An object falling under the pull of gravity is acted upon by a frictional force of air resistance. The magnitude of this force is approximately proportional to the speed of the object, which can be written as f = bv. Assume b = 16 kg/s and m = 58 kg.
(a) What is the terminal speed the object reaches while falling?
m/s
(b) Does your answer to part (a) depend on the initial speed of the object?
Yes
No
Oh, you're talking about falling objects and air resistance? That's a classic physics problem, but let's give it a humorous twist!
(a) To find the terminal speed of the object, we need to balance the forces. At terminal speed, the force of gravity pulling the object down is exactly countered by the force of air resistance pushing up. So, we have:
mg = bv
Substituting the given values, we get:
58g = 16v
Now, we just need to divide by 16 to solve for v:
v = (58g)/16
And voila! That's the terminal speed, but unfortunately, I can't give it to you in meters per second because I don't know the value of g. So, let's move on to part (b) for some more fun!
(b) Does the answer to part (a) depend on the initial speed of the object? Well, it's like this: if you drop a snail from the top of a skyscraper, its terminal speed will be considerably lower than if you drop a formula one race car. So yes, the answer depends on the initial speed.
But hey, no matter the initial speed, gravity and air resistance always make for an interesting fall! Just make sure to bring a parachute if you're planning on joining the fun!
To determine the terminal speed of the object, we need to find the speed at which the force of air resistance (f) becomes equal in magnitude but opposite in direction to the force of gravity acting on the object (mg). At this point, the net force on the object becomes zero, resulting in a constant velocity or terminal speed.
We can start by setting up the equation for the net force:
f - mg = 0
Substituting the expression for air resistance force (f = bv), we get:
bv - mg = 0
Rearranging the equation gives:
bv = mg
Now, let's substitute the given values:
b = 16 kg/s
m = 58 kg
g = acceleration due to gravity (approximately 9.8 m/s^2)
16v = 58 * 9.8
Solving for v, we find:
v = (58 * 9.8) / 16
Calculating this expression, we get:
v ≈ 35.7175 m/s
Therefore, the terminal speed of the object while falling is approximately 35.7175 m/s.
Now, to answer part (b) of the question, yes, the terminal speed does depend on the initial speed of the object. If the initial speed is greater than the terminal speed, the object will slow down to reach the terminal speed. If the initial speed is less than the terminal speed, the object will accelerate until it reaches the terminal speed.