Concept explainers
The kinetic energy lost of the plate when edge C of the plate hits the obstruction.
Answer to Problem 18.51P
The energy loss of circular disc after impact is
Explanation of Solution
Given information:
Mass of circular plate is
Expression of moment of inertia along the x-axis.
Here, the radius of the disc is.
Expression of moment of inertia along y-axis and z-axis.
Expression of moment of inertia along z-axis.
Expression for conservation of linear momentum.
Here,
Compare x-component of Equation (I) on both side.
Compare y-component of Equation (I) on both side.
Compare z-component of Equation (I) on both side.
Expression of relative position of C according to center of mass.
As
Expression of the velocity of circular disc C.
Substitute
Substitute
Compare y-component of Equation (V) on both sides.
Substitute
Expression of moment about center of mass.
Expression for kinetic energy of the circular plat before impact.
Expression for kinetic energy of the circular plat after impact.
Expression of energy loss.
Calculation:
Substitute,
Compare x-component of Equation (XII) on both side.
Compare y-component of Equation (XII) on both side.
Compare z-component of Equation (XII) on both side.
Substitute
Substitute
Equate Equation (XIII) and Equation (XIV).
Substitute
Substitute
Expression for velocity along x-axis, y-axis and z-axis.
Substitute 0 for
Substitute
Substitute
Substitute
Conclusion:
Thus, the energy loss of circular disc after impact is
Want to see more full solutions like this?
Chapter 18 Solutions
Vector Mechanics for Engineers: Dynamics
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY