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Some old clocks were powered by coil springs that gradually lost torque as they unwound. A “fusee” was used to compensate for the gradual loss of torque, allowing more accurate timekeeping. The fusee is a cone-shaped pulley with a helical groove around it, wound with a cord or chain which is attached to the mainspring. Suppose the spring develops a torque of Ts = kθ, where the torsional stiffness k = 0.02 Nm/rad and θ is the angle of twist of the spring in radians. When θ = 4 rad, the cord acts on the part of the fusee with a radius of 10 mm. If the fusee provides constant torque for all θ, what should the radius be when θ = 3 rad?

Some old clocks were powered by coil springs that gradually lost torque as they unwound. A “fusee” was used to compensate for the gradual loss of torque, allowing more accurate timekeeping. The fusee is a cone-shaped pulley with a helical groove around it, wound with a cord or chain which is attached to the mainspring. Suppose the spring develops a torque of Ts = kθ, where the torsional stiffness k = 0.02 Nm/rad and θ is the angle of twist of the spring in radians. When θ = 4 rad, the cord acts on the part of the fusee with a radius of 10 mm. If the fusee provides constant torque for all θ, what should the radius be when θ = 3 rad?

College Physics
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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Some old clocks were powered by coil springs that gradually lost torque as
they unwound. A “fusee” was used to compensate for the gradual loss of torque, allowing more accurate timekeeping. The fusee is a cone-shaped pulley with a helical groove around it, wound with a cord or chain which is attached to the mainspring. Suppose the spring develops a torque of Ts = kθ, where the torsional stiffness k = 0.02 Nm/rad and θ is the angle of twist of the spring in radians. When θ = 4 rad, the cord acts on the part of the fusee with a radius of 10 mm. If the fusee provides constant torque for all θ, what should the radius be when θ = 3 rad?

1. Wound up D. F 日 前 EREA館 每可日 2. Unwound
Transcribed Image Text:1. Wound up D. F 日 前 EREA館 每可日 2. Unwound
Expert Solution
Step 1

Given:

Relation for torque Ts=kθ

Where 

k=0.02 Nm/rad

When

θ=4 rad

radius r= 10 mm=0.01 m

To find radius at θ= 3 rad

steps

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