By Don Lincoln, Ph.D., University of Notre Dame
When many factors are considered constant in falling or throwing an object, the movement should be parabolic. However, rarely does the shape look like a perfect parabola. Air resistance and drag force affect the object’s movement and velocity, relative to its shape.
When a ball is tossed, its movement will shape a parabola. The ball goes forward and upward, then gravity stops its upward motion and drags it down, but the forward movement continues. However, the second half of the parabola usually covers a shorter distance than the first half. This is while the movement is actually parabolic. When the tossed object is a feather or a handkerchief, the motion might not form anything special at all.
This shows that the elements involved in falling can affect it in different ways. The first of these elements is air resistance. Other elements include velocity, the shape and surface area of the object, drag force, and the angle at which the object is thrown.
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When an object moves through air – or any other fluid – the substance resists against the movement. The extent depends on many factors, but the experience is daily and familiar. When a person walks, air resistance almost does not affect and does not disturb them. However, if the person extends their arm out of the window of a speeding car, they feel the air resistance, tangibly. Thus, speed, or velocity, is a determining factor in air resistance.
Velocity and air resistance are proportional. Mathematically, sometimes it is proportional to the square of the velocity. Nonetheless, as velocity increases, so does air resistance. When an object is shot or thrown, at the first moment, it has the highest velocity and, consequently, experiences the highest air resistance. The resistance pushes the object backward, or in other words, pulls it back. This pullback force is called the drag force.
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When air resistance is at its highest, the force that it generates is called ‘drag’, which is at an angle opposite the direction of motion. Drag has two components: one in the horizontal direction and one in the vertical direction. Depending on the angle of the movement, one component can be bigger than the other. Therefore, gravity and drag both try to slow down the moving object, the first in vertical and the latter in a horizontal direction.
The reason an object’s movement in the air changes from a perfect parabola is the drag force. A very important factor in drag is the fluid’s density. Drag force in the thin air at high altitude, normal air, and in water is different. Another important factor is the object’s shape and size.
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Shape and Size of the Object
A baseball might weigh as much as a blown-up beach ball, but the baseball’s trajectory is far more like a parabola than a beach ball. The beach ball has a bigger surface area and undergoes higher air resistance, i.e., drag force. In case of a handkerchief weighing the same as the baseball, the movement will be even more disturbed by the drag. What if the object is falling from a very high distance above the ground?
Falling from Great Heights
When an object falls, its initial velocity is zero. Freefalling can be a good example. When a person jumps off a plane, they have no horizontal movement, and their vertical movement is affected by gravity and the upward drag. Thus, the velocity at which the person is falling is: velocity equals negative-g times time. Does this mean the velocity will keep going high as the object keeps falling further down?
After some time, gravity force and the upward drag force gain equal amounts. Hence, the person’s acceleration stops, and the velocity reaches its maximum. The maximum speed of falling is called the terminal velocity.
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Terminal velocity is the result of gravity and upward drag balancing each other out. For example, a skydiver in the usual position, i.e., arms spread out and facing the ground, reaches a terminal velocity of about 120 miles per hour. When an open parachute is attached, the terminal velocity reduces to 12 miles per hour, ideally slow enough to land standing and walk away.
Accordingly, falling is affected by a variety of factors, and the controllable part is the object’s surface area, angle, and weight. The combination of these controls and physics rules has made parachuting and freefalling possible.
Common Questions about Air Resistance
Air resistance happens when an object moves through the air. Depending on the velocity, shape, and area of the object, resistance differs. The faster an object moves and the greater its area, the higher the air resistance gets. Parachutes go up in the air since the area is big enough to create enough resistance to push the parachute up. Flying is a familiar example where air resistance is easily felt.
Air resistance depends on velocity, area, and shape of the object going through the air. Altitude, temperature, and humidity change air density and, consequently, its resistance. The higher the speed and the bigger the area, the higher the resistance.
Air resistance can be calculated by multiplying air density by the drag coefficient, multiplied by area all over two, and then multiplied by velocity squared. Sometimes, to simplify other equations, some elements are considered constant. The unit used to show the force of air resistance is Newtons (N).
With air resistance, acceleration throughout a fall gets less than gravity (g) because air resistance affects the movement of the falling object by slowing it down. How much it slows the object down depends on the surface area of the object and its speed. Usually, resistance is not very high at low speed or for small or sharp objects.