Force of Friction

The force of friction depends on the properties of the surface between the two objects (which will determine the friction coefficient) and on the normal force. (On a flat surface, the normal force, N, is just the weight, mg.)

The force of static friction is given by

$\mu$_s is the coefficient of static friction. This force only acts while the object does not move. Also please note the all-important inequality sign ($\leq$). It means that the static friction force always adjusts itself to exactly balance all other forces in its direction, provided that their net force does not exceed F_s,max. Only when this the net external force becomes bigger than the maximum possible static friction force, does the object begin to move.

In the upper figure, the applied external force is not big enough to overcome the static friction force, and the object remains at rest. Please note that the length of the red arrow (friction force) is exactly the same as that of the external force of the pushing hand, blue arrow. Also, please note that the length of the narrow of the normal force, purple arrow, is exactly the same as that of the weight of the object, green arrow. This means that in this case all forces are balanced and add up to 0 net force => the object remains at rest.

Once the object is moving, we have the force of kinetic friction, F_k, acting in the opposite direction of the motion, see lower figure on the right. The magnitude of the kinetic friction force is:

where $\mu$_k is the coefficient of kinetic friction. Also, please note that this equation contains an equal sign and not a less-or-equal sign as the equation above.

In general, the coefficient of static friction, $\mu$_s, is greater than the coefficient of kinetic friction, $\mu$_k:

In fact, could it be otherwise? If kinetic friction were greater than static friction, a force just big enough to overcome static friction would be too small to keep the body going.

© MultiMedia Physics, 1999