Common Forces

• Dynamics is the study of the relationship between forces and motion.
• Some common forces are introduced below:

Weight

• Weight W refers to the gravitational pull that Earth exerts on an object of mass m.
• Assuming the acceleration of free fall to be g = 9.81 m s-2,

W = mg

• Near Earth’s surface, it is a constant force that is always directed vertically downward.
• (more detail)

Contact Force

1. Normal Contact Force
• When two surfaces are pressed against each other, their molecular lattice repel each other, resulting in normal contact forces N.
• As the name suggests, normal contact force is in the direction normal (perpendicular) to the two surfaces.

2. Friction

• Friction f refers to the forces between two surfaces which are sliding, or tending to slide (static friction), across each other.
• The frictional force between two particular surfaces depends on (1) the normal contact force N (relating to how hard the two surfaces are pressed together) and (2) the coefficient of friction μ (relating to how “sticky” the two surfaces are to each other).

= μN

• The direction of the frictional forces is always parallel to the two surfaces, and always such as to (try to) hold the two surfaces together.

Viscous Forces

• Viscous forces fdrag refer to the resistive forces that a fluid exerts on an object moving through the fluid.
• The magnitude of viscous force depends on (1) the viscosity of the fluid, (2) how streamline the object is and (2) the speed at which the object is moving through the fluid v.
• Under laminar flow conditions, viscous drag is proportional to v.

fdrag = kv

• Under turbulent conditions, viscous drag is proportional to the square of v.

fdrag = kv2

Tension

• Tension forces T refer to the forces exerted by a stretched molecular lattice, e.g. a stretched spring, a taut rope, an extended wire etc.
• Most springs obey Hooke’s Law (to a certain limit of stretching), meaning T is directly proportional to the extension (from the original length) x.

T= kx

• The direction of the tension forces is always inward at both ends. For example, the bottom end of the spring exerts an upward tension force on the weight, while the top end of the spring exerts a downward tension force on the ceiling.