Force

From Combat Robot

Force is an influence that may cause a body to accelerate. It may be experienced as a lift, a push, or a pull. The actual acceleration of the body is determined by the vector sum of all forces acting on it (known as net force or resultant force). In an extended body, force may also cause rotation or deformation of the body. Rotational effects and deformation are determined respectively by the torques and stresses that the forces create.

Force is mathematically defined as the rate of change of the momentum of the body. Since momentum is a vector quantity (has both a magnitude and direction), force also is a vector quantity.

Examples

• A heavy object is in free fall. Its momentum changes as dp/dt = mdv/dt = ma =mg (if the mass m is constant), thus we call the quantity mg a "gravitational force" acting on the object. This is the definition of weight (w=mg) of an object.
• A heavy object on a table is pulled (attracted) downward toward the floor by the force of gravity (i.e., its weight). At the same time, the table resists the downward force with equal upward force (called the normal force), resulting in zero net force, and no acceleration. (If the object is a person, he actually feels the normal force acting on him from below.)
• A heavy object on a table is gently pushed in a sideways direction by a finger. However, it doesn't move because the force of the finger on the object is now opposed by a new force of static friction, generated between the object and the table surface. This newly generated force exactly balances the force exerted on the object by the finger, and again no acceleration occurs. The static friction increases or decreases automatically. If the force of the finger is increased (up to a point), the opposing sideways force of static friction increases exactly to the point of perfect opposition.
• A heavy object on a table is pushed by a finger hard enough that static friction cannot generate sufficient force to match the force exerted by the finger, and the object starts sliding across the surface. If the finger is moved with a constant velocity, it needs to apply a force that exactly cancels the force of kinetic friction from the surface of the table and then the object moves with the same constant velocity. Here it seems to the naive observer that application of a force produces a velocity (rather than an acceleration). However, the velocity is constant only because the force of the finger and the kinetic friction cancel each other. Without friction, the object would continually accelerate in response to a constant force.
• A heavy object reaches the edge of the table and falls. Now the object, subjected to the constant force of its weight, but freed of the normal force and friction forces from the table, gains in velocity in direct proportion to the time of fall, and thus (before it reaches velocities where air resistance forces becomes significant compared to gravity forces) its rate of gain in momentum and velocity is constant.