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Why do plastic rulers make you measure between two lines, instead of starting at the edge?
tl;dr: Never use the edge of a ruler or the "zero" of any analog measuring device when you are making careful measurements if you can help it. Instead try measuring between two equivalent demarkations.
from this answer; doesn't start moving until T+00:00:07!
Better yet, measure several times, plot it, and draw a line through your measurements and determine the slope.
Newton's $F = ma$ means that $a = F/m$. But $F$ has to be the total force, and there are two big ones in opposite directions, and that's what lifting off the Earth is all about!
acceleration pointing up
This is the thrust of the rocket and Wikipedia's Falcon 9 says that for F9 v1.2 or Full Thrust it is +7,607,000 Newtons where the plus sign means "up".
The loaded mass is 549,054 kg, so
$a_{thrust} = F_{thrust}/m = \text{13.85 m/s}^2$
acceleration pointing down
At liftoff and while it's not going really really fast yet, so gravity is the only important one. Earth's standard gravityis 9.80665 m/s2.
So the rocket will initially accelerate at roughly 13.85 - 9.81 = 4.04 m/s2.
Using $v = at$ and assuming the mass doesn't change too much in the first ten seconds (it does a bit of course) then I get 72.7 and 145.4 kph after 5 and 10 seconds, just like you.
what could be the difference?
Never start a measurement at zero. Never use the zero of a ruler; if something is about 10 cm long, measure from 1 cm to 11 cm, that way if the manufacturer screwed up slightly cutting it it won't make a difference.
Play the video slowly, like 1/4 or 1/8 speed, and stop it each time the timer changes from one seconds digit to the next, and write down the velocity.
Try this:
Plot v vs t on a graph, and you'll see it is probably a fairly straight line but it hits zero at around 1 or 1.5 seconds, not zero.
Then read all the answers and all the comments on What "actually" happens at T-minus-0
update:
You're doing just fine!
I see you are active in Stack Overflow so I'll add some Python script. I took your numbers and did two things:
- you have the h and v switched in the 7.5 second line so I switched them back
- included a 3.5 second offset between whatever T=0 is in the video and time since the rocket starts moving.
- plotted your simulation as solid black line
- plotted your video measurements as blue dots
- Added a red dashed line for a simple 4.04 m/s2 acceleration
The resulting fit is quite nice; all three agree fairly well already! You are doing just fine and you can extend this further in time now, and check more effects.
import numpy as np
import matplotlib.pyplot as plt
time = np.array([0, 2.5, 5, 7.5, 10])
time_smooth = np.arange(0, 16, 0.1)
model_h = np.array([0, 15, 58, 124.7, 221.5])
model_v = np.array([0, 10.7, 21.5, 32.5, 44])
video_v = np.array([0, 2, 7.8, 16.5, 26.3])
T_start = 3.5
a_guess = 4.04
plt.figure()
plt.subplot(2, 1, 1)
plt.plot(time +T_start, model_v, '-k')
plt.plot(time, video_v, 'ob')
plt.plot([-1, 14], [0, 0], '-k', linewidth=0.5)
plt.plot(time_smooth, a_guess * (time_smooth - T_start).clip(0, None), '--r')
plt.xlim(-1, 14)
plt.ylim(-2, 42)
plt.title('vertical speed (m/s)')
plt.subplot(2, 1, 2)
plt.plot(time + T_start, model_h, '-k')
plt.plot(time_smooth, 0.5 * a_guess * (time_smooth - T_start).clip(0, None)**2, '--r')
plt.plot([-1, 14], [0, 0], '-k', linewidth=0.5)
plt.xlim(-1, 14)
plt.ylim(-10, 210)
plt.title('vertical height (m)')
plt.xlabel('time (sec)')
plt.show()
