The 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 can use the given information about the experiment.
We are given two sets of values for F and L:
1) When F = 5.6, L = 8.0
2) When F = 4.4, L = 2.0
Let's use these values to form two equations:
Equation 1: 5.6 = a(8.0) + b
Equation 2: 4.4 = a(2.0) + b
We can solve these two equations simultaneously to find the values of "a" and "b".
First, let's rearrange Equation 1:
a(8.0) + b = 5.6
Now we can rearrange Equation 2:
a(2.0) + b = 4.4
We now have a system of linear equations. We can solve this system using various methods such as substitution or elimination. Here, we will use the method of elimination.
Multiply Equation 2 by 4:
4(a(2.0) + b) = 4(4.4)
8a + 4b = 17.6
Now, subtract Equation 1 from the above equation:
(8a + 4b) - (8a + b) = 17.6 - 5.6
7b = 12
b = 12/7
Substitute the value of b back into Equation 1:
a(8.0) + (12/7) = 5.6
8a = 5.6 - (12/7)
To simplify, let's convert 5.6 to a fraction over 7:
8a = (39/7) - (12/7)
8a = (39 - 12)/7
8a = 27/7
a = (27/7) * (1/8)
a = 27/56
Therefore, we have found the values of "a" and "b" to be:
a = 27/56
b = 12/7
To find the value of F when L = 6.5, we can use the equation:
F = aL + b
Substitute the values of "a" and "b" we found earlier:
F = (27/56)(6.5) + (12/7)
Now, simplify this expression:
F = (27/56)(13/2) + (12/7)
F = (27*13)/(56*2) + (12/7)
F = 351/112 + (24/7)
To add these fractions, we need a common denominator, which is 112:
F = (351 + 24*16)/(112*7)
F = (351 + 384)/(112*7)
F = 735/784
F ≈ 0.938
Therefore, when L = 6.5, the value of F is approximately 0.938.