Category: 02 Kinematics

Feather and Hammer (BBC)

Below is a famous video of an Apollo 15 astronaut conducting the feather and hammer demo on the Moon.

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And then there is this BBC video of the same demo conducted in a GIGANTIC vacuum chamber.

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On one hand, gravitational pull on an object is directly proportional to its mass (F=mg). On the other hand, the acceleration of an object is inversely proportional to its mass (Newton’s 2nd Law resulting in F=mg). These two factors together means that every object accelerates at g=9.81 m s-2 regardless of their masses.

Shoot the Monkey (Harvard Natural Sci)

The key to understanding this puzzle is to realize that both the projectile motion of the bullet and the vertical fall of the monkey have the same exact acceleration (9.81 m s-2  downward).

Let’s start off by pretending that there is no gravity. By aiming at the monkey directly, the bullet would have travelled along a straight line, and the monkey would have hovered in the air, resulting in a hit.

Now let’s switch gravity back on. The bullet would now travel in a parabolic path, falling below the zero-gravity-straight-line path by a distance of 0.5gt2. The monkey would have fallen down by a distance of 0.5gt2. Because gravity affected both motions equally, gravity or not, the monkey is doomed to be hit.

 

112 Vertical Bounce of a Ball

Except for the brief instants when the ball was in contact with the table, it was free falling. Whether it was on the way up, or on the way down, it was experiencing a downward acceleration of 9.81 m s-2. Since acceleration was constant, the ball’s displacement’s varies with time quadratically.

It is quite fun to see in slow motion how the golf ball comes to a complete rest at the peak of the bounce.

It is also interesting to note that the ball’s displacement is symmetrical about the peak. In fact, if the video is played in reverse, the motion of the ball between bounces would have looked exactly the same.

111 Ball Rolling down an Incline

Because the ball was released from rest, and because it was accelerating at a constant rate, its displacement varied with time according to the formula s=1/2 a t2.

By noting the positions of the golf ball at equal time intervals, we confirm that the displacement was indeed increasing quadratically with time.

This video also tells me that my eyes are not very good at judging velocity, and totally hopeless at judging acceleration. Haha.

 

110 Travellator

From my point of view from the moving travellator, the ball was moving vertically up and down.

But from the point of view of a stationary observer, the ball was moving in a parabolic path.

This video illustrates the fact that projectile motion can be understood as a vertical throw superposed with a horizontal constant speed motion. This should make it obvious why the maximum height and time of flight of a projectile motion is unaffected by the initial horizontal velocity, and how the range of a projectile is affected by both the initial vertical and horizontal velocity.

Another point to note is that from the point of view of the stationary observer, the initial velocity of the orange is the summation of the horizontal velocity of the travellator and the vertical velocity at which the ball left my hand. The orange “inherits” the velocity of the travellator, so to speak. If I had merely released the orange, it would have been a horizontal projectile motion to the stationary observer.

 

108 Horizontal Projectile

This demonstration illustrates the fact that the vertical and horizontal motion of a projectile motion are independent of each other.

The coins were launched with the same initial vertical velocity of zero, but different horizontal velocities. Since the vertical motion is totally determined by the initial vertical velocity, all the coins drop vertically at the same rate, and land at the same time. The horizontal velocity determines how fast the coin moves forward. Since they land at the same time, the coin with the highest horizontal velocity lands furthest away.

How does the “launcher” work?

Basically, different parts of the ruler have the same angular velocity but different linear velocity (v=rω). Upon collision, the coins are thus launched at speeds proportional to the distance away from the pivot. In the video, the furthest coin is about 2 times away from the pivot as the nearest coin. So the furthest coin was launched at about 2 times initial speed as the nearest, resulting in it landing about 2 times as far as the nearest coin.

 

 

 

005 What does the ringing say? (about projectile motion)

The force of gravity is the only force acting on the ball when it was in the air. Since gravity is constant and acts vertically downward, the vertical motion is uniform acceleration motion at g = 9.81 m s-2 (downward), whereas the horizontal motion is constant speed motion.

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The fact that the horizontal speed of a projectile is constant is confirmed in the video by the regular spacing of the chimes, as the ball crosses the regularly spaced vertical lines at equal time intervals.