Concept explainers
The normal reaction at point
Answer to Problem 13.71P
The minimum normal reaction is
Explanation of Solution
Given:
Radius of arc
Radius of arc
Mass of car and occupants is
Velocity at point
Angle of Arc from
Concept used:
Write the expression for the displacement of car from
Here,
Write the expression for kinetic energy at point
Here,
Write the expression for kinetic energy at point
Here,
Write the expression for the potential energy at point
Here,
Write the expression for the potential energy at point
Here,
Write the expression for conservation of energy for point
Substitute
Simplify the above expression.
Substitute
Solve the above expression for
Write the expression for the normal acceleration of car.
Here,
Apply Newton’s Law of motion for carat position
Here,
Write the expression for kinetic energy at point
Here,
Write the expression for the work done at point
Here,
Write the expression for the work energy principle for point
Substitute
Substitute
Rearrange the above expression for
Write the expression for the normal acceleration at point
Here,
Apply Newton’s Law of motion for carat position
Here,
Calculation:
Substitute
Substitute
Substitute
Substitute
Simplify above expression for
Substitute
Substitute
Substitute
Simplify above for
The minimum normal reaction is
Conclusion:
Thus, the minimum normal reaction is
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Chapter 13 Solutions
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