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?).

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter7: Dry Friction

Section: Chapter Questions

Problem 7.72P

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