Falling Objects

FREE FALL

An object falling without air resistance or friction is defined to be in free-fall.

• If air resistance and friction are negligible, then in a given location all objects fall toward the center of Earth with the same constant acceleration, independent of their mass.

• The force of gravity causes objects to fall toward the center of Earth. The acceleration of free-falling objects is therefore called the acceleration due to gravity.

• The acceleration due to gravity is so important that its magnitude is given its own symbol, g. It is constant at any given location on Earth and has the average value g = 9.80 m/s².

• Although g varies from 9.78 m/s² to 9.83 m/s², depending on latitude, altitude, underlying geological formations, and local topography, the average value of 9.80 m/s²

DRAG FORCE

Another interesting force in everyday life is the force of drag on an object when it is moving in a fluid (either a gas or a liquid). You feel the drag force when you move your hand through water. You might also feel it if you move your hand during a strong wind. The faster you move your hand, the harder it is to move. You feel a smaller drag force when you tilt your hand so only the side goes through the air—you have decreased the area of your hand that faces the direction of motion. (Read only)

• Like friction, the drag force always opposes the motion of an object.

• The air drag force depends on several factors, including the speed at which the object is falling (v), the surface area of the object (A), the density of the air (d), and the drag coefficient (C), which is determined by how aerodynamic the object is.

Drag Force= 0.5 x d x v² x A x C

The most important factor in determining the air drag force is the velocity of the object. As the body speeds up, the drag force becomes larger and larger.

The maximum velocity reached by an object where the drag force is equal to the driving force, the object falls with a constant velocity of motion called terminal velocity.

Terminal Velocity

(Read only)

Some interesting situations connected to Newton’s second law occur when considering the effects of drag forces upon a moving object. For instance, consider a skydiver falling through air under the influence of gravity. The two forces acting on him are the force of gravity and the drag force (ignoring the small buoyant force). The downward force of gravity remains constant regardless of the velocity at which the person is moving. However, as the person’s velocity increases, the magnitude of the drag force increases until the magnitude of the drag force is equal to the gravitational force, thus producing a net force of zero. A zero net force means that there is no acceleration, as shown by Newton’s second law. At this point, the person’s velocity remains constant and we say that the person has reached his terminal velocity. Since drag force is proportional to the speed squared, a heavier skydiver must go faster for drag force to equal his weight.

The size of the object that is falling through air presents another interesting application of air drag. If you fall from a 5-m-high branch of a tree, you will likely get hurt—possibly fracturing a bone. However, a small squirrel does this all the time, without getting hurt. You do not reach a terminal velocity in such a short distance, but the squirrel does.

Think and answer:

Q1. Why can a squirrel jump from a tree branch to the ground and run away undamaged, while a human could break a bone in such a fall?

Q2. During sky diving when the parachute bag opens, the drag force increases enabling the divers to land safely. What does this show and how does it affect the drag force?