Concept explainers
A 10-kg block is attached to spring A and connected to spring B by a cord and pulley. The block is held in the position shown with both springs unstretched when the support is removed and the block is released with no initial velocity. Knowing that the constant of each spring is 2 kN/m, determine (a) the velocity of the block after it has moved down 50 mm, (b) the maximum velocity achieved by the block.
Fig. P13.30
(a)
Find the velocity (v) of the block after it has moved down
Answer to Problem 13.30P
The velocity (v) of the block after it has moved down
Explanation of Solution
Given information:
The mass of the block (m) is
The spring constant at A
The spring constant at B
The depth where the spring A moves down
Assume the acceleration due to gravity (g) is
Calculation:
Show the free body diagram of the block with two spring’s attachment acting as in Figure (1).
Calculate the depth of spring B moves down due to block
Substitute
Calculate the weight of the block (W) using the relation:
Substitute
Here, the initial kinetic energy
Calculate the final kinetic energy
Substitute
Calculate the work done
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 velocity (v) of the block after it has moved down
Substitute 0 for
Therefore, the velocity (v) of the block after it has moved down
(b)
Find the maximum velocity
Answer to Problem 13.30P
The maximum velocity
Explanation of Solution
Given information:
The mass of the block (m) is
The spring constant at A
The spring constant at B
The depth where the spring A moves down
Assume the acceleration due to gravity (g) is
Calculation:
Assume x be the distance moved down by the
Calculate the work done
Substitute
Calculate the work done
Substitute
Calculate the work done
Substitute
Calculate the total work done
Substitute
Differentiate the above equation with respect to ‘x’.
Substitute
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 maximum velocity
Substitute 0 for
Therefore, the maximum velocity
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Chapter 13 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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