Month: February 2016

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.

 

 

 

106 Cartesian Diver

I have built a variety of Cartesian divers over the years. Some divers have openings for water to go in and out, others are sealed. But the underlying principle is the same: The diver sinks when its weight is larger than the upthrust it receives from the surrounding water.

The diver in the above video has an opening at the bottom. At 0:11, you can see clearly water rising through the opening into the diver to fill up more of the air pocket on the top of the diver. This increases the weight of the diver, and it sinks.

The trigger for the water to rise up the diver was my hand squeezing the bottle. Squeezing the bottle caused the water level in the bottle to rise up and press against the bottle cap, thus increasing the water pressure in the bottle. The increased water pressure forces water into the diver, until the pressure of the air pocket in the diver matches the new water pressure.

In the above video, I used my fingers to directly compress the air pocket on top of the bottle. The increased air pressure means that the pressure in the water also increased. Water is forced into the diver, and the same thing happens.

The diver in the above video is a candy in an air-tight packaging. Needless to say, water cannot not go in and out of this diver. But it can be seen clearly at 0:19 that when the bottle is squeezed and unsqueezed, the candy shrinks and expands. As if the diver is breathing in and out! When the bottle is squeezed, the increased pressure forces on the candy squashes it. With a decreased volume, the candy displaces less water. The upthrust decreases, and it sinks.