Concept explainers
A 7.5-lb collar is released from rest in the position shown, slides down the inclined rod, and compresses the spring. The direction of motion is reversed and the collar slides up the rod. Knowing that the maximum deflection of the spring is 5 in., determine (a) the coefficient of kinetic friction between the collar and the rod, (b) the maximum speed of the collar.
Fig. P13.29
(a)
Find the coefficient of kinetic friction between the collar and rod
Answer to Problem 13.29P
The coefficient of kinetic friction between the collar and rod
Explanation of Solution
Given information:
The weight of the collar
The maximum deflection of the spring (x) is
The distance between the spring and collar (d) is
The spring constant (k) is
The angle of the inclined rod
Assume the acceleration due to gravity (g) is
Calculation:
Show the free body diagram of the inclined rod with the forces acting as in Figure (1).
Here, the initial kinetic energy
Calculate the work done
Here, F is the frictional force.
Substitute
Substitute
Substitute
Calculate the work done
Substitute
Calculate the work done
Substitute
Calculate the total work done
Substitute
Use work and energy principle which states that kinetic energy of the particle at a displaced point can be obtained by adding the initial kinetic energy and the work done on the particle during its displacement.
Find the coefficient of kinetic friction between the collar and rod
Substitute 0 for
Therefore, the coefficient of kinetic friction between the collar and rod
(b)
Find the maximum speed
Answer to Problem 13.29P
The maximum speed
Explanation of Solution
Given information:
The weight of the collar
The maximum deflection of the spring (x) is
The distance between the spring and collar (d) is
The spring constant (k) is
The angle of the inclined rod
Assume the acceleration due to gravity (g) is
Calculation:
Calculate the kinetic energy
Substitute
Calculate the work done
Here, F is the frictional force.
Substitute
Substitute
Substitute
Calculate the work done
Substitute
Calculate the total work done
Substitute
Substitute 0.159 for
Use work and energy principle which states that kinetic energy of the particle at a displaced point can be obtained by adding the initial kinetic energy and the work done on the particle during its displacement.
Find the maximum speed
Substitute 0 for
Therefore, the maximum speed
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Chapter 13 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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