The radius of the roll of paper shown below is 7.6 cm and its moment of inertia is I= 3.3 x 10³ kg-m². The roll is initially at rest, then a downward force F = 3.5 N is exerted on the end of the roll for 1.3 s, as shown. A constant frictional torque (t,) with magnitude 0.11 N-m that slows the clockwise rotation acts on the roll from the moment it starts rotating until the moment it stops rotating. After the force F is removed (at the end of 1.3 s), the roll slows and eventually comes to a stop due to t. Assume that the paper is so thin that the radius of the roll remains constant while it is unrolling. (a) Calculate the total length of paper that unrolls from the moment the force F was applied until the moment that the roll stops moving. (answer: 7.3 m) (b) The thickness of the paper is about 0.01 cm. Is the assumption that the radius of the roll remained constant justified? That is, estimate the fractional decrease in the radius of the roll, Ar/r, where Ar is the decrease in the radius of the roll and r is the original radius of the roll. (answer: Ar/r 0.02 (2%). Do you think 2% is a negligible change?).

The radius of the roll of paper shown below is 7.6 cm and its moment of inertia is I= 3.3 x 10³ kg-m². The roll is initially at rest, then a downward force F = 3.5 N is exerted on the end of the roll for 1.3 s, as shown. A constant frictional torque (t,) with magnitude 0.11 N-m that slows the clockwise rotation acts on the roll from the moment it starts rotating until the moment it stops rotating. After the force F is removed (at the end of 1.3 s), the roll slows and eventually comes to a stop due to t. Assume that the paper is so thin that the radius of the roll remains constant while it is unrolling. (a) Calculate the total length of paper that unrolls from the moment the force F was applied until the moment that the roll stops moving. (answer: 7.3 m) (b) The thickness of the paper is about 0.01 cm. Is the assumption that the radius of the roll remained constant justified? That is, estimate the fractional decrease in the radius of the roll, Ar/r, where Ar is the decrease in the radius of the roll and r is the original radius of the roll. (answer: Ar/r 0.02 (2%). Do you think 2% is a negligible change?).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Net torque, moment of inertia, and constant angular acceleration
The radius of the roll of paper shown below is 7.6 cm and its moment of inertia is I= 3.3 x 10-3 kg-m². The
roll is initially at rest, then a downward force F = 3.5 N is exerted on the end of the roll for 1.3 s, as shown.
A constant frictional torque (Tf.) with magnitude 0.11 N-m that slows the clockwise rotation acts on the roll
from the moment it starts rotating until the moment it stops rotating. After the force F is removed (at the
end of 1.3 s), the roll slows and eventually comes to a stop due to tr.
Assume that the paper is so thin that the radius of the roll remains constant while it is unrolling.
(a) Calculate the total length of paper that unrolls from the moment the force F was applied until the moment
that the roll stops moving. (answer: 7.3 m)
(b) The thickness of the paper is about 0.01 cm. Is the assumption that the radius of the roll remained
constant justified? That is, estimate the fractional decrease in the radius of the roll, Ar/r, where Ar is the
decrease in the radius of the roll and r is the original radius of the roll. (answer: Ar/r = 0.02 (2%). Do you
think 2% is a negligible change?).
useful
@ = @o + at
Δθ ω0t + αt
o? = wo? + 2aAO
As = rA0
Tnet
= la
T = rFsin0 = F(length of lever arm)

Expert Solution

Step 1

Solution:

Given Data:

F = 3.5 N

r = 7.6 cm

I = 3.3 X 10^-3 kg-m²

^{t = 1.3 s}

^{T_f = 0.11 N-m}

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