Julie-Ann’s Bungee Jumping Case Study - Python Function & Code, Acceleration - IT Assignment Help

Assignment Task

1 Part 1

Julie-Ann’s friends pressure her into going bungee jumping for the first time. Julie-Ann is a cautious woman, so she isn’t going to jump unless she is sure it is safe to do so. She decides that she’d like you to simulate the bungee jump using Python, since you’ve taken a course in Computer Science, and show her the results. 

1. In the first step of this part, you’ll simulate a free fall in the absence of air friction.

2. In the second step, you’ll include calculations for air friction. 

3. In the third step, you’ll add the spring forces of the bungee cord. 

Task 

2.0 Loop over time steps  Update position, velocity, time (step 1) 

2.0 Air friction: Update forces, update acceleration (changes from step 1) 

2.0 Bungee: Update forces (changes from step 2) 

1.1 Step 1 

Using Julie-Ann’s (wearing her clothes, the harness, and bungee cord) weight of 70kg, simulate the motion of a free fall, without considering the forces of friction or the effect of the bungee. In other words (in the simulation), let’s let Julie-Ann fall to her death (for science!). Only gravity will affect Julie-Ann’s fall. For simplicity, use positive numbers to represent downward motion, so the length will represent how far from the platform Julie-Ann has traveled. 

Note: Let’s assume that Julie-Ann’s height is infinite so that we can see the pattern of her fall more easily. 

Create a Python function (simulateFreeFall), which takes 3 arguments: - mass: The mass of Julie-Ann (or any falling object) - deltaT: The length of time (in seconds) of each time interval, for the simulation - simulation time: The length of time (in seconds) of the entire simulation 

The function will calculate from deltaT and simulation time how many time steps there should be. For each of these time steps, you will calculate the length (distance from the platform, in meters), velocity (in metres/s), and acceleration (which will be constant, 9.81 meters per second squared). 

At each time step, record each of the following values in a Python list: 

• elapsed time: deltaT * the number of time steps that have passed 

• length: the distance between the object (Julie-Ann) and the platform at that time step

• velocity: the velocity of the object (Julie-Ann) at that time step 2 

• acceleration: the acceleration on the object at that time step 

The function will return a tuple containing all four of these lists (times, lengths, velocities, accelerations). 

Updating the length: 

When updating the length, use the current velocity and the current elapsed time, in the formula: delta = v * delta 

If you use a single time step duration for deltaT (deltaT), and the current velocity for v, then delta will be the change in length, which you’ll need to add to the previous length. 

Updating the velocity: 

When updating velocity, we’ll calculate how the current acceleration will affect the value, using the following formula: 

delta = a * delta 

If you use a single time step duration for deltaT (deltaT), and the current acceleration for a, then delta will be the change in velocity, which you’ll need to add to the previous velocity. 

Updating the acceleration: 

This part of the assignment does not require any modification to acceleration. JulieAnn will continue to accelerate downwards for the duration of the simulation. 

Write some Python code to call your function, collecting the four input lists it returns. 

• Use 70kg for Julie-Ann’s mass, deltaT of 0.01 seconds, and simulation time of 60 seconds.

• Chart the length values vs. elapsed time values, with red squares for markers, using Mat PlotLib. 

1.2 Step 2 

For the second step of this part, you will simulate another free fall, but this time you will incorporate air friction (also known as drag). Start by making a copy of your function from step 1, and rename it simulateFallFriction. Our function will have one new argument, in addition to the previous arguments: 

• surfaceArea: The surface area (in m2) of the falling person/object 

We’ll perform this calculation by adding up all forces on our object. In this part, we have two forces: 

• 1. the force due to gravity (we’ll call this Freight) 
• 2. the force due to air friction (we’ll call this Friction) 
• Updating the length and velocity: 
• Updating the length and the velocity will use the same procedure as in the previous step, but now the acceleration is not constant, since it depends on air friction (which itself is dependent upon velocity). 
• Updating the acceleration: 
• We didn’t really consider forces in the previous section, so we’ll need to consider the force created by gravity, using the following formula: 
• Fweight = m * g 
• A simplified formula for air resistance at sea level is given below: 
• Friction = -0.65 * surface area * v * |v| (|v| - absolute value of v) 
• For the sake of this simulation, we’ll use 0.2m2 for Julie’s surface area. 
• Now, the total force (Ftotal = Fweight + Ffriction) can be used to calculate the acceleration: a = Ftotal / mass 
• As before, write some Python code to call your function and collect the returned lists. 

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