A uniform bar AB of weight W = 25 N is supported by two springs, as shown in the figure. The spring on the left has a stiffness k[= 300 N/m and natural length Lt=250 mm. The corresponding quantities for the spring on the right are k2= 400 N/m and L^ = 200 mm. The distance between the springs is L = 350 mm, and the spring on the right is suspended from a support that is a distance it = SO mm below the point of support for the spring on the left. Neglect the weight of the springs.
(a) At what distance x from the left-hand spring (figure part a) should a load P = 18 N be placed in order to bring the bar to a horizontal position? (b) If P is now removed, what new value of k{is required so that the bar (figure part a) will hang in a horizontal position underweight If?
(c) If P is removed and kt= 300 N/m. what distance b should spring ktbe moved to the right so that the bar (figure part a) will hang in a horizontal position under weight II"?
(d) If the spring on the left is now replaced by two springs in series (kt= 300 N/m, kt) with overall natural length Lt= 250 mm (see figure part b). what value of k; is required so that the bar will hang in a horizontal position under weight IF?
(a)
Location of load
Answer to Problem 2.2.16P
Location of load
Explanation of Solution
Given:
Weight,
Spring stiffness on left and right,
Natural lengths of both springs,
Distance between the springs,
Load,
Distance from support,
We have to use statics to get forces in both springs.
Now, we use constraint equation to define horizontal position, then solve for location
We are required to substitute expressions for
(b)
New value of spring constant
Answer to Problem 2.2.16P
New value of spring constant
Explanation of Solution
Given:
Weight,
Spring stiffness on left and right,
Natural lengths of both springs,
Distance between the springs,
Load,
Distance from support,
New value of spring constant
Now,
Since,
Same constant equation as above but now:
Now, solve for
(c)
Distance moved by spring
Answer to Problem 2.2.16P
Distance moved by spring
Explanation of Solution
Given:
New position for
Weight,
Spring stiffness on left and right,
Natural lengths of both springs.
Distance between the springs,
Load,
Distance from support,
Use
But relocate spring,
So, that bar ends up in horizontal position underweight
Statics are as follows:
Now, we have the constraint equation − substitute above expression for
Use the following data:
Spring stiffness on left and right.
Natural lengths of both springs:
Distance between the springs.
By substituting
(d)
Value of
Answer to Problem 2.2.16P
The required value is,
Explanation of Solution
Given:
Weight,
Spring stiffness on left and right,
Natural lengths of both springs,
Distance between the springs:
Load,
Distance from support,
Value of
New constraint equation is as follows:
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Mechanics of Materials - Text Only (Looseleaf)
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