An engineer uses a bolt to connect a joint. The force provided by the bolt F is a function of the external load P that it must bear. The bolt applies a force of 200 lb against an external load of 100 lb. The same bolt must apply a force of 400 lb against an external load of 600 lb. Find the joint constant C, and preload Fi (in lb), that satisfies the linear equation describing the force, F = CP + Fi.
F = P +
To find the joint constant C and preload Fi that satisfy the linear equation, we can use the given information.
We are given two scenarios:
Scenario 1:
F = 200 lb
P = 100 lb
Scenario 2:
F = 400 lb
P = 600 lb
Using the linear equation F = CP + Fi, we can substitute the values from the two scenarios to form a system of equations:
Equation 1:
200 = C * 100 + Fi
Equation 2:
400 = C * 600 + Fi
Now, we need to solve this system of equations to find the values of C and Fi that satisfy both equations.
To do this, we can use a method such as substitution or elimination. However, in this case, we will use the elimination method.
To eliminate the Fi term, we can subtract Equation 1 from Equation 2:
(400 - 200) = (C * 600 - C * 100) + (Fi - Fi)
Simplifying, we have:
200 = 500C
Now, we divide both sides by 500 to solve for C:
C = 0.4
We have found the value of C as 0.4.
To find the preload Fi, we can substitute this value of C into one of the original equations, such as Equation 1:
200 = 0.4 * 100 + Fi
Simplifying, we have:
200 = 40 + Fi
Subtracting 40 from both sides, we get:
Fi = 160
Therefore, the joint constant C is 0.4 and preload Fi is 160 lb.