Exercise 6: The uniform beam has a mass of 50 Kg per meter of length. Compute the reactions at the support \( \mathbf{O} \).

To compute the reactions at support \( \mathbf{O} \) for a uniform beam, you first need to consider its weight. The beam has a mass of 50 kg per meter, which means that if the beam's length is \( L \), the weight \( W \) can be calculated as \( W = 50 \, \text{kg/m} \times L \times g \), where \( g \approx 9.81 \, \text{m/s}^2 \). The total weight acts at the center of gravity, which for a uniform beam is at its midpoint. Summing moments around point \( O \) and considering the equilibrium of forces will help you find the reaction forces at this support. By setting the sum of vertical forces equal to zero and considering the moments, you can solve for these reactions. Now, remember to check that your units are consistent and that you've accounted for all forces acting on the beam. A common mistake is neglecting the weight or improperly calculating distances when summing moments. Always double-check your assumptions about support reactions!