Short Answer 
To analyze the problem of a 19.5 kg block suspended by two cables at angles of 17¬¨‚àû and 27¬¨‚àû, one must identify the forces, apply Newton’s second law, and set up equations for vertical and horizontal forces. Solving these equations yields tensions of T1 = 22.6 N and T2 = 16.6 N in the cables for equilibrium.
Step 1: Analyze the Problem
Begin by identifying the components of the problem. We have a block with a mass of 19.5 kg suspended by two cables. The cables are positioned at angles of 17¬¨‚àû and 27¬¨‚àû. It’s essential to understand the forces acting on the block, which include the gravitational force and the tensions in the cables.
Step 2: Apply Newton’s Second Law
Using Newton’s second law, set up equations for the vertical and horizontal forces. You will need to calculate the gravitational force acting on the block, which is the weight ((mg)). Then, express the tensions (T1 and T2) in terms of their respective angles. This gives you a system of equations to work with:
- Weight (W) = mg = 19.5 kg * 9.81 m/s²
- Vertical equilibrium: T1*sin(17°) + T2*sin(27°) = W
- Horizontal equilibrium: T1*cos(17°) = T2*cos(27°)
Step 3: Solve the System of Equations
With the equations established, solve for the unknown tensions T1 and T2. This can be done using substitution or elimination methods. After calculation, you will find:
- T1 = 22.6 N
- T2 = 16.6 N
The values represent the tensions in the cables required to keep the block in equilibrium.