hwk01-1

hwk01-1 - ME563 – Fall 2006 Purdue University West...

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Unformatted text preview: ME563 – Fall 2006 Purdue University 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 Purdue University West Lafayette, IN 47907-2088 If you choose to scan in your completed solution, please email this solution to krousgri@purdue.edu by midnight of the due date given above. Name Location _________________________________________ 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 and ground. 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. x M 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 f θ G A F ...
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