Concept explainers
A 3-kg block rests on top of a 2-kg block supported by, but not attached to, a spring of constant 40 N/m. The upper block is suddenly removed. Determine (a) the maximum speed reached by the 2-kg block, (b) the maximum height reached by the 2-kg block.
Fig. P13.26
(a)
Find the maximum speed
Answer to Problem 13.26P
The maximum speed
Explanation of Solution
Given information:
The mass of the block A
The mass of the block B
The spring constant (k) is
Assume the acceleration due to gravity (g) is
Calculation:
Consider the position 1, the block B has been removed.
Calculate the spring stretch
Here,
Substitute
Substitute
Take the position 2 be later position while the spring still in contact with block A.
Calculate the work of the force exerted
Integrate the above equation with respect to ‘x’.
Substitute,
Calculate the work of the gravitational force
Substitute,
Calculate the total work done
Substitute
Here, the initial kinetic energy
Calculate the kinetic energy
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.
Write the expression for the principle of work and energy:
Substitute 0 for
At the maximum speed, differentiate the velocity equation with respect to ‘x’.
Substitute
Substitute
Therefore, the maximum speed
(b)
Find the maximum height (h) reached by the
Answer to Problem 13.26P
The maximum height (h) reached by the
Explanation of Solution
Given information:
The mass of the block A
The mass of the block B
The spring constant (k) is
Assume the acceleration due to gravity (g) is
Calculation:
Consider the position 3, the block A reached the maximum height and assume that the block has separated from the spring so the spring is zero at the separation.
Calculate the work of the force exerted
Integrate the above equation with respect to ‘x’.
Substitute,
Calculate the work of the gravitational force
Substitute
Calculate the total work done
Substitute
At the maximum height, the velocity
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 height (h) reached by the
Substitute 0 for
Therefore, the maximum height (h) reached by the
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Chapter 13 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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