An object move from the point A to B through air and in the second case a similar object travels from A to B through water? Which object do you think encounters more resistance?
Answers
As mentioned earlier in Lesson 1, an object moving in uniform circular motion is moving in a circle with a uniform or constant speed. The velocity vector is constant in magnitude but changing in direction. Because the speed is constant for such a motion, many students have the misconception that there is no acceleration. "After all," they might say, "if I were driving a car in a circle at a constant speed of 20 mi/hr, then the speed is neither decreasing nor increasing; therefore there must not be an acceleration." At the center of this common student misconception is the wrong belief that acceleration has to do with speed and not with velocity. But the fact is that an accelerating object is an object that is changing its velocity. And since velocity is a vector that has both magnitude and direction, a change in either the magnitude or the direction constitutes a change in the velocity. For this reason, it can be safely concluded that an object moving in a circle at constant speed is indeed accelerating. It is accelerating because the direction of the velocity vector is changing.
Explanation:
I often look at cases where things are falling. We typically call this "free fall" motion because the object is moving only under the influence of the gravitational force. With only the gravitational force, the object has a constant acceleration and the motion is fairly simple to model.
However, objects on the surface of the Earth usually have an air resistance force on them also. When can we ignore this extra force and when is it important?
Modeling Air Resistance
Let's say I drop a ping pong ball. As it falls, I can draw the following force diagram.
The most common model for the air resistance says that the magnitude of the force depends on:
The density of air (ρ). This typically has a value around 1.2 kg/m3.
The cross sectional area of the object (A). A ping pong ball would have a cross sectional area equal to π*r2.
The drag coefficient (C). This depends on the shape of the object. For a spherical object, a unitless value of 0.47 is typical.
The magnitude of the velocity squared. The faster you go, the greater the air resistance force.
The direction of the air resistance force is in the opposite direction as the velocity of the object. That's why there is a negative sign in the expression along with the r - hat (which is a unit vector in the direction of the velocity).
But how do you find values for the drag coefficients for different objects? The real answer is that you must measure them experimentally. However, Wikipedia has a nice list of some values. What about a falling human? I often have to model the motion of a falling human, but there isn't a C value listed. There is one trick I can use.
The trick involves terminal velocity. Suppose a human jumps out of a stationary hot air balloon. At first, only the gravitational force acts on the human giving an acceleration of -9.8 m/s2. However, as the human increases in speed, the air resistance force also increases. At some point, the air resistance force will be equal in magnitude to the gravitational force and the human will no longer increase in speed. We call this "terminal velocity".