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An object falling through a fluid is observed to have acceleration given by a = g − bv where g = gravitational acceleration and b is constant. After a long time of release, it is observed to fall with constant speed. The value of constant speed is
- a)g/b
- b)b/g
- c)bg
- d)b
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
An object falling through a fluid is observed to have acceleration giv...
Here, a = g − bv
When an object falls with constant speed vc, its acceleration becomes zero.
∴ g − bvc = 0 or vc = g/b
When an object falls with constant speed vc, its acceleration becomes zero.
∴ g − bvc = 0 or vc = g/b
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An object falling through a fluid is observed to have acceleration giv...
Understanding the Problem
When an object falls through a fluid, it experiences two forces: gravitational force pulling it downward and a drag force opposing its motion. The acceleration of the object is given by the equation:
a = g - bv
Here, g is the acceleration due to gravity, b is a constant representing the drag coefficient, and v is the velocity of the object.
Long-Term Behavior
Over time, the object reaches a steady state where its velocity becomes constant. At this point, acceleration becomes zero (a = 0) because the object is no longer speeding up or slowing down.
Setting Up the Equation
Since the object has constant speed, we can substitute a = 0 into the equation:
0 = g - bv
This leads to:
bv = g
Finding Constant Speed
To isolate v (the constant speed), we can rearrange the equation:
v = g/b
Conclusion
The constant speed the object achieves after a long time of falling through the fluid is:
g/b
Thus, the correct answer is option 'A', indicating that as the object falls, it eventually reaches a terminal velocity proportional to the gravitational acceleration divided by the drag coefficient. This balance of forces illustrates the concept of terminal velocity in fluid dynamics.
When an object falls through a fluid, it experiences two forces: gravitational force pulling it downward and a drag force opposing its motion. The acceleration of the object is given by the equation:
a = g - bv
Here, g is the acceleration due to gravity, b is a constant representing the drag coefficient, and v is the velocity of the object.
Long-Term Behavior
Over time, the object reaches a steady state where its velocity becomes constant. At this point, acceleration becomes zero (a = 0) because the object is no longer speeding up or slowing down.
Setting Up the Equation
Since the object has constant speed, we can substitute a = 0 into the equation:
0 = g - bv
This leads to:
bv = g
Finding Constant Speed
To isolate v (the constant speed), we can rearrange the equation:
v = g/b
Conclusion
The constant speed the object achieves after a long time of falling through the fluid is:
g/b
Thus, the correct answer is option 'A', indicating that as the object falls, it eventually reaches a terminal velocity proportional to the gravitational acceleration divided by the drag coefficient. This balance of forces illustrates the concept of terminal velocity in fluid dynamics.
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