EAS208_Exam02_102910_FINAL_Solutions

EAS208_Exam02_102910_FINAL_Solutions - EAS208 Fall 2010...

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EAS208 Fall 2010 – Exam 2 SOLUTIONS Name: Person Number: Problem 1: The collar is given a downward velocity of 2 kg 4 A m v s = when it is at . If the spring has an unstretched length of 1 and, and the velocity of the collar at is A m 1 sm = 5 C m v s = , determine the stiffness of the spring. k (30 points) Solution: The only forces that perform work on the collar are conservative. Apply Conservation of Total Mechanical Energy from position A to position C (assume the datum at position ): A 12 EE = g Ae AA g Ce C VVT C + += + + 22 2 11 0 C kS mv mgs kS mv ++ = 2 C () ( ) 2 2 2 AC C A mv v m g s kS S −+ = ( ) 2 CA m g s k SS = where 4 A m v s = 5 C m v s = 1 Ao =− =−= 1 m 1 1 Co Ss S 5 1 m = +−= +− = 1 = Substitute the above expression for the spring stiffness relation: ( ) 2 2 4 5 2 2 9 . 8 1 1 40.24 51 1 m g s N kk m == = −− The stiffness of the spring is k 40.24 N k m = .
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EAS208 Fall 2010 – Exam 2 SOLUTIONS Name: Person Number: Problem 2: A pellet of mass 1.4 p mk g = is projected horizontally with a velocity 10 o m v s = against the cart with mass 5 c g = , as shown in the figure. The cart is initially at rest and with the spring unstretched. The spring stiffness is
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This document was uploaded on 10/27/2011 for the course EAS 208 at SUNY Buffalo.

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EAS208_Exam02_102910_FINAL_Solutions - EAS208 Fall 2010...

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