Concept explainers
Solve Prob. 16.137 when θ = 90°.
16.137 In the engine system shown, l = 250 mm and b = 100 mm. The connecting rod BD is assumed to be a 1.2-kg uniform slender rod and is attached to the 1.8-kg piston P. During a test of the system, crank AB is made to rotate with a constant angular velocity of 600 rpm clockwise with no force applied to the face of the piston. Determine the forces exerted on the connecting rod at B and D when θ = 180°. (Neglect the effect of the weight of the rod.)
Fig. P16.137
The forces exerted on the connecting rod at B and D when
Answer to Problem 16.138P
The forces exerted on the connecting rod at B is
The forces exerted on the connecting rod at D is
Explanation of Solution
Given information:
The length of the rod BD is
The length of the rod AB is
The mass of the rod BD is
The mass of the piston P is
The angular velocity of AB is
Calculation:
Consider the acceleration due to gravity
Calculate the angular velocity in
Sketch the Free body Diagram of the system as shown in Figure 1.
Refer to Figure 1.
Calculate the distance
Substitute
Calculate the position vectors as shown below.
Position of B with respect to A.
Position of D with respect to B.
Position of mass center G with respect to D.
Calculate the velocity at B
Substitute
Calculate the velocity at D
Substitute
Resolving the i and j components as shown below.
For j component.
For i component.
Substitute
Consider that the angular acceleration as
Calculate the acceleration at B
Substitute
Calculate the acceleration
Substitute
Resolving i and j components as shown below.
For j component.
For i component.
Substitute
Calculate the acceleration of mass center G of bar BD
Substitute
Resolving the components as shown below.
Calculate the mass moment of inertia for BD
Substitute
Sketch the Free Body Diagram of the piston with the bar BD as shown in Figure 2.
Refer to Figure 2.
Apply the Equilibrium of forces along x direction as shown below.
Substitute
Apply the Equilibrium of moment about B as shown below.
Substitute
Apply the Equilibrium of forces along y direction as shown below.
Substitute
Calculate the force acting at B as shown below.
Substitute
Hence, the forces exerted on the connecting rod at B is
Sketch the Free Body Diagram of the piston as shown in Figure 3.
Refer to Figure 3.
Calculate the force acting on the rod at D as shown below.
Substitute
Calculate the magnitude of force at D as shown below.
Therefore, the forces exerted on the connecting rod at D is
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