In a laboratory experiment, a very large fish tank is filled with water. At the bottom of the tank, a rigid rod oflength L is pinned to the frictionless floor and the other end is connected to a small object of mass m with a rocket nozzle onit. The rocket will exert a constant thrust force of magnitude F, directed in the tangential direction. The object will startfrom rest, rotating about a circle in the horizontal plane when the rocket motor is turned on. Since it is under water, theobject experiences a drag force that depends linearly on the objects velocity D=-bỷ where b is a constant and v is theobject's velocity vector (the minus sign just means that the drag force points in the direction OPPOSITE the object'svelocity).a) Draw a complete FBD of the object while it is speeding up. Use an over-head view.b) “Fill out" Newton's 2nd law in the radial and tangential directions. Do NOT solve for anything.c) Newton's 2nd Law in the tangential direction gives you a differential equation to solve for the tangential component of the-bFTobject's velocity as a function of time. The solution is va(t)=). What is the maximum speed reached bymthe object? Use Newton's 2nd Law to show this is correct when the tangential component of the object's acceleration iszero.d) Show that energy is conserved for this system by demonstrating that the Power input to the system by the thrust forceacting on the block is exactly equal to the absolute value of the Power removed from the block by the drag force aftermaximum velocity has been reached.e) If the rod keeping the object moving about a circle is not strong enough to withstand the tension force when the objectreaches maximum velocity, find the time that the rod will break. Call the maximum tension the rod can withstand T,HINT: en (x)= x and In(e*)=xтахf) What is the kinetic energy of the object at the moment the rod breaks?g) (Extra Credit + 2 Points!!) At what rate is the water heating up at the moment the rod breaks?

a) It is given that for the laboratory experiment, a large fish tank is taken and a rigid rod of…

In a laboratory experiment, a very large fish tank is filled with water. At the bottom of the tank, a rigid rod of length L is pinned to the frictionless floor and the other end is connected to a small object of mass m with a rocket nozzle on it. The rocket will exert a constant thrust force of magnitude Frdirected in the tangential direction. The object will start

In a laboratory experiment, a very large fish tank is filled with water. At the bottom of the tank, a rigid rod of length L is pinned to the frictionless floor and the other end is connected to a small object of mass m with a rocket nozzle on it. The rocket will exert a constant thrust force of magnitude Frdirected in the tangential direction. The object will start

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter12: Rotation I: Kinematics And Dynamics

Section: Chapter Questions

Problem 77PQ

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Concept explainers

Rotational Equilibrium And Rotational Dynamics

In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.

Equilibrium of Forces

The tension created on one body during push or pull is known as force.

Question

In a laboratory experiment, a very large fish tank is filled with water. At the bottom of the tank, a rigid rod of
length L is pinned to the frictionless floor and the other end is connected to a small object of mass m with a rocket nozzle on
it. The rocket will exert a constant thrust force of magnitude F, directed in the tangential direction. The object will start
from rest, rotating about a circle in the horizontal plane when the rocket motor is turned on. Since it is under water, the
object experiences a drag force that depends linearly on the objects velocity D=-bỷ where b is a constant and v is the
object's velocity vector (the minus sign just means that the drag force points in the direction OPPOSITE the object's
velocity).
a) Draw a complete FBD of the object while it is speeding up. Use an over-head view.
b) “Fill out" Newton's 2nd law in the radial and tangential directions. Do NOT solve for anything.
c) Newton's 2nd Law in the tangential direction gives you a differential equation to solve for the tangential component of the
-b
FT
object's velocity as a function of time. The solution is va(t)=
). What is the maximum speed reached by
m
the object? Use Newton's 2nd Law to show this is correct when the tangential component of the object's acceleration is
zero.
d) Show that energy is conserved for this system by demonstrating that the Power input to the system by the thrust force
acting on the block is exactly equal to the absolute value of the Power removed from the block by the drag force after
maximum velocity has been reached.
e) If the rod keeping the object moving about a circle is not strong enough to withstand the tension force when the object
reaches maximum velocity, find the time that the rod will break. Call the maximum tension the rod can withstand T,
HINT: en (x)= x and In(e*)=x
тах
f) What is the kinetic energy of the object at the moment the rod breaks?
g) (Extra Credit + 2 Points!!) At what rate is the water heating up at the moment the rod breaks?

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