A couple M with a magnitude of 100 N·m is applied as shown to the crank of the engine system. Knowing that AB = 50 mm and BC = 200 mm, determine the force P required to maintain the equilibrium of the system when (a) θ = 60°, (b) θ = 120°.
Fig. P10.22
(a)
Find the magnitude of the force P required to maintain the equilibrium.
Answer to Problem 10.22P
The magnitude of the force P required is
Explanation of Solution
Given information:
The magnitude of the couple M is
The distance between the point A and B is 50 mm.
The distance between the point B and C is 200 mm.
The value of the angle
Calculation:
Show the free-body diagram of the engine system as in Figure 1.
Consider the geometry of the Figure 1.
Use the Law of sines;
Differentiate the equation;
Find the horizontal displacement
Differentiate the equation;
Substitute
Use the principle of virtual work;
Substitute
Substitute 50 mm for AB, 200 mm for BC, and
Substitute
Therefore, the magnitude of the force P required is
(b)
Find the magnitude of the force P required to maintain the equilibrium.
Answer to Problem 10.22P
The magnitude of the force P required is
Explanation of Solution
Given information:
The magnitude of the couple M is
The distance between the point A and B is 50 mm.
The distance between the point B and C is 200 mm.
The value of the angle
Calculation:
Refer part (a) for calculation;
Substitute 50 mm for AB, 200 mm for BC, and
Substitute
Therefore, the magnitude of the force P required is
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