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VideoStrobe Examples

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Parabola (was Galileo right?)

 
When you throw a ball it follows a parabolic path through the air.
 
An aside: I always thought parabola came from the Greek for "like a throw,"  but it seems this is not so. According to the Collins English Dictionary the word comes from the Greek word "parabolē: a setting alongside." This choice of word was most likely made because of the construction a parabola from a cone by cutting it with a plane set alongside or parallel to  the side of the cone (see Dr Math), and almost certainly has nothing to do with the path of a projectile. Although para means 'beside' and bolē means 'throw' the word parabolē is has nothing to do with throwing something as a projectile, but rather with throwing or putting something into place. Galileo appears to be the first to associate the geometric shape of a parabola with a thrown object, and Newton provided the calculus that allows the formula to be derived from knowledge of the force of gravity.
 
Most people would agree that when you throw a ball it follows a curved path, but how can you demonstrate that it follows a parabola and not some other curve such as an elliptical arc? Galileo managed by rolling balls up a slope and hence diluting gravity and slowing things down enough to see what was going on. With modern technology we can capture an image of the ball at each point of its path, and show how closely it fits a parabolic curve.
 
This video was shot with a yellow tennis ball against a backdrop of blue venetian blinds. The yellow on blue gives excellent contrast. Two students were filmed tossing the ball from one to the other. Using VideoStrobe, frames from exactly one throw were selected and the strobographic image was imported into GeoGebra for curve fitting.
 
 
 
Possible extensions to this activity:
  1. Get students to try fitting other equations to the path e.g. sine, ellipse, cubic, hyperbola. Can you get a better fit?
  2. Include a ruler in the video so that distances can be calibrated. Get students to predict the path of the ball using kinematics, and then check their predictions using VideoStrobe and GeoGebra.

Parachute (detailed motion analysis)

We were planning to launch a high-altitude balloon which would come down with a parachute. We needed to know the descent speed so we could predict where the balloon capsule would land. Knowing the terminal velocity at sea level was enough - the software that carries out the prediction uses this value as an input.

We threw the capsule rigged with the parachute off a six storey building, and videoed the landing. Here's the video...

Getting detailed motion analysis with stop watches would have been almost impossible. It is not enough to know how long the capsule took to fall six storeys, we need to know that it has reached terminal velocity and what that velocity is when it lands. Motion analysis with VideoStrobe is the answer.

First the strobographic image. The child in red (Note that red and blue have been inverted in some of thse examples. This is a problem with VideoStrobe 2.0.2 inverting red and blue. This issue has been fixed in Version 2.0.3, but the examples made with v2.0.2 have not all been updated. It does not affect the kinematics of the situation.) is carrying a pole which was to have been used in calibration, but it does not show up clearly enough in the strobographic image. Instead we use the fact that he was 1.6 metres tall. Using this measurement was difficult off the strobographic image, so a still shot from the video was used. These images were imported into GeoGebra (screenshot below) and calibrated. (Horizontal lines were drawn over the x-axis and at y = 1.6. The images were adjusted so that the child in the still fits between these lines. The x and y coordinates now read metres.)

Next we draw points on the top of the radar reflector each time it appears in the strobographic image. GeoGebra gives us the coordinates in the algebra panel on the left.

We used My Computer - Properties to get the frame rate of the video (screenshot below).

Finally we transfer only the y coordinates to Excel and examine the data (screenshot below). It becomes obvious that the parachute is falling at 6.4 m/s and accelerating at 1 m/s2. This is one tenth the acceleration of gravity so it is nearly at terminal velocity, but not quite. We need to find a taller building.

In reality we used the figure of 6.4 m/s and it was too low - the chute came down faster than that. You might wonder why we did such a stupid thing. The reason is that we did not use Excel to perform the linear regression, and we assumed that the chute had reached terminal velocity.

 

 

Friction

A projectile follows a parabola because it is subject to a uniform force: the force of gravity. The force of gravity is independent of velocity. It turns out that the force of kinetic friction is also independent of velocity (more or less). The question is, how much is 'more or less'. Does a rolling ball, being slowed by kinetic friction, slow down parabolically. Enter our hero, VideoStrobe, to answer that question.

First, here's the video (we chose carpet because the ball rolls straight and slows quickly) ...

This is a one dimensional motion, so we use VideoStrobe's x-shift function to spread out the images with time along the x-axis. We get this image...

The frames have been rotated so that we can have time along the x-axis. The shape along the bottom is my hand releasing the ball, and the spikes are the shadow of the ball.

Attempting the curve fitting in GeoGebra we discover...

a near perfect fit to a parabola. Note how the curve straightens when the ball comes to a standstill and static friction kicks in.

 Simple Harmonic Motion

I filmed this one with the camera held on its side...

Fortunately its easy to rotate it in VideoStrobe. With a bit of x-shift we get a lovely...

well what shape do you think? Try fitting a sine function here. (If you have trouble with this link, download the GeoGebra file for offline use. It is attached below.)

Last edited by System Administrator .
Page last modified on Monday 15 of November, 2010 10:27:04 NZST.


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