Suppose we have an object with mass m = 1 kg, falling from an initial height $y_0$ = 1000 m through air with a density $\rho$ = 1.20 kg/mĀ³. The frontal area area is 0.01 mĀ², the drag coefficient is 0.5 and it is falling due to a constant gravitational force of $F_g$ = -mg. This is a one-dimensional problem.
Question 2- Calculate the value of a for this scenario.
Question 3- Neglecting air drag for now, what is the time $t_1$ needed for the object to fall to y = 0, using the kinematics we learned earlier in this course?
Set up a spreadsheet to calculate the height of the object at a series of regular time intervals $\Delta t$ = 1 s apart. You should have columns for: time (s), height (m), velocity (m/s), drag force (N), net acceleration (m/sĀ²). The net acceleration results from the net force (gravity plus drag force), which changes the velocity. The velocity changes the position.
Note: The "Euler-Cromer" method from the tutorial from this week is not necessary for this scenario.
Drag your formulas down until you include your time $t_1$ from question 3.
Question 4- What are the approximate height and velocity at $t_1$? Use the line with the closest time.
Keep dragging your formulas down until the object hits the ground (y goes from positive to negative).
Question 5- What do you observe about the velocity and acceleration columns near the end?
Make graphs of height vs time and velocity vs time.
Question 6- How do your height & velocity graphs differ from the ones for regular free-fall without air drag?
Question 7- Terminal velocity is the maximum velocity when air drag balances the graviational force for a falling object. You know $F_g$ = -mg and $F_d$ = $av^2$, so calculate v directly and compare it to the value at the bottom of your spreadsheet calculations. How many time steps to you need to calculate so that the velocity is correct to two decimal places?