For Problem 3, calculate the tension force T in the cable [N]. For Problem 3, calculate the support reaction Ax [N]. For Problem 3, calculate the support reaction Ay [N].

Steps to Solve

1. Calculate the Weight of the Mass First, calculate the force due to the mass ( M ): $$ W = M \cdot g $$ where ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )). Substituting the values: $$ W = 75 , \text{kg} \cdot 9.81 , \text{m/s}^2 = 735.75 , \text{N} $$

2. Resolving Forces at the Pin Support Use static equilibrium conditions. The sum of vertical forces must equal zero: $$ \sum F_y = 0 \implies A_y + T \cdot \sin(\theta) - W = 0 $$ Where ( T ) is the tension in the cable and ( \theta ) can be determined from the geometry. The horizontal sum gives: $$ \sum F_x = 0 \implies A_x - T \cdot \cos(\theta) = 0 $$

3. Calculating the Angle ( \theta ) Determine the angle ( \theta ) using the geometry:

• The horizontal distance ( a = 0.6 , \text{m} ) and vertical distance ( 1.25a = 0.75 , \text{m} ). The tangent gives: $$ \tan(\theta) = \frac{1.25a}{a} = \frac{1.25}{1} $$ $$ \theta = \tan^{-1}(1.25) $$

4. Substituting ( T ) into Equations Now, substitute ( T ) from the tension equation back into the vertical and horizontal equilibrium equations:

• From the vertical equation, calculate ( A_y ): $$ A_y = W - T \cdot \sin(\theta) $$
• From the horizontal equation, calculate ( A_x ): $$ A_x = T \cdot \cos(\theta) $$

5. Calculating Tension and Reactions Solve for ( T ) using the previously calculated weight: Substituting values and solving for both reactions ( A_x ) and ( A_y ):

• Calculate ( A_y ) using the previously computed ( T ) and ( W ).
• Then calculate ( A_x ) using the ( T ) value determined.