Concept explainers
A slender rod AB with a weight W is attached to two blocks A and B that can move freely in the guides shown. Knowing that the spring is unstretched when AB is horizontal, determine three values of θ corresponding to equilibrium when W = 300 lb, l = 16 in., and k = 75 lb/in. State in each case whether the equilibrium is stable, unstable, or neutral.
Fig. P10.79 and P10.80
Find three values of
Answer to Problem 10.80P
The value of
The equilibrium is
The equilibrium is
The equilibrium is
Explanation of Solution
Given information:
The weight of the slender rod AB is
The length of the slender rod AB is
The spring constant is
Calculation:
The spring is unstretched when AB is horizontal.
Show the free-body diagram of the arrangement as in Figure 1.
Find the elongation of the spring s using the relation.
Here, the length of the slender rod AB is l.
Find the potential energy (V) using the relation;
Differentiate the equation;
Here, the weight of the slender rod AB and the spring constant is k.
Differentiate the Equation (1).
Equate the Equation (1) to zero for equilibrium.
Substitute 300 lb for W,
Solve the equation by trial and error procedure.
Therefore, the value of
For
Substitute 300 lb for W,
Therefore, the equilibrium is
For
Substitute 300 lb for W,
Therefore, the equilibrium is
For
Substitute 300 lb for W,
Therefore, the equilibrium is
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Chapter 10 Solutions
Vector Mechanics for Engineers: Statics
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