M-S 1: Normal and frictional components of the force exerted by surfaces in contact

PIRA: 1J30.10

Equipment: special inclined plane set at 30 with weights calculated to furnish replacement for the normal and frictional components exerted on the cart on the plane by the plane, block and C-clamp to act as a chock for the cart. This is kept in rm 71 along the East hallway.

Procedure: Many are inclined to weigh the cart, calculate the values for the weights required to support it, then make an experimental check to show that intruth the plane's action on the cart can be replaced by appropriate forces from another source. This is a sure way to bore the average students to complete inattention.

I recommend the following. Forget the numbers; they are inconsequential compared to the main purpose, instilling into the student not only the knowledge but the belief that forces and their components can be replaced by truly equivalent forces from a different source.

When the students enter the room, the plane is already set up with the cart on it placed so that the cord from the upper pulley makes a right angle with the plane, the chock is firmly held in place by the C-clamp, and the weights are on the table although the cords for them are draped over their pulleys. Point out that equilibrium exists; therefore, the plane must push upward by a force equal to the weight of the cart. For convenience this force is conventially thought of in terms of a component normal or perpendicular to the plane and a frictional component lying in the plane. To separate these two functions clearly, the cart is equipped with wheels which make it impossible to transmit a force parallel to the plane to the cart by way of the contact points of the wheels on the plane, since such forces, being tangential to the wheels' periphery, would merely rotate the wheels. Hence, it is necessary to clamp a block in front of the wheels to furnish sufficient force of frictional character to the cart from the plane. Since the plane cannot exert a force on the wheels without making them turn unless this force line is through the axle as well as through the contact point, the force of the plane other than friction must be perpendicular to the plane.

Proceed with chatter in this vein. "We know how to calculate these normal and frictional components from the properties of vectors and the conditions for equilibrium; this was done before class. I will now place the yellow weight which supplies just this amount of 'frictional' force on its hanger at the left, then we will no longer need the chock." Carefully remove the chock without disturbing the cart. "Now we know how to calculate the normal component also; this has been done. I will now place the red weight which supplies just this amount of force on its hanger at the top. Then we no longer need the incline." Carefully slide the incline horizontally out of the grooves without disturbing the cart which remains suspended in space in the same place and in the same attitude as when the plane was holding it up.

This procedure properly carried out will never fail to elicit a gasp from the audience as the plane comes free of its grooves.