Friction force

Friction and motion: Why do moving objects slow down?

Push a cart gently on the table. Newton's second law suggests that if the net force on the cart (after you push it) is zero, the cart will not accelerate, and therefore it will move with constant velocity. Does it? (Probably not.) Why not? Maybe the net force is not zero. Maybe there is a force tending to make it slow down. Can you measure this "friction" force?

Set up the experiment sketched below.

Hang a small weight m₁ (~ 50 gm) from the string. Let the cart be pulled by the weight. Does the cart accelerate? How do you know? Make a spark tape record, plot the distance traveled versus time, the velocity versus time and the acceleration versus time.

If you use a smaller mass, you should be able to find a small enough mass that the cart neither speeds up nor slows down. You will have to nudge the cart to get it started. After that it should move with relatively constant velocity. In that case, the friction between the table and the cart is exactly balanced by the weight pulling the cart. Find the value of m₁ that allows the cart to travel with constant velocity. Make a spark tape record. Plot the distance traveled versus time and the velocity versus time. Use the INDEX(LINEST( ),1) command to find the slope of the velocity versus time plot. What is the slope? What should it be if the cart is neither speeding up nor slowing down?

In this case the picture below may help your understanding. The weight pulling down is m₁g (where g is the acceleration due to gravity). If the mass and cart are moving at constant velocity, then the net force on m₁ is zero. If that is true, then what is the tension in the string? Since you can determine the tension in the string, and m₂ is also not accelerating, then you can find the friction force f pulling on the cart. What is it?

Place a sandbag on the cart. What is the friction force now? (Go through a complete analysis to demonstrate that the acceleration of the cart is zero.)

Predict what will happen to the friction force if you place a second sandbag on the cart. Now place a second sandbag on top of the first and determine the new friction force. Was your prediction confirmed?