A wheel of mass mg = 5 kg, outer radius r, = 0.6m, r; = 0.3m, and mass moment of inertia lG = (mg*r.³)/2 rolls without slipping on a horizontal surface. A spring of stiffness k = 100 N/m is wrapped around the inner hub and is initially unstretched. An inextensible string is wrapped around the outer radius of the wheel, passes over a massless, frictionless pulley, and attaches to a mass mc = 2 kg which is initially a height h = 0.4 m above the ground. (a) Find the speed of the mass C when it hits the ground, and (b) Find the smallest value for mc that ensures that it actually strikes the ground. Ans: (a) vc = 1.3145 m/s, (b) minimum mc = 1.1468 kg В k A C mc G h

A wheel of mass mg = 5 kg, outer radius r, = 0.6m, r; = 0.3m, and mass moment of inertia lG = (mg*r.³)/2 rolls without slipping on a horizontal surface. A spring of stiffness k = 100 N/m is wrapped around the inner hub and is initially unstretched. An inextensible string is wrapped around the outer radius of the wheel, passes over a massless, frictionless pulley, and attaches to a mass mc = 2 kg which is initially a height h = 0.4 m above the ground. (a) Find the speed of the mass C when it hits the ground, and (b) Find the smallest value for mc that ensures that it actually strikes the ground. Ans: (a) vc = 1.3145 m/s, (b) minimum mc = 1.1468 kg В k A C mc G h

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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The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m. Ignore the spring's mass. (5) At state 2, how long the spring is stretched from its unstretched state (length difference):________(m) (two decimal places) (6) The elastic potential energy of the spring at the state 2 is_______(N·m) (two decimal places) (7) The instantaneous center of zero velocity (IC) of the wheel at state 1 is (8) The mass moment of inertial of the wheel about its mass center G is IG =_________(kg·m2 ) (two decimal places)
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The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m. Ignore the spring's mass. (5) At state 2, how long the spring is stretched from its unstretched state (length difference):________(m) (two decimal places) (6) The elastic potential energy of the spring at the state 2 is_______(N·m) (two decimal places) (7) The instantaneous center of zero velocity (IC) of the wheel at state 1 is (8) The mass moment of inertial of the wheel about its mass center G is IG =_________(kg·m2 ) (two decimal places) (9) The mass moment of inertial of the wheel about its…
The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m. (7) The instantaneous center of zero velocity (IC) is A. Point A B. Point O C. Point G