A toy submarine of mass m = 0.830 kg moves around a submerged circular track of radius R = 1.97 m. The submarine's engine provides a constant propulsion force of F = 4.93 N. When the sub is in motion, it is subject to a viscous drag force exerted by the water. This force is proportional to the sub's speed; the proportionality factor is C = 1.26 kg/s. Assuming it starts from rest at t = O s, the speed v (t) of the submarine at a later time t is given by F v() = (1 - e-Cilm) where e is the base of the natural logarithm. How much time has passed when the submarine's speed reaches 59% of its terminal value? What is the magnitude of the submarine's acceleration a at this time?

A toy submarine of mass m = 0.830 kg moves around a submerged circular track of radius R = 1.97 m. The submarine's engine provides a constant propulsion force of F = 4.93 N. When the sub is in motion, it is subject to a viscous drag force exerted by the water. This force is proportional to the sub's speed; the proportionality factor is C = 1.26 kg/s. Assuming it starts from rest at t = O s, the speed v (t) of the submarine at a later time t is given by F v() = (1 - e-Cilm) where e is the base of the natural logarithm. How much time has passed when the submarine's speed reaches 59% of its terminal value? What is the magnitude of the submarine's acceleration a at this time?

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Description: A toy submarine of mass m = 0.830 kg moves around asubmerged circular track of radius R = 1.97 m. Thesubmarine's engine provides a constant propulsion force ofF = 4.93 N. When the sub is in motion, it is subject to aviscous drag force exerted by the

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Newton's First Law of Motion

If a very smooth ball is rolled down an inclined surface with zero friction, the ball will continue to roll indefinitely for an infinite time, in an attempt to reach to the same height on the opposite hill!

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Question

A toy submarine of mass m = 0.830 kg moves around a
submerged circular track of radius R = 1.97 m. The
submarine's engine provides a constant propulsion force of
F = 4.93 N. When the sub is in motion, it is subject to a
viscous drag force exerted by the water. This force is
proportional to the sub's speed; the proportionality factor is
C = 1.26 kg/s. Assuming it starts from rest at t = 0 s, the
speed v (t) of the submarine at a later time t is given by
v (1) = (1 - e-Cim)
%3D
where e is the base of the natural logarithm.
How much time has passed when the submarine's speed
reaches 59% of its terminal value?
t =
S
What is the magnitude of the submarine's acceleration a at
this time?
m/s?
a =

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