Tag: a-level

3.1.1 Inertia Made Obvious in the International Space Station

On Earth, objects have a tendency to fall down and slow down, thanks to the ubiquitous forces of gravity and friction. As a result, the concept of inertia is obscured from unsuspecting earthlings.

Now watch this video of NASA astronauts living the “high life” in the International Space Station orbitting high above the Earth.

Question

See how many times you can see evidences of Newton’s 1st Law.

Answer

00:17
The luggages (and the lady) remain moving along a straight lines, until they are “forced” to change their directions.

00:34
The shaver remains at rest, hovering at mid air, unless it is “forced” to move.

01:26
The astronauts remain gliding through air at constant speed since there is no external forces to change their motion.

02:01
The food pieces (pizza slices?) remain in straight line motion at constant speed, until some external forces cause a change in their velocities. The orange ball, in particular, was seen travelling along a perfect straight line, until it bounces off the camera lens.

Flying Coins

Q: Which coin will land first?

Answer:

Notice that all six coins have the same exact vertical motion. This is because all of them have the same initial vertical velocity of zero (and the acceleration of 9.81 m s-2). Their horizontal motions however differ because they had different initial horizontal velocities.

Delving Deeper

Are you wondering why the horizontal spacing among the six coins look so evenly spaced out? Well, as the ruler swivels, different parts along the ruler travel at different speeds according to the formula v=rω. Because the coins were arranged evenly spaced out along the ruler, the ruler collided into them at speeds which are evenly spaced out. As a result, the (initial) momentum (and thus horizontal velocity) imparted to coins are also evenly spaced out.

The Sound of Projectile Motion

Q: What does a projectile motion sound like?

Answer:

The key to simplifying projectile motion is to separate the vertical motion
from its horizontal motion.

Horizontal Motion

A projectile motion has a constant horizontal velocity. Horizontally, the
ball moves forward at a constant speed. This is why equally spaced
“ting” sounds are made as the ball crosses the vertical lines.

Vertical Motion

Gravity acts vertically downward. Vertically, the ball slows down on the way
up, and speeds up on the way down (at a constant rate of 9.81 m s-2
downward). This is why the “ting” sounds become more and more spaced out on the
way up, and become closer and closer on the way down.

Bouncing Ball

Q: Does a bouncing ball experience constant acceleration?

Answer:

The answer is NO during the bounces, but YES in between bounces.

In between bounces, the ball is always having a downward acceleration of g=9.81 m s-2. As such, the displacement at equal time intervals display a square number sequence 0, 1, 4, 9, 16, 25… This makes sense since the s-t relationship is quadratic.

If we calculate the difference between each pair of square numbers (4-1, 9-4, 16-9, 25-16,…), we obtain the arithmetic progression 1, 3, 5, 7, 9… This shows that the distance travelled between equal time intervals increases at a constant rate. This makes sense since the v-t relationship is linear.