Types of Forces II. Resistive Forces (Frictional Force. Drag). Terminal Velocity

In these revision notes for Types of Forces II. Resistive Forces (Frictional Force. Drag). Terminal Velocity, we cover the following key points:

• The meaning of resistive forces
• Which resistive forces are more relevant in daily life?
• What are the factors affecting resistive forces?
• How to calculate the frictional force between two surfaces in contact?
• Where does drag differs from the frictional force?
• What is terminal velocity and in which conditions it is observed?

Types of Forces II. Resistive Forces (Frictional Force. Drag). Terminal Velocity Revision Notes

All objects are under the effect of certain resistive forces during their motion. Frictional Force and Drag are examples of such resistive forces.

Frictional force is a force produced at the contact region between the ball and the ground. Frictional force has an intermolecular nature. This means that molecules of the two objects in contact resist to the change of structure driven from the friction between them. As a result, the object loses energy during its motion and eventually it stops because all the initial energy of motion (Kinetic Energy) converts into other forms of energy, such as heat energy etc.

Drag is a resistive force produced when an object moves inside a fluid (a liquid or a gas). The object tries to displace the fluid's molecules during the motion to make place to itself. As a result, a resistive force is produced by the fluid, which tries to maintain its original position and structure. In the special case, when drag is produced by the air while it is resisting to a moving object, this resistive force is known as "air resistance."

The factors affecting the frictional force are:

1. Roughness of surfaces in contact. It is represented mathematically through the dimensionless constant known as "coefficient of friction, μ".
2. Weight of the object. Heavier the object, more it presses the ground and therefore it becomes more difficult to move it horizontally. Since when dealing with the frictional force we are interested in the friction caused by the environment to the object, we replace the weight with its counterpart, i.e. the normal force N⃗ exerted by the ground on the object. It has the same magnitude as the weight but opposite direction.

The equation of frictional force is

The angle θ is relevant only when the object is on an inclined plane (slope). When the object slides along a horizontal plane, the angle θ to the horizontal direction is zero. Therefore, cos 00 = 1 and therefore, this part can be removed from the formula.

Frictional force does not depend on the size of the area in contact. Indeed, no area exist in the formula of frictional force.

Machinery constructors use to lubricate parts that are more exposed to friction. Lubrication reduces the friction as the liquid fills the gaps on rough surfaces. Therefore, these gaps become less evident.

As for the drag, one of the factors affecting it, is the density of fluid in which the object is moving. Denser the fluid, harder the motion through it.

Another factor (unlike in the frictional force) affecting the drag's value is the surface of contact. This means sharper the object moving through a fluid, easier its motion. This is the reason why car designers pay particular attention to the aerodynamic form of the car. When the aerodynamic form is perfect, the car moves easier through the air and as a result, it saves fuel.

When an object is at rest, there is neither frictional force nor drag produced. When the object starts moving, the frictional force is the first resistive force that appears in the process. When objects move at low velocities, the air drag is negligible. It becomes considerable only when the velocity increases at certain values that create air currents in the opposite direction of motion.

When air drag (resistance) reaches such a value that when added to the frictional force they balance the moving force, the object cannot speed up anymore. It continues to move at constant velocity - the value of the last velocity before the equilibrium was reached. This constant velocity produced when moving force equals the sum of frictional force and drag, is known as "terminal velocity." It depends on the mass and the surface of objects.

Parachute is an example of terminal velocity application in daily life as it has a large surface and as a result, the terminal velocity during the downfall is low, and as a result, we don't get hurt when falling down with parachute.