Drag Force

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What is the factor that slows down the balls on the pool table? There are exactly two opposing forces which slow down the balls till they come to a complete rest. These are air resistance force, and the frictional force. But because the air resistance on such dense objects as pool balls is very small, we will disregard its effects. Thus friction is the major drag force to the balls and this force exist between the two surfaces which are in contact: one from the cloth of the table and the other from the balls. To analyze what causes friction, we must study what happens in the very small, molecular level of objects. Matters are held together by series of bonds that exist between molecules and atoms. When the surface of an object comes in contact with another, there is a new attraction between the two surfaces and the overall effect of this is the frictional force. This force is a drag force and thus opposes the direction in which an object is moving.

If you have tried to slide a very heavy box across carpet or other surfaces, you probably felt that more force was required to start the movement of the box than it did once it began to move. The explanation for this comes from two different kind of friction: stationary friction and kinetic friction. And the words describe what the two are very well. Stationary friction is the opposing force which occur in the initial acceleration of an object (the object is initially at rest). Once the object has begun to slide, the friction which is opposing its motion is the kinetic friction (the object is moving). Imagining this in the molecular level, stationary friction is the force that exist in the attraction between the two surfaces. And as the surfaces begin to slide against each other, the series of molecular tears and bonds create the kinetic friction.

 

These two frictional forces are described by the two following equations:
Stationary friction => f_s = m_sN
Kinetic friction => f_k = m_kN
N is the normal force exuded by either surfaces which are in contact. Refer back to the previous Force section for definition and calculations for the normal force in the main menu.
m_s and m_k are the frictional coefficients for the two different frictions. These constants are determined by the chemistry of materials. For example, rubbers have significantly higher frictional coefficients than solid ice.

Now we apply friction to the mechanics of spinning. Remember that friction is always at the surface of objects and thus this force provides for an optimum torque on the balls. Note however, that the friction which spins the balls is the stationary friction. Kinetic friction only occurs when objects are sliding.

 

You may now understand why the balls sometimes spin when you have supplied the force in the center which gives zero torque. This is because as the ball is intially translating, there is a stationary friction which will give enough torque to result an angular acceleration on the ball.

Sample Problem
If a student is sitting on solid ice, what is the maximum force that could be exerted on the student before he/she begins to move? (mass = 80kg, g = 9.81, m_s = 0.2)

Your Answer:

Solution