A 2-kg collar is attached to a spring and slides without friction in a vertical plane along the curved rod ABC. The spring is undeformed when the collar is at C and its constant is 600 N/m. if the collar is released at A with no initial velocity, determine its velocity (a) as it passes through B, (b) as it reaches C.
(a)
Velocity of collar as it passes through
Answer to Problem 13.64P
Velocity of collar as it passes through
Explanation of Solution
Given:
Mass of collar is
Spring constant is
Initial velocity at
Concept used:
Refer to Fig.P13.64;
Calculate the elongation of the spring when collar is at point
Here,
Calculate the elongation of the spring when collar is at point
Here,
Calculate the elongation of the spring when collar is at point
Here,
Write the expression for Potential energy of spring at point
Here,
Write the expression for Potential energy of spring at point
Here,
Write the expression for Potential energy of spring at point
Here,
Write the expression for the kinetic energy of collar at point
Here,
Write the expression for the kinetic energy of collar at point
Here,
Write the expression for the kinetic energy of collar at point
Here,
Consider the datum to be the surface.
Write the expression for the gravitational potential energy at point
Here,
The gravitational potential energy at point
Write the expression of conservation of energy for the system at point
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Simplify the above expression for
Velocity of collar as it passes through
Conclusion:
Thus, Velocity of collar as it passes through
(b)
Velocity of collar as it passes through
Answer to Problem 13.64P
Velocity of collar as it passes through
Explanation of Solution
Write the expression of conservation of energy for the system at point
Calculation:
Substitute
Substitute
Simplify the above expression for
Velocity of collar as it passes through
Conclusion:
Thus, Velocity of collar as it passes through
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Chapter 13 Solutions
Vector Mechanics for Engineers: Dynamics
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