is -20m/s because the jumper was in free fall for 2 seconds before the first bounce, so using the equation a=(vf-vi)/T, 9.8=(vf-0)/2, vf=20m/s. So, the impulse on the jumper during the first bounce was 40*m N*s.

 

[ZCV99]

The graph can also be found here: http://www.narragansett.k12.ri.us/NHS/scienceweb/quansweb/bungee.htm