4) This Atwood's machine includes two blocks connected by a cable, going over a pulley without slipping. Block 1 (30.0 kg) is connected to a spring (70.0 N/m), and slides on a horizontal surface with a coefficient of kinetic friction of 0.0100. Block 2 is 50.0 kg, and hangs vertically from the cable. The pulley is a disk with a
4) This Atwood's machine includes two blocks connected by a cable, going over a pulley without slipping. Block 1 (30.0 kg) is connected to a spring (70.0 N/m), and slides on a horizontal surface with a coefficient of kinetic friction of 0.0100. Block 2 is 50.0 kg, and hangs vertically from the cable. The pulley is a disk with a
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:4) This Atwood's machine includes two blocks connected by a cable, going over a pulley without slipping.
Block 1 (30.0 kg) is connected to a spring (70.0 N/m), and slides on a horizontal surface with a coefficient of
kinetic friction of 0.0100. Block 2 is 50.0 kg, and hangs vertically from the cable. The pulley is a disk with a
radius of 0.500 m, and its moment of inertia about the center of mass is 10. 0 kg-m“.
a) Draw the three free body diagrams, and write out Newton's 2nd Law for each.
b) Derive the equation of motion (inhomogeneous 2nd order ODE) for this system.
c) Use u-substitution to rewrite this as a homogeneous 2nd order ODE.
d) Assume the position x as a function of time t is of the form
x(t) = A cos (wt + p)
I disk
for undamped natural frequency w, phase angle P, and
amplitude A. The initial conditions are: x(0)
v(0) = -3. 00 m/s. Solve for the position of the mass as a
function of time (you need to solve for w, 4, and A).
= 2. 00 m and
Mz
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