Suppose the magnitude of the "drag force" acting on the falling object of mass m is Dv2. Find the expression for the magnitude of the terminal velocity of this object. (Use any variable or symbol stated above along with the following as necessary: g. Do not substitute numerical values; use variables only.
v= sqr(mg/D)
To find the expression for the magnitude of the terminal velocity of the falling object, we need to balance the downward force of gravity with the upward drag force.
First, let's define the variables:
m = mass of the falling object
D = proportionality constant for drag force
v = velocity of the falling object
g = acceleration due to gravity
The downward force of gravity is given by the equation: F_gravity = m * g
The upward drag force is given by the equation: F_drag = D * v^2
At terminal velocity, the upward drag force is equal in magnitude and opposite in direction to the downward force of gravity. So, we can write the equation:
F_gravity = F_drag
m * g = D * v^2
Now, let's solve for the magnitude of the terminal velocity, v.
Divide both sides of the equation by D:
(m * g) / D = v^2
Take the square root of both sides:
sqrt((m * g) / D) = v
Hence, the expression for the magnitude of the terminal velocity of the falling object is:
v = sqrt((m * g) / D)