Ps 1: Conceptual questions for kinematics of parabolic motion

by Quirino Sugon Jr.

PARABOLIC MOTION

Choose the word or phrase inside the parenthesis that makes the statement true.  Write your answer on the space provided before each number.

1. If you throw a stone upwards, the path of the stone in space is a (line, parabola)
2. The path of the stone in height vs time graph is a (line, parabola).
3. If you release the stone on the level of your head, and your coordinate system is positive pointing up and zero at the ground, then the initial height of the stone is (negative, zero, positive),
4. the initial velocity of the stone is (negative, zero, positive),
5. and the gravitational acceleration is (negative, zero, positive).
6. When the stone reaches its maximum height, the velocity of the stone is (negative, zero, positive)
7. and the acceleration of the stone is (negative, zero, positive).
8. The acceleration of the stone just after it was released is (smaller, same, bigger) in magnitude compared to that when the stone reached its maximum height.
9. When the stone falls down again after it reaches its maximum height, the speed of the stone is (smaller, same, bigger) in time.
10. If the stone hits your head, the velocity of the stone is (upwards, downwards).
11. This means that the velocity of the stone is (negative, positive).
12. The speed of the stone just after it was released near the top of your head is (smaller than, same as, bigger than) the speed of the stone when it hits your head upon its return.
13. Suppose instead that you are standing on top of a train that is uniformly moving in one direction, which is the same direction you are facing.  If you throw the stone upwards as before, the stone will (fall far behind you, hit your head, fall far in front of you).
14. For a person standing on the ground looking at you, the path of the stone in space as it moves up and down is a (line, parabola).
15. For the person standing on the ground, the speed of the stone along the horizontal is (slower than, equal to, greater than) the speed of the train.
16. The magnitude of the acceleration of the stone along the horizontal is equal to (zero, gravitational acceleration) .
17. Now, suppose you are riding instead a plane.  And instead of throwing a stone upwards, you drop a bomb.  From your point of view, the bomb is falling in a (linear, parabolic) motion.
18. From the point of view of a person on the ground, the bomb is falling in a (linear, parabolic) motion.
19. The faster the plane travels, the (shorter, farther) will the bomb hit the ground.
20. Just before the bomb hits the ground, the horizontal velocity of the bomb is (smaller than, equal to, greater than) the constant speed of the plane, assuming there is no air friction.
21. If there is air friction, the horizontal velocity of the bomb would be (smaller than, equal to, greater than) the constant speed of the plane.
22. If there is no air friction, the magnitude of the vertical acceleration of the bomb is (smaller than, equal to, greater than) the constant gravitational acceleration.
23. If there is air friction, the magnitude of the vertical acceleration of the bomb is (smaller than, equal to, greater than) the constant gravitational acceleration.

Scientific method as drama: setting, characters, conflict, climax, and denouement.

by Quirino Sugon Jr.

Scientific method is a method for knowing the relationship between different physically measurable concepts.  There is no one way to do science, but its essential parts can be gleaned from the example of falling bodies.  You will notice that it has all the ingredients of a drama: setting, characters, conflict, climax, and denouement.

A.  Setting and Characters: Observation

For example, if you throw a stone upwards and video the result, you can measure both the height of the rock  and also the time it took for the rock to reach a particular height.  From this two data, you can plot the position vs time function and obtain a parabola.  Then you can find the instantaneous rate of change of position with respect to time to obtain velocity.  You can do likewise for velocity and obtain acceleration.  And you obtain a constant acceleration equal to .

The main characters of the story are time and position.  The supporting casts are velocity and acceleration.  The setting is free fall motion.

B.  Conflict:  The Search for Universals

Then you ask: is this value of acceleration constant for all objects on the surface of the earth?  Is the constant gravitational acceleration a universal law that governs the relationship between position and time?

And you find out that it is not true: a feather falls slower than a stone.  So you ask yourself why.

If you are Aristotle, you shall propose the following universal law in two statements:

1. All matter can be broken down into four components: earth, water, air, and fire.
2. The heavier elements goes toward the center of the earth; the lighter elements goes away from the center of the earth.
3. The speed of the body is proportional to its weight.

People tend to scoff at Aristotelian physics, but there are some truths in it.  Replace earth, water, and air by our concepts of solid, liquid, and gas.  Replace fire by temperature.   Plotting the pressure vs temperature of a substance leads to the classification of different phases of solid, liquid, and gas.

Aristotle’s third statement is also true, provided we assume that the speed is what we call as the terminal speed.  Raindrops fall faster and faster then slower and slower until they travels at a constant speed, due to friction with the air.  This constant speed is the terminal speed.

But what happens if the speed is not the terminal speed?  Then Galileo showed that Aristotelian physics collapses.  Galileo dropped a small and large cannonball from the top of the Tower of Pisa and showed that they arrived at the ground at the same time.  We need a new physics.

C.  Climax: The Scientific Laws

The endless struggle by scientists to find universals in the physical world resulted to the many laws of Physics.  But we must always remember that these laws have a certain range of validity.  Newton’s law of Universal Gravitation may be valid for the falling apple, for the moon around the earth, for the earth around the sun, and for other planets around the sun.  But when we go to the level of galaxies, things go awry.  Newton’s theory predicts that stars near the center of a galaxy travel faster than those far from the center.  But it turns out that in many galaxies, the stars near the center and away from the center have the same orbital speeds.

To resolve this problem, scientists propose a new kind of matter–not anymore earth, water, air, and fire–but something else, something dark and mysterious because we can’t observe it.  So they simply call this thing as “dark matter”, which permeates the voids between the stars.  Other scientists don’t like this idea.  They propose instead that the equation for Newton’s law of Gravitation should be modified.

D.  Denouement: Application of Universal Laws

Once the scientific law has been found, scientists apply them to different problems, instead of a smooth cannonball, we can have the whole London bridge falling down or an airplane flying up.  To do this, we cannot anymore rely on one universal.  We have to use others.

We first make a survey of what has been done before, define the concepts needed, determine the known values or imposed parameters,  write down the universal equations that relate these concepts and their values at certain conditions, describe the method for measuring the known and knowable parameters, present your results, write your conclusions, and list your references.  These are the parts of a scientific paper, which is published so that other scientists can duplicate what you did, learn from your mistakes, and use your results in proposing a new universal law.