You are told that the linear "drag coefficient" due to air resistance for a particular object is 0.64 N · s/m and the object has a mass of 0.0010 kg. Find the magnitude of the terminal velocity of this object when dropped from rest. (Assume the object's speed is relatively low
To find the magnitude of the terminal velocity of the object, we need to consider the balance between the gravitational force acting on the object and the drag force due to air resistance.
The gravitational force acting on an object is given by the equation Fg = mg, where m is the mass of the object (0.0010 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
The drag force on an object due to air resistance can be calculated using the equation Fd = bv, where b is the drag coefficient (0.64 N · s/m) and v is the velocity of the object.
At terminal velocity, the object's acceleration becomes zero as the gravitational force and the drag force balance each other, Fg = Fd.
Setting up the equation, we have:
mg = bv
Solving for v, we get:
v = mg/b
Substituting the values we have:
v = (0.0010 kg) * (9.8 m/s²) / (0.64 N · s/m)
Calculating this, we find:
v ≈ 0.0153 m/s
Therefore, the magnitude of the terminal velocity of the object when dropped from rest is approximately 0.0153 m/s.