The buoyancy force on the 490 balloon is F = 6kN , and the air resistance is F_D = (100v)N, where is in m/s.
Determine the terminal or maximum velocity of the balloon if it starts from rest.
vmax = ?
490 what units?
To determine the terminal or maximum velocity (vmax) of the balloon starting from rest, we need to consider the forces acting on it and use Newton's second law of motion.
Here are the given forces:
1. Buoyancy force (F): F = 6kN
2. Air resistance force (F_D): F_D = (100v)N, where v is in m/s
From Newton's second law, we know that the net force acting on an object is equal to its mass (m) multiplied by its acceleration (a). In this case, the net force is the difference between the buoyancy force and the air resistance force:
Net force (F_net) = F - F_D
For the balloon to reach its maximum velocity, the net force acting on it must be zero (since it will no longer accelerate). So, we can set the net force equal to zero:
F_net = F - F_D = 0
Now, we can substitute the values given:
6kN - (100v)N = 0
To solve for the terminal velocity, we need to convert the kilonewtons to newtons:
6kN = 6000N
Substituting this value back into the equation:
6000N - (100v)N = 0
Now, we can solve for v:
6000N = 100v
Divide both sides by 100N:
6000N / 100N = v
60 = v
Therefore, the terminal or maximum velocity of the balloon starting from rest is 60 m/s.