Composition of Motions

Figure 1

Figure 1

Figure2

Figure 2

 

This demo shows the independence of horizontal and vertical motion. The apparatus simultaneously drops one ball and launches a second ball horizontally. The balls land at the same time.

Materials:

  1. Base and rod with clamp
  2. Drop-shoot apparatus
  3. 2 non-bouncy balls (dull black ones work well)
  4. 2 pieces of sheet metal (optional)

Explanation:

To begin this discussion we must first give some background on vectors. Any vector (whether that be a velocity vector, a force vector, a momentum vector etc.) that can be defined at an angle can be described as a sum of two or more perpendicular vectors. Perpendicular components of a vector act independently of one another. It’s easy to see this in day to day life: If you push a coffee cup along a table it will not suddenly gain or lose any vertical acceleration, because you are not applying a force in the vertical direction. A change in the x component of a vector will not affect the y component and vice versa.

For this demo, we will be using x and y to describe motion in the horizontal and vertical directions, respectively. This demo shows that when two balls fall, as long  as the y component of their velocity is the same, they will land at the same time.

canonball

http://www.physicsclassroom.com/class/vectors/Lesson-2/Characteristics-of-a-Projectile-s-Trajectory

This image gives a good representation of what we see in this demo with respect to the x and y components of the velocity. We can see that the cannonball falls at the same speed when it is launched with a velocity in the x direction as when it is simply dropped from the same height.

We can also see that the cannonball takes the same amount of time to travel the same distance x when it is launched subject to gravity and when it is launched and not subject to gravity. This is because the force of gravity (ma) only affects a projectile velocity and acceleration in the y direction.

This demo also shows that the motion of an object launched with a velocity in the x direction moves along a parabola, whose width is governed by its velocity in the x direction. This is because while it takes the same amount of time to fall in either case, when it has a greater x velocity, it can travel a greater distance x in the same amount of time that it takes for the ball to hit the ground and come to rest.

Note: Use some sheet metal as a landing surface so students can hear the moment the balls strike.

Written by Sophia Sholtz