   Chapter 4, Problem 45P

Chapter
Section
Textbook Problem

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 = 15 kg/s and m = 50 kg. (a) What is the terminal speed the object reaches while falling? (b) Does your answer to part (a) depend on the initial speed of the object? Explain.

(a)

To determine

The terminal speed of the object.

Explanation

Given Info: Mass of the object is 50 kg. The proportionality constant (b) is 15kg/s.

The free body diagram is given below.

In the above diagram,

mgbv=ma

• f is the frictional force of air resistance.
• g is the acceleration due to gravity.
• v is the velocity.
• a is the acceleration.
• m is the mass of the object.

On Re-arranging,

a=g(bm)v                                            (I)

At Equilibrium, the net force is zero. As a result, acceleration is zero. This corresponds to the terminal speed.

Substitute 0ms2 for a and vter for v in Equation (I)

(b)

To determine

The relation between terminal speed (vter) and initial velocity (u).

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