Problem 15.140 | A particle of mass m is attached to a light string that runs through a smooth hole in a circularly shaped bowl that lies in the vertical plane. A force P is applied to the other end of the string so that the mass can rotate in a horizontal circle with constant speed 01. Use sin 30° = 1/2 and cos 30° = √√3/2 in your calculations. (a) If the tension in the string is P1 = mg when the mass is in ①, determine its speed v₁ as a function of g and R. (b) If the force is increased to P2 so that the mass moves to the new circular path shown in ②, determine the new speed of the mass v2. √√√3+1 (c) Determine, as a function of m and g, the required tension in the string P2 in ②. Use sin 15° = √√3-1 2√2 and cos 15° = 2√√2 30° m 30° R Figure P15.140
Problem 15.140 | A particle of mass m is attached to a light string that runs through a smooth hole in a circularly shaped bowl that lies in the vertical plane. A force P is applied to the other end of the string so that the mass can rotate in a horizontal circle with constant speed 01. Use sin 30° = 1/2 and cos 30° = √√3/2 in your calculations. (a) If the tension in the string is P1 = mg when the mass is in ①, determine its speed v₁ as a function of g and R. (b) If the force is increased to P2 so that the mass moves to the new circular path shown in ②, determine the new speed of the mass v2. √√√3+1 (c) Determine, as a function of m and g, the required tension in the string P2 in ②. Use sin 15° = √√3-1 2√2 and cos 15° = 2√√2 30° m 30° R Figure P15.140
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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Transcribed Image Text:Problem 15.140 |
A particle of mass m is attached to a light string that runs through a smooth hole in a circularly shaped bowl that lies in the vertical plane.
A force P is applied to the other end of the string so that the mass can rotate in a horizontal circle with constant speed 01. Use
sin 30° = 1/2 and cos 30° =
√√3/2 in your calculations.
(a) If the tension in the string is P1 = mg when the mass is in ①, determine its speed v₁ as a function of g and R.
(b) If the force is increased to P2 so that the mass moves to the new circular path shown in ②, determine the new speed of the mass v2.
√√√3+1
(c) Determine, as a function of m and g, the required tension in the string P2 in ②. Use sin 15° =
√√3-1
2√2
and cos 15° =
2√√2
30°
m
30°
R
Figure P15.140
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