## Equilibrium and Center of Mass

• ME4.1 Pendulum Cart (for use with Air Track)

The sled with the pendulum is used in this demo. First, with the air turned off, show the class that the sled remains in place and the swinging of the pendulum is quickly damped. Then with the air on, the sled moves in the opposite direction of the pendulum so as to conserve its center of mass.

• ME4.2 Bicycle Wheel Rolling Uphill

This demo consists of two tires rolling in opposite directions on an incline. One is weighted at a point on the tire changing the center of mass, which causes it to roll upwards; the other tire is normal and rolls downwards.

• ME4.5 Cylindrical Body Rolling Uphill

This demo consists of an inclined ramp and an object that looks like two cones connected to their bases. The class assumes that the object will roll down, but because of its center of mass, it appears to roll uphill.

• ME4.6 Hanging Body

This is asymmetric figure that has hooks to be hung by at various points. The object is to find the center of mass-the point on which gravity acts. By drawing a straight line from the hook in the direction of gravity for each hook, the center of mass can be found at the intersection of all the lines.

• ME4.7 Leaning Tower of Pisa

This is a piece of wood that stands on a slant. If the top is put on shifting the center of mass, then the tower falls.

• ME4.8 Pendulum on Cart

This is a pendulum rigidly attached to a rolling cart. As in the case of the air track, the cart moves in the opposite direction of the pendulum in order to keep the center of mass constant. However, due to friction, the cart tends to travel across the floor rather than stay in the same area while the pendulum swings.

• ME4.9 Weights and Fish Scale

The fish scale is horizontally attached to two strings. Each string has an equal weight of mass m hanging vertically over pulleys. Pose the question to the students if the scale should read m or 2m. Since one side is attached to the spring while the other is attached to the actual scale, the scale should read m. The tension in the rope is mg, not 2mg.

• ME4.10 Cart on Inclined Plane

A car is placed on an inclined board. A string is attached to the end of the car and is strung up the incline, over a pulley at the top and then straight down. A mass is attached to the end. Another string is attached to the top of the car and is strung so that it is exactly perpendicular to the car over a pulley. Again a mass is attached at that end. After a bit of Newton's second law and trigonometry, the masses are 330gm for the parallel string and 570gm for the perpendicular one. The demonstration is that when the inclined plane is removed, the car is suspended in mid-air with the same angle.