1. Solving Simultaneous Equations in Mathcad

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3. Σ 𝐹 𝑥 =− 𝐹 𝐴 ∙𝑐𝑜𝑠 32° + 𝐹 𝑐 ∙𝑐𝑜𝑠 10° =0 Two equations and two unknowns
Class Problem: Uncle Fred, who weighs 200 lbs., is trying out his new zip line. Unfortunately, the bearings in his homemade zip line lock up, causing him to come to rest as shown. Determine the tension in the zip line on each side of the pulley. NOTE: The tension on each side of a frictionless pulley is ALWAYS equal, and if the pulley was frictionless, Uncle Fred would come to rest when the angles in front of him and behind him became equal. However, this pulley is NOT frictionless.
Solution:
Force A
𝐹 𝐴𝑥 =− 𝐹 𝐴 ∙𝑐𝑜𝑠 32°
𝐹 𝐴𝑦 = 𝐹 𝐴 ∙𝑠𝑖𝑛 32° A
32°
10°
𝐹 𝐴
𝐹 𝐶
𝑊𝑒𝑖𝑔ℎ𝑡=200𝑙𝑏𝑠 C B
Force C
𝐹 𝐶𝑥 = 𝐹 𝑐 ∙𝑐𝑜𝑠 10°
𝐹 𝐶𝑦 = 𝐹 𝑐 ∙𝑠𝑖𝑛 10°
Force W (weight)
𝑊 𝑥 =0
𝑊 𝑦 =−200𝑙𝑏
Σ 𝐹 𝑥 =− 𝐹 𝐴 ∙𝑐𝑜𝑠 32° + 𝐹 𝑐 ∙𝑐𝑜𝑠 10° =0
Two equations and two unknowns
Σ 𝐹 𝑦 = 𝐹 𝐴 ∙𝑠𝑖𝑛 32° + 𝐹 𝑐 ∙𝑠𝑖𝑛 10° −200𝑙𝑏=0

4. Solving Simultaneous Equations in Mathcad
Set up your sheet using proper formatting
Enter all known variables
Insert the Solve Block
Math Tab > Solve Block
Three sections of the Solve Block:
Guess Values: Enter initial guess values for the unknowns to provide a starting point which allows the algorithm to converge toward a solution
Constraints: Enter the equations, using <ctrl> =
Solver: Solves the simultaneous equations
Be sure to assign a new name to the unknown variables in the column matrix
Press <shift> :
Type find and then enter the names of the variables defined in “constraints” in parentheses
Press =
Refer to the sample worksheet on the downloads page for more tips