Figure 1

Description:

This apparatus simultaneously drops a ball and a square of aluminum foil into an evacuated cylinder to demonstrate the independence of mass and gravitational acceleration. It is a good idea to drop the ball and foil by hand in front of the audience and then follow this procedure.

Materials:

1. Plexiglass cylinder with copper coils at the top (Figure 1)
2.  Vacuum with tube (Figure 4)
3. Cap with valve (Figure 2)
4. 9V Battery (Figure 3)
5. 2x battery leads with alligator clips (red/black) (Figure 4)
6. 1x Magnetic ball, 1x paper clip, and aluminum foil
7. Clamp stand for cylinder

Figure 3

Figure 4

Figure 2

Demo:

1. Connect the battery leads to the 9v battery attached to the tube to allow a current through the coils, thus creating a magnetic field.
2. Lift the cap off of the cylinder and place the ball and foil onto the magnetic holders at the top of the tube. The foil can be held onto the magnet using a paper clip.
3. Gently press the cap into top of the cylinder, and connect the vacuum to the valve via the tube provided, making sure the valve is open.
4. To evacuate the cylinder, turn on the vacuum and wait till the pressure gauge has maximized (Usually around 27 inHg). Then, shut the valve and turn off the vacuum.
5. To release the ball and foil, unclip one of the leads from the battery so that the coil is no longer magnetized. The two objects should fall at the same rate.
6. To retrieve the ball and foil, release the valve gradually to let air in, then remove the cap. One can either remove the cylinder from the clamp and flip it upside down, or feed a string with a magnet towards the bottom of the tube and lift the objects out.

Explanation:

We can explain why in the vacuum the ball and the piece of foil fall at the same acceleration by using Newton’s second law of motion, F = ma.
Here we need to distinguish between two quantities, the acceleration due to gravity, which is constant (mostly, at sea level); and the force acting on the object due to gravity. We will show that the forces due to gravity are different with math, but you can also tell for yourself with a simple experiment.

If we hold a piece of foil in our hand, it requires less force to hold it in equilibrium. Remember that to hold an object in equilibrium, the forces must be balanced. You can then tell the relative force of gravity just by seeing what force is required to keep it still (how heavy it is!). A plastic ball with a magnet within has a greater force due to gravity, and you have to exert more force to keep it in equilibrium with your hand (it weighs more).
The differences in the force due to gravity are because the masses are different, and according to F = ma, a greater mass leads to a greater force.
Take a 1kg brick and a 1 gram feather under the acceleration of gravity (9.8 m/s2). FgB is the force of gravity acting on the brick, and FgF is the force of gravity acting on the feather.

FgB = mB a = (1kg)(9.8m/s2) = 9.8 N
FgF = mF a = (0.001 kg)(9.8m/s2) = 0.0098 N

This shows us that the gravitational force acting on each object is different, but the force of gravity is not the only thing governing the motions of objects in free fall. Inertia plays an equally important part.

Inertia can be explained by Newton’s first law of motion: an object at rest will stay at rest unless acted on by an external force; an object in motion will continue in motion at constant speed and direction unless acted on by an external force. The greater mass an object has, the greater its tendency to resist a force acting on it. You can see this with another simple experiment: place two bricks, one of cement and the other of styrofoam on a table and push them. The styrofoam brick will begin to move with a much smaller force than is needed to move the cement brick. This shows how mass affects inertia.*

This concept of inertia is displayed in the vacuum tube, and explains why even though the ball has a greater force of gravity acting on it compared to the foil, they fall with the same acceleration. Because the foil is lighter than the ball, it has less inertia and therefore has a smaller tendency to oppose a change in motion. This means that less force is required to start moving it. Conversely, because the ball is heavier than the foil, it has a greater tendency to oppose any force applied to it, and it needs a greater force to begin moving from rest. This means that a ball and foil will fall with the same acceleration because they are opposing the change in motion (from rest to falling with gravity) to different degrees, proportional to their masses. The small Fg on the foil is enough to start it moving, where the ball needs a substantially larger Fg to get it moving.

Now it is obvious to wonder why the vacuum tube is necessary to demonstrate this property of objects. All objects that fall in the atmosphere are affected to a certain degree by the force of air resistance, which opposes all direction of motion. The vacuum tube creates a vacuum so there is no air for air resistance to play a part. The two most important contributing factors to air resistance are the cross-sectional area of the object and the speed of the object. An increase in either of these will lead to an increase in the air resistance acting to oppose the direction of motion.

Terminal velocity is the speed at which an object is falling such that the force of air resistance (FAR) opposing the direction of motion is equal to the force of gravity acting on an object. Because at this point the forces are balanced, the object will stop accelerating and will maintain a constant velocity (VT). For a more massive object which has a greater Fg, it will require a greater FAR to balance the forces to stop the object from accelerating. Because air resistance is proportional to velocity, it will need to accelerate to a greater velocity to achieve the FAR necessary to balance the forces. Equally, for a light object, there is a very small Fg. This means that there will need to be a very small FAR acting in the opposite direction to stop the acceleration. A small air resistance force can be achieved at very low speeds (especially if there is a large cross-sectional area), so it will reach terminal velocity shortly after it begins accelerating. This is shown in the following image with the example of an elephant and a feather.

Notes:
Works well but can only be seen from the first few rows without a video camera
Works best at max vacuum pressure (27-30 inHg on gauge)

Written by Sophia Sholtz