Concept explainers
(a)
The units and dimensions of the constant
(a)
Answer to Problem 27P
Dimension of
The unit of
Explanation of Solution
Given Information:
Formula Used:
The drag force equation is
Calculation:
The drag force equation is
Dimension of force
The dimension of speed
Solving the drag force equation for
Substitute the dimensions of
So, the units ofb is
(b)
Using dimensional analysis, determine the units and dimensions of the constant
(b)
Answer to Problem 27P
Dimension of
The units of
Explanation of Solution
Given Information:
Calculation:
The drag force equation is
Dimension of force
The dimension of speed
Solving the drag force equation for
Substituting the dimensions of
So, the units of
(c)
To Show: Air resistance of a falling object with a circular cross section should be approximately
(c)
Explanation of Solution
Given Information:
Air resistance of a falling object with a circular cross section should be approximately
Calculation:
According to the expression of drag force,
So the dimensions of drag force is
The drag force is given as
The dimension of drag force is
Conclusion:
Hence, the expression for drag force is dimensionallyconsistent .
(d)
To Find: The terminal speed of the skydiver.
(d)
Answer to Problem 27P
Explanation of Solution
Given Information:
Mass of skydiver =
Disk of radius =
Density of air near the surface of Earth is
Formula Used:
The terminal speed is given by relation
Calculation:
Mass
Acceleration due to gravity
Density
Radius
The terminal speed is given by relation
(e)
To Calculate: The terminal velocity at the given height.
(e)
Answer to Problem 27P
The terminal velocity is
Explanation of Solution
Given Information:
Height =
Density of air near the surface of Earth is
Formula Used:
The terminal speed is given by relation
Calculation:
Mass,
Acceleration due to gravity,
Density,
Radius
Substitute the values:
Conclusion:
Thus, the terminal speed at the given height is
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