A disk of radius R moves at all times in a vertical plane so that it rotates with constant angular speed ω. The disk als
Posted: Mon May 02, 2022 4:28 pm
A disk of radius R moves at all times in a vertical plane so that it rotates with constant angular speed ω. The disk also
it rolls without slipping on a horizontal line that moves with a constant speed 'v' . In the disk there is a smooth radial groove in which a particle of mass m moves, which is also attached to the center (C) of the disk by a spring of elastic constant k and zero natural length. It is requested:
a.Express the differential equation of motion of the particle in the slot.
b. Obtain the minimum value of k so that the movement of the particle with respect to
of the groove is of the oscillating type.
c.Express the reaction exerted by the groove on the particle.
d. Assuming that at the initial instant the slot is horizontal and the particle
is at the right edge of the disk and at rest relative to the disk.
Calculate the work of the reaction between t = 0 and an instant when the slot it has turned a quarter of a turn
(t = π/(2ω)).
Particularize this calculation to
k = 10mg/R, ω =sqrt(g/R) and v = (5/6)ωR
(Midterm exam, 11/25/2000)
Kindly, I demand all, the answers a , b , c , d . Perform full free body analyses. Thank you 
3 k m V
it rolls without slipping on a horizontal line that moves with a constant speed 'v' . In the disk there is a smooth radial groove in which a particle of mass m moves, which is also attached to the center (C) of the disk by a spring of elastic constant k and zero natural length. It is requested:
a.Express the differential equation of motion of the particle in the slot.
b. Obtain the minimum value of k so that the movement of the particle with respect to
of the groove is of the oscillating type.
c.Express the reaction exerted by the groove on the particle.
d. Assuming that at the initial instant the slot is horizontal and the particle
is at the right edge of the disk and at rest relative to the disk.
Calculate the work of the reaction between t = 0 and an instant when the slot it has turned a quarter of a turn
(t = π/(2ω)).
Particularize this calculation to
k = 10mg/R, ω =sqrt(g/R) and v = (5/6)ωR
(Midterm exam, 11/25/2000)
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3 k m V