he law connecting friction F and load L for an experiment is of the form F =aL+b, where a and b are constants. When F =5.6, L=8.0 and when F =4.4, L=2.0. Find the values of “a” and “b “and the value of F when L=6.5.
To find the values of "a" and "b" in the equation F = aL + b, we need to use the given data points and solve a system of linear equations.
Let's use the first set of data points: F = 5.6 when L = 8.0.
Plugging these values into the equation, we get:
5.6 = a(8.0) + b ---(Equation 1)
Now, let's use the second set of data points: F = 4.4 when L = 2.0.
Plugging these values into the equation, we get:
4.4 = a(2.0) + b ---(Equation 2)
We have a system of two equations with two unknowns (a and b). Now, we need to solve this system.
First, we will solve Equation 1 for b:
b = 5.6 - a(8.0)
Next, substitute this expression for b in Equation 2:
4.4 = a(2.0) + (5.6 - a(8.0))
Now, let's simplify and solve for a:
4.4 = 2a + 5.6 - 8a
4.4 = -6a + 5.6
-6a = 4.4 - 5.6
-6a = -1.2
a = (-1.2)/(-6)
a = 0.2
Now that we have found the value of "a" as 0.2, we can substitute it back into either Equation 1 or Equation 2 to find the value of "b."
Using Equation 1:
b = 5.6 - (0.2)(8.0)
b = 5.6 - 1.6
b = 4.0
So, the values of "a" and "b" are 0.2 and 4.0, respectively.
To find the value of F when L = 6.5, we can substitute the values of "a," "b," and "L" into the equation F = aL + b:
F = (0.2)(6.5) + 4.0
F = 1.3 + 4.0
F = 5.3
Therefore, when L = 6.5, F = 5.3.