a uniform beam 6.0m long and weighing 4kg rest support p and q place left and right 1.0m of beam of weight from each of the beam weight of mass 10kg and 8kg and are placed near p and q respectively on each of the beam. calculate the reaction of p and q

Solution

To calculate the reaction at supports P and Q, we need to consider the forces acting on the beam and use the principles of equilibrium.

Let's break down the problem into smaller steps:

Step 1: Determine the total weight of the beam:
The beam weighs 4 kg, which corresponds to a weight of approximately 4 x 9.8 N = 39.2 N.

Step 2: Calculate the total weight acting on support P:
On the left side of the beam, we have a weight of 10 kg. This corresponds to a weight of approximately 10 x 9.8 N = 98 N.
Additionally, we have the weight of the beam acting at the center, which we previously determined to be 39.2 N.
Therefore, the total weight acting on support P is 98 N + 39.2 N = 137.2 N.

Step 3: Calculate the total weight acting on support Q:
On the right side of the beam, we have a weight of 8 kg. This corresponds to a weight of approximately 8 x 9.8 N = 78.4 N.
Additionally, we have the weight of the beam acting at the center, which we previously determined to be 39.2 N.
Therefore, the total weight acting on support Q is 78.4 N + 39.2 N = 117.6 N.

Step 4: Calculate the reaction at support P:
The beam is in equilibrium, which means that the sum of the forces acting vertically on the beam must be zero.
The reaction at support P is equal in magnitude but opposite in direction to the total weight acting on support P.
Therefore, the reaction at support P is -137.2 N.

Step 5: Calculate the reaction at support Q:
Similarly, the reaction at support Q is equal in magnitude but opposite in direction to the total weight acting on support Q.
Therefore, the reaction at support Q is -117.6 N.

In summary:
- The reaction at support P is -137.2 N (pointing downwards).
- The reaction at support Q is -117.6 N (pointing downwards).