A bobcat weighing 74.5 N jumps out of a tree. (Assume that "up" is the positive direction.)
(b) What is the drag force on the bobcat when it falls at 70% of its terminal velocity?
(d) What is the acceleration when it falls at 70% of its terminal velocity?
(b) Drag force is proportional to V^2. At the full terminal velocity, the drag force equals the weight. At 70% of that velocity, the drag force is 0.70^2 = 0.49 times the weight. That is 36.5 N.
(d) Net force = 0.51 M g = M a
M cancels out.
Solve for a
To answer these questions, we first need to understand the concept of terminal velocity. Terminal velocity is the constant speed that an object experiences when the drag force on it equals the force due to gravity. At terminal velocity, the net force on the object becomes zero, so there is no further acceleration.
Given the weight of the bobcat (74.5 N), we can determine its terminal velocity using the formula:
terminal velocity = weight / drag coefficient
However, we don't have the drag coefficient for the bobcat, so we need to estimate it. For a falling object in air, the drag coefficient usually ranges between 0.5 and 1.0. Let's assume a value of 0.8 for the bobcat's drag coefficient.
(a) Calculating Terminal Velocity:
terminal velocity = 74.5 N / 0.8 ≈ 93.125 m/s
(b) To find the drag force when the bobcat falls at 70% of its terminal velocity, we multiply the weight by the ratio of the velocity at 70% terminal velocity to the actual terminal velocity:
velocity at 70% terminal velocity = 0.7 * terminal velocity
drag force = weight * (velocity at 70% terminal velocity / terminal velocity)
drag force = 74.5 N * (0.7 * 93.125 m/s / 93.125 m/s)
drag force ≈ 65.59 N
Therefore, the drag force on the bobcat when it falls at 70% of its terminal velocity is approximately 65.59 N.
(d) At 70% terminal velocity, the net force on the bobcat is still not zero, so it will continue to accelerate. To calculate the acceleration, we need to use Newton's second law of motion:
net force = mass * acceleration
Since the weight is the only significant force acting on the bobcat, we can rewrite the equation as:
weight - drag force = mass * acceleration
acceleration = (weight - drag force) / mass
Given that the weight is 74.5 N, drag force is 65.59 N, and the mass is not provided, we cannot calculate the acceleration precisely.
Therefore, we need the mass of the bobcat to calculate its acceleration when it falls at 70% of its terminal velocity.