6.07: Free Fall and Equilibrium

Most real objects on earth do not fall in a vacuum.

The forces on a baseball when dropped over the side of a moderately tall building include not only the downward force of gravity, but also air resistance, called drag, which opposes the baseball's motion downward. Now any calculations require determining net force on the baseball. The air resistance force is in a direction opposite to velocity. The added air resistance as the object falls downward is opposite in direction to gravity, so it reduces the net force. Real objects fall downward but do not always speed up as you might expect. Notice the snow in the movie, and the multitude of different types of motion from different snowflakes.

The only force acting on an object during free fall is gravity.

An object is in free fall Opens in modal popup window if the only force acting on it is gravity. Imagine a vertical tube that is a total vacuum. If a marble is put in it at the top, the marble will fall to the bottom of the tube. The only force acting on it is gravity. The marble is in free fall. If an object is in free fall, it must be going down, right? Wrong. If a toy rocket is shot into the air, it is in free fall (neglecting air resistance) the instant the launching force ends, even if it continues to travel upward due to inertia. The definition of an object in free fall is that the only force acting on it is gravity. The object's velocity (including direction) does not matter; only the forces on the object determine whether it is in free fall.

Real objects are usually in free fall only as an approximation.

An object is in free fall when gravity is the only force acting on it, whether the object is moving upward or downward. Kinematic equations with g=−9.8 m/s2 g equal negative 9.8 m pers squared can be used to calculate details of motion in free fall. Air resistance increases with velocity, and it is always in the direction opposite to velocity. When the velocity of an object reaches its terminal velocity, the air resistance balances the weight, and the object is in equilibrium and does not accelerate.

Newton's laws and the kinematic equations apply to objects in free fall.

Because weight and mass are proportional to each other, Newton's second law Fnet=ma F subscript net end subscript equals m a predicts that all objects in free fall accelerate at the same rate. Newton's second law leads to the specific relation between weight and mass Fg=ma F subscript g equals m a, in terms of the acceleration g due to gravity, of −9.8 m/s2 negative 9.8 m divided by s squared at locations near the surface of the earth. The value is negative because the motion is toward the reference point—that is, toward the ground.

The acceleration due to gravity is downward, even while the object is moving up.

Suppose a tennis ball is tossed straight up in a vacuum. The only force acting on the ball is its weight. So the tennis ball is in free fall, even when it is moving upward. The force downward is constant and produces a constant acceleration downward. The acceleration without air resistance is g=−9.8 m/s2 g equals negative 9.8 m divided by s squared(downward) at all times, whether the velocity v is upward or downward. As the ball rises, its upward velocity and downward acceleration are in opposite directions, and the velocity of the ball decreases. It has zero velocity only for the instant it reverses direction. After that, the acceleration and velocity are in the same direction downward, and the velocity increases.

Air resistance is a force acting against gravity when an object falls.

The direction of air friction is opposite to velocity. If an object is falling downward, then air resistance or friction is upward. The air resistance then decreases the acceleration downward from gravity. If the object is moving upward, air friction opposes the motion and points downward. The acceleration downward from gravity is increased, and the ball reaches zero velocity and its greatest height sooner. The result is that the ball takes less time on its way upward than it takes on its way downward when there is air resistance. For real objects on earth, free fall is only an approximation.

A falling object reaches terminal speed when the drag force equals its weight.

When an object dropped from a great height is first released, its velocity is small, air resistance is small, and the net force is nearly equal to the object's weight, or the force of gravity on it. It accelerates at close to g=−9.8 m/s2 g equals negative 9.8 m pers squared. As the object moves faster, air resistance increases. This decreases the net force, decreasing the acceleration. Eventually, the air resistance force and the weight are equal, and the net force becomes zero. The object moves at a constant velocity and does not accelerate any further. The velocity when this happens is the object's terminal velocity. Different objects reach terminal velocity at different rates. Notice that the snow in this video has reached terminal velocity, while the climbers continue to accelerate so that they are quickly falling faster than the snow.