Slip sliding away
If a ball sits on the surface of the gravity well it is on an inclined plane sloped toward the center. The inclined plane exerts a force on the ball toward the center of the well. Here are a couple of ways to feel that force.
Put the bowling ball into the nylon stocking.
Nail the boards together with other pieces of wood so that there is a 2.5 cm gap between the two boards.
To Do and Notice
Pull the stocking through the slot between the boards.
Hold the end of the stocking on the side of the board opposite the side the bowling ball is on.
Have someone else begin to tip the boards to one side.
You keep the bowling balls from sliding down with a horizontal force on the stocking.
As the boards are inclined at a steeper and steeper angle the force you have to apply gets larger and larger. Remember to pull only in a horizontal direction.
You may also see the force you are applying in the length to which the stocking is stretched.
Place the bowling ball at rest on the gravity well. Put three fingers on the side of the bowling ball toward the center of the gravity well. Push horizontally outward and feel the force on the bowling ball you have to exert to keep it in place. Notice that you have to exert a large force near the center of the well and a small force near the rim.
What's Going on?
The bowling ball is on an inclined plane.
The force of gravity is vertically downward.
The force from the inclined plane on the ball has two components, a vertical part which must be equal and opposite to gravity and a horizontal part which you are exerting. The horizontal component goes up quickly as the angle of the board is increased.
In the gravity well, a bowling ball placed at rest on the gentle slope near the outer edge will have a small force toward the center, a bowling ball placed on the steep slope near the center will have a large force toward the center.
When the bowling ball is in a circular orbit inside the gravity well, the force toward the center of the well is the only horizontal force. (The vertical component of the force is opposed and canceled by gravity.) This force causes the ball to accelerate toward the center of the well. This central force is called the centripetal force.
A force directed toward the center is required to make an object orbit in a circle at a constant speed. This force is created by the slope of the gravity well.
The magnitude of the central force, Fc, is related to the speed of the object, v, and the radius of its circular motion, r by the equation:
Fc = v2/r
Thus if the force toward the center is inverse square:
Fc = 1/r2 = v2/r then
v = 1/r
At smaller radii the velocity is higher.
As we observe in the gravity well.
Scientific Explorations with Paul Doherty
2 August 2001