The maximum additional deformation of the spring.
Answer to Problem 13.69P
The maximum additional deflection is
Explanation of Solution
Given:
Mass of the package is
Spring stiffness is
Angle of inclination is
Initial compression of spring is
Velocity of package is
Concept used:
Draw the diagram of the package moving to different positions as shown below:
Consider the package is moving from position (0) to (1).
Write the Expression for the kinetic energy of package at position (0).
Here,
Write the Expression for the kinetic energy of package at position (1).
Here,
Write the expression for the work done from bringing the package from (0) to (1).
Here,
Write the expression for normal reaction from the ground.
Write the expression for work energy principle between point (0) and (1).
Consider the motion of package from position (1) to (2).
Write the Expression for the kinetic energy of package at position (2).
Here,
Write the expression for the initial potential energy at position (2).
Here,
Write the Expression for the kinetic energy of package at final position.
Here,
Write the expression for the final potential energy at position (2).
Here,
Write the expression for the law of conservation between points (2) and the final position.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Simplify the above expression for
Substitute
Substitute
Substitute
Substitute
Substitute
Simplify the above expression for
Substitute
Simplify above expression for
The maximum additional deflection is
Conclusion:
Thus, the maximum additional deflection is
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Chapter 13 Solutions
Vector Mechanics for Engineers: Dynamics
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