A spring of constant 15 kN/m connects points C and F of the linkage shown. Neglecting the weight of the spring and linkage, determine the force in the spring and the vertical motion of point G when a vertical downward 120-N force is applied (a) at point E, (b) at points E and F.
Fig. P10.5 and P10.6
(a)
Find the force in the spring and the vertical motion of point G when a vertical load of
Answer to Problem 10.6P
The force in the spring is
The vertical motion of point G is
Explanation of Solution
Given information:
The spring constant is
Calculation:
Show the free-body diagram of the spring assembly as in Figure 1.
Write the relation of the deflections at point G, H, F, E, D with C as follows;
The deflection
Assume the spring force Q is in tension.
Find the force in the spring Q using the relation.
Here, the spring constant is k.
Substitute
Use the virtual work principle:
Here,
Substitute 0 for C,
The spring force Q is in compression. The assumption is incorrect.
Therefore, the force in the spring is
Substitute –120 N for Q in Equation (1).
Find the vertical motion
Substitute –4 mm for
Therefore, the vertical motion of point G is
(b)
Find the force in the spring and the vertical motion of point G when a vertical load of 120-N force is applied at point E and F.
Answer to Problem 10.6P
The force in the spring is
The vertical motion of point G is
Explanation of Solution
Given information:
The spring constant is
Calculation:
Use the virtual work principle:
Here,
Substitute 0 for C,
The spring force Q is in compression. The assumption is incorrect.
Therefore, the force in the spring is
Substitute –300 N for Q in Equation (1).
Find the vertical motion
Substitute –10 mm for
Therefore, the vertical motion of point G is
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