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Solved: When the mass m of a body is changing with time,
Chapter 1, Problem 21E(choose chapter or problem)
When the mass m of a body is changing with time, Newton’s second law of motion becomes
\(F=\frac{d}{d t}(m v)\),
where F is the net force acting on the body and mv is its momentum. Use (17) in Problems 21 and 22.
A small single-stage rocket is launched vertically as shown in Figure 1.3.19. Once launched, the rocket consumes its fuel, and so its total mass m(t) varies with time t > 0. If it is assumed that the positive direction is upward, air resistance is proportional to the instantaneous velocity v of the rocket, and R is the upward thrust or force generated by the propulsion system, then construct a mathematical model for the velocity v(t) of the rocket. [Hint: See (14) in Section 1.3.]
Text Transcription:
F=d/dt (mv)
Questions & Answers
QUESTION:
When the mass m of a body is changing with time, Newton’s second law of motion becomes
\(F=\frac{d}{d t}(m v)\),
where F is the net force acting on the body and mv is its momentum. Use (17) in Problems 21 and 22.
A small single-stage rocket is launched vertically as shown in Figure 1.3.19. Once launched, the rocket consumes its fuel, and so its total mass m(t) varies with time t > 0. If it is assumed that the positive direction is upward, air resistance is proportional to the instantaneous velocity v of the rocket, and R is the upward thrust or force generated by the propulsion system, then construct a mathematical model for the velocity v(t) of the rocket. [Hint: See (14) in Section 1.3.]
Text Transcription:
F=d/dt (mv)
ANSWER:Step 1 of 3
The goal is to build a numerical model for the speed v(t) of the rocket
Accept a rocket of mass m, moving speed v.
Once propelled, the rocket devours its fuel so its aggregate mass m(t) shifts with time t >0.
In the event that the mass m of body is changing with time at that point Newton's second law of movement moves toward becoming,
……(i)
Here, F is the net constraint following up on the body and mv is its energy.