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Unformatted text preview: ME563 – Fall 2006
West Lafayette, IN Homework Set No. 1
Assignment date: Wednesday, August 23
Due date: Wednesday, August 30
Please attach this cover sheet to your completed homework assignment. If on
campus, please bring to lecture on the due date. If off campus, mail to the
address below with a postmark no later than midnight of the due date given
above: C.M. Krousgrill
585 Purdue Mall
West Lafayette, IN 47907-2088
If you choose to scan in your completed solution, please email this solution to
email@example.com by midnight of the due date given above.
Problem 1.1 __________________ Problem 1.2 __________________ Problem 1.3 __________________ TOTAL __________________ ME 563 – Fall 2006
Homework Prob. 1.1
Consider the system below:
• A spool having a mass of m, a centroidal mass moment of inertia IG and
an outer radius of R that rolls without slipping on a horizontal surface.
• A block of mass M that is in contact with the inner radius of the spool and
is constrained to move only in a horizontal direction such that the block
does not slip on the spool.
• A spring of stiffness k that is connected between the center of the spool G
Let x describe the position of G as measured from the position of G when the
spring is unstretched. Using the Newton-Euler formulation, determine the
equation of motion for the system using the coordinate x.
Note that this system has a single degree of freedom. Draw the free body
diagrams of the spool and block individually before writing down the NewtonEuler equations.
k G smooth m
r R no slip ME 563 – Fall 2006
Homework Prob. 1.2
Repeat Homework Problem 1.1 except here use the power equation. Compare
your result here with that found in Problem 1.1. ME 563 – Fall 2006
Homework Prob. 1.3
A thin homogeneous bar of mass m and length L is suspended by an inextensible
cord of length L/2. Let φ be the angular rotation of the cord and θ be the angular
rotation of bar, with both φ and θ measured positively counterclockwise from a
vertical line. A horizontal force f acts at the centroid G of the bar. A second force
F acts at end A of the bar in such a way that F always acts in a direction aligned
with the length of the bar. Note that this system has two degrees of freedom.
a) Determine the inertia coefficients for the system in terms of the generalized
coordinates φ and θ.
b) Determine the generalized forces due to the forces f and F acting on the
system in terms of the generalized coordinates φ and θ.
If it has been a while since you have dealt with rigid body kinematics, you might
want to see the review of rigid body kinematics under the "Help" link on the
course website. L /2
B φ L
G A F ...
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