The two conditions for equilibrium often result in a system of equations such as
F1 + F2 = 44.0 N
and
3.00F1 − 8.00F2 = 0.
(Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)
(a) Find F1.
N
(b) Find F2.
N
This is the oddest AP physics class I have ever eeen, I assure you, if this is "college" level, you are being mislead. This is Algebra II, systems of equations.
multipy the first equation by 8
add the equations
I get
11F1=8*44
solve for F1
then, in equation 2, solve for F2
(a) Find F1:
To solve for F1, we can use the second equation and express F2 in terms of F1:
3.00F1 - 8.00F2 = 0
Rearranging the equation:
8.00F2 = 3.00F1
Dividing both sides by 8.00:
F2 = (3.00/8.00)F1
Substituting this expression for F2 in the first equation:
F1 + (3.00/8.00)F1 = 44.0
Combining like terms:
(11.00/8.00)F1 = 44.0
Dividing both sides by (11.00/8.00):
F1 = 44.0 * (8.00/11.00)
Calculating F1:
F1 ≈ 32.00 N
Therefore, F1 ≈ 32.00 N.
(b) Find F2:
Substituting the value of F1 in the second equation:
3.00(32.00) - 8.00F2 = 0
Multiplying 3.00 by 32.00:
96.00 - 8.00F2 = 0
Rearranging the equation:
-8.00F2 = -96.00
Dividing both sides by -8.00:
F2 = 12.00
Therefore, F2 = 12.00 N.
Final answers:
(a) F1 ≈ 32.00 N
(b) F2 = 12.00 N
To solve the system of equations for F1 and F2, you can use the method of substitution or elimination. Let's solve it using the method of substitution.
Given:
F1 + F2 = 44.0 N ...(1)
3.00F1 − 8.00F2 = 0 ...(2)
(a) To find F1, we can solve for F1 in equation (1) and substitute it into equation (2).
From equation (1), we have:
F1 = 44.0 N - F2
Substituting F1 in equation (2) with 44.0 N - F2:
3.00(44.0 N - F2) - 8.00F2 = 0
Expanding and simplifying the equation:
132.0 N - 3.00F2 - 8.00F2 = 0
132.0 N - 11.00F2 = 0
Rearranging the equation:
11.00F2 = 132.0 N
Dividing both sides by 11.00:
F2 = 132.0 N / 11.00
F2 = 12.0 N
(b) To find F2, substitute the value of F2 (12.0 N) into equation (1):
F1 + 12.0 N = 44.0 N
Subtracting 12.0 N from both sides:
F1 = 44.0 N - 12.0 N
F1 = 32.0 N
Therefore:
(a) F1 = 32.0 N
(b) F2 = 12.0 N
To find the values of F1 and F2 in the given system of equations, we can solve them using the method of substitution or elimination.
(a) Method of Substitution:
Start with the first equation: F1 + F2 = 44.0 N.
Rearrange the equation to solve for F1: F1 = 44.0 N - F2.
Now substitute this expression for F1 into the second equation: 3.00F1 - 8.00F2 = 0.
Replace F1 with the expression we found: 3.00(44.0 N - F2) - 8.00F2 = 0.
Expand and simplify the equation:
132.0 N - 3.00F2 - 8.00F2 = 0.
Combine like terms: -11.00F2 = -132.0 N.
Divide both sides by -11.00: F2 = 12.0 N.
(b) Now that we have found the value of F2, we can substitute it back into either of the original equations to find F1.
Using the first equation: F1 + 12.0 N = 44.0 N.
Subtract 12.0 N from both sides: F1 = 32.0 N.
So the values of F1 and F2 are:
(a) F1 = 32.0 N.
(b) F2 = 12.0 N.