Final answer:
To solve the system of equations f1 + f2 = 44.0 N and 3.00f1 - 2.00f2 = 0, we can use the method of substitution. By substituting an expression for f1 in terms of f2 into the second equation, we can solve for f2. Substituting this value of f2 back into the first equation allows us to solve for f1. The values of f1 and f2 are 17.6 N and 26.4 N, respectively.
Step-by-step explanation:
The two conditions for equilibrium are that the net external force on the system must be zero and the net torque must also be zero. In this case, we have the following system of equations:
f1 + f2 = 44.0 N (Equation 1)
3.00f1 - 2.00f2 = 0 (Equation 2)
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From Equation 1, we can express f1 in terms of f2: f1 = 44.0 - f2
Substituting this expression for f1 into Equation 2:
3.00(44.0 - f2) - 2.00f2 = 0
Simplifying the equation:
132.0 - 3.00f2 - 2.00f2 = 0
Combining like terms:
132.0 - 5.00f2 = 0
Adding 5.00f2 to both sides:
132.0 = 5.00f2
Dividing both sides by 5.00:
f2 = 26.4 N
Substituting this value of f2 back into Equation 1:
f1 + 26.4 = 44.0
Subtracting 26.4 from both sides:
f1 = 17.6 N
Therefore, the values of f1 and f2 are 17.6 N and 26.4 N, respectively.