28 N + T2 sin 12 = T1 sin 42
T2 cos 12 = T1 cos 42
T2 sin 12 + T3 sin 54 = W2
T2 cos 12 = T3 cos 54
Im solving for T1,2,3 and W2
I just cant seem to get the system to work
To solve the given system of equations, let's go step by step:
Equation 1: 28N + T2 sin 12 = T1 sin 42
Equation 2: T2 cos 12 = T1 cos 42
Equation 3: T2 sin 12 + T3 sin 54 = W2
Equation 4: T2 cos 12 = T3 cos 54
To solve for T1, T2, T3, and W2, we can use the method of substitution and elimination:
Step 1: Solve Equation 2 for T1
Rearrange Equation 2:
T1 = (T2 cos 12) / cos 42
Step 2: Substitute T1 in Equation 1 with the value obtained in Step 1
Substitute T1 = (T2 cos 12) / cos 42 into Equation 1:
28N + T2 sin 12 = ((T2 cos 12) / cos 42) sin 42
Step 3: Simplify Equation 1
Multiply through by cos 42 and simplify:
(28N cos 42) + (T2 sin 12 cos 42) = T2 cos 12
Step 4: Solve Equation 4 for T3
Rearrange Equation 4:
T3 = (T2 cos 12) / cos 54
Step 5: Substitute T3 in Equation 3 with the value obtained in Step 4
Substitute T3 = (T2 cos 12) / cos 54 into Equation 3:
T2 sin 12 + ((T2 cos 12) / cos 54) sin 54 = W2
At this point, we have two equations with two variables (T2 and W2). We can solve these equations simultaneously to find the values of T2 and W2.
Step 6: Simplify Equation 5
Multiply through by cos 54 and simplify:
(T2 sin 12 cos 54) + T2 cos 12 = W2 cos 54
Now, you have two equations:
Equation 1: (28N cos 42) + (T2 sin 12 cos 42) = T2 cos 12
Equation 2: (T2 sin 12 cos 54) + T2 cos 12 = W2 cos 54
These equations can be solved using various algebraic methods such as substitution, elimination, or matrices. You can choose the method you are most comfortable with or use a calculator or computer software to solve these equations numerically.
It is important to note that if you are experiencing difficulties in getting the system to work, it could be due to errors in calculations or a mistake in the equations themselves. Double-check the coefficients, signs, and units in each equation to ensure accuracy.