When the rope is at an angle of
(a)
The velocities of A and B just after the impact.
Answer to Problem 13.188P
Explanation of Solution
Given information:
Mass of sphere is
Mass of wedge is
Concept used:
The total linear momentum of two particles is conserved. Therefore:
The co-efficient of restitution is defined as.
The principle of conservation of energy is defined as.
“When a particle moves under the action of conservation of forces. the sum of kinetic energy and potential energy of that particle remains constant.”
Calculation:
At initial stage:
Find the Kinetic and potential energies.
Just before the impact:
Therefore.
Substitute and solve:
Draw impulse momentum diagram.
Apply conservation of momentum in t direction.
Therefore:
For both A and B :
Apply conservation of momentum in x direction.
Substitute:
Therefore:
Apply co-efficient of restitution equation.
Substitute:
Solve.
Solve equation 1 and 2.
Find the magnitude of
Find the angle.
Conclusion:
The velocities of A and B just after the impact is equal to:
(b)
The maximum deflection of the spring.
Answer to Problem 13.188P
Maximum deflection of the spring is
Explanation of Solution
Given information:
Mass of sphere is
Mass of wedge is
Concept used:
The principle of conservation of energy is defined as:
“When a particle moves under the action of conservation of forces. the sum of kinetic energy and potential energy of that particle remains constant”
Calculation:
According to the conservation of energy:
Just after the impact.
Rearrange:
According to sub part a.:
Substitute and solve:
Therefore.
Conclusion:
The maximum deflection is equal to
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Chapter 13 Solutions
Vector Mechanics For Engineers
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