A falling object is said to be at terminal velocity when the force of gravity pushing it down is exactly counterbalanced by the force of air resistance (a special case of friction) pushing up on it. Given that the net force on an object at terminal velocity is 0, use Newton’s 2nd law to determine the acceleration of a body at terminal velocity?
zero force ... zero acceleration ... hence the name "terminal velocity"
To determine the acceleration of a body at terminal velocity using Newton's 2nd law, we start with the equation:
Fnet = ma
Since the body is at terminal velocity, the net force on the body is 0. This means that the force due to gravity (mg) is exactly counterbalanced by the force of air resistance (FAR). Therefore, we can write:
Fnet = mg - FAR = 0
Simplifying the equation, we get:
mg = FAR
Now, we know that the force of air resistance is proportional to the velocity of the object squared (v^2). So, we can rewrite the equation as:
mg = kv^2
Where k is the drag coefficient. Rearranging the equation, we can solve for acceleration (a):
a = g - (kv^2 / m)
In this equation, g is the acceleration due to gravity, v is the velocity of the object, m is the mass of the object, and k is the drag coefficient.
It's important to note that at terminal velocity, the acceleration of the object is zero. This means that the force of gravity pulling the object down is exactly counterbalanced by the force of air resistance pushing it up. The object is no longer accelerating and reaches a constant velocity.