Concept explainers
(a)
The frequency
(a)
Answer to Problem 19.14P
The frequency
Explanation of Solution
Given Information:
The mass
The mass
The spring constant (k) is
The value of acceleration due to gravity (g) is
Calculation:
Show the electromagnet with cable and crane arrangement as in Figure (1).
Refer Figure (1), when the electromagnet is off, the tension in the cable is equal to the force due to the mass of the electromagnet.
Express the force balance equation for the first case.
Here,
Calculate the natural circular frequency
Substitute
Calculate the natural frequency
Substitute
By referring the Figure 1, when the electromagnet is on, the tension in the cable is equal to the force due to the mass of the electromagnet and that due to mass of the scrap steel.
Express the force balance equation for the second case.
Here,
Substitute Equation (1) in Equation (2).
Calculate the amplitude
Substitute
Calculate the maximum velocity
Substitute
Therefore, the frequency
(b)
The minimum tension
(b)
Answer to Problem 19.14P
The minimum tension
Explanation of Solution
Given Information:
The mass
The mass
The spring constant (k) is
The value of acceleration due to gravity (g) is
Calculation:
The minimum value of tension occurs when the displacement (x) is maximum at upward direction
Express the minimum tension
Substitute Equations (1) and (3) in Equation (4).
Calculate the minimum tension
Substitute 150 kg for
Therefore, the minimum tension
(c)
The velocity
(c)
Answer to Problem 19.14P
The velocity
Explanation of Solution
Given Information:
The mass
The mass
The spring constant (k) is
The value of acceleration due to gravity (g) is
Calculation:
Express the displacement (x) of the simple harmonic motion at any instant.
Here,
When time (t) is 0, the initial displacement is
Substitute 0 for t and
For the above equation to satisfy the value of
Calculate the velocity
Substitute
Therefore, the velocity
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Chapter 19 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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