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.
I would sub in the first values for F and L to get an equation with a and b
then sub in the second set to get another eqution in a and b
Now that you have two equations in a and b, solve for a and b.
Now you have the actual equation, sub in L = 6.5
My answers for that question
Well, it seems like you're looking for some mathematical answers! Let's put on our math hats and figure this out.
We're given two sets of values: F = 5.6 when L = 8.0, and F = 4.4 when L = 2.0. We can use these to find the values of "a" and "b" in the equation F = aL + b.
Using the first set of values, we can substitute them into the equation: 5.6 = 8a + b.
Similarly, with the second set of values: 4.4 = 2a + b.
Now we have a system of two equations with two variables. Let's solve it using some clown math magic.
Subtracting the second equation from the first, we get:
5.6 - 4.4 = 8a + b - (2a + b).
Simplifying this gives us:
1.2 = 6a.
Dividing both sides by 6, we find:
a = 0.2.
Plugging this value of a back into the first equation and solving for b:
5.6 = 8 * 0.2 + b,
5.6 = 1.6 + b,
b = 5.6 - 1.6,
b = 4.
So we have found the values of a and b to be a = 0.2 and b = 4.
Now, let's get to the final part of your question. When L = 6.5, we can plug it into our equation F = aL + b:
F = 0.2 * 6.5 + 4,
F = 1.3 + 4,
F ≈ 5.3.
So, when L = 6.5, F is approximately 5.3.
Remember, these values might not be exact, but I hope the math and my clowning abilities were still enjoyable!
To find the values of "a" and "b," we can use the information given when F = 5.6 and L = 8.0, and when F = 4.4 and L = 2.0.
Let's start with the first set of values: F = 5.6 and L = 8.0.
Substituting these values into the equation F = aL + b, we get:
5.6 = a(8.0) + b
Now, let's use the second set of values: F = 4.4 and L = 2.0.
Substituting these values into the equation, we get:
4.4 = a(2.0) + b
Now we have a system of two equations with two unknowns:
Eq1: 5.6 = a(8.0) + b
Eq2: 4.4 = a(2.0) + b
We can solve this system of equations simultaneously. Subtracting Eq2 from Eq1 will eliminate the term "b," allowing us to solve for "a."
(5.6 - 4.4) = (a(8.0) + b) - (a(2.0) + b)
1.2 = 8a - 2a
1.2 = 6a
Dividing both sides by 6, we find:
a = 1.2 / 6
a = 0.2
Now that we have the value of "a," we can substitute it back into either Eq1 or Eq2 to solve for "b."
Let's use Eq1:
5.6 = a(8.0) + b
5.6 = 0.2(8.0) + b
5.6 = 1.6 + b
Subtracting 1.6 from both sides, we get:
5.6 - 1.6 = b
4.0 = b
Therefore, the values of "a" and "b" are: a = 0.2 and b = 4.0.
Now that we have the values of "a" and "b," we can find the value of F when L = 6.5.
Using the formula F = aL + b:
F = 0.2(6.5) + 4.0
F = 1.3 + 4.0
F = 5.3
Therefore, when L = 6.5, the value of F is 5.3.