A uniform beam 6m long and weighing 4kg rest on support p and q placed left and right 1m from each end of the beam. Weight of mass 10kg and 8kg are placed near p and q respectively. On ecah end of the beam. Calculate the reation at p and q
125N, 95N
pls answer the above question
To calculate the reaction at supports P and Q, we need to consider the forces acting on the beam. Here's how you can approach the problem:
1. Calculate the total weight of the beam: The beam weighs 4 kg. Weight = mass × acceleration due to gravity. Assuming the acceleration due to gravity is 9.8 m/s^2, the weight of the beam is 4 kg × 9.8 m/s^2 = 39.2 N.
2. Calculate the total weight of the masses: The mass near support P weighs 10 kg, and the mass near support Q weighs 8 kg. Using the same acceleration due to gravity of 9.8 m/s^2, the weight of the mass near P is 10 kg × 9.8 m/s^2 = 98 N, and the weight of the mass near Q is 8 kg × 9.8 m/s^2 = 78.4 N.
3. Calculate the distance of the beam center of gravity (CG) from supports P and Q: The beam is 6 m long, and support P is 1 m from the left end, while support Q is 1 m from the right end. CG = L/2, where L is the length of the beam. Therefore, the CG of the beam is at 6 m/2 = 3 m from either support.
4. Calculate the moment about support P: The moment is the product of the force and the distance from the pivot. The moment about support P is the sum of the moments of the beam and the mass near Q. It can be calculated as follows:
Moment about P = (Weight of the beam × Distance from P) + (Weight of the mass near Q × Distance from P to the CG of the beam)
= (39.2 N × 1 m) + (78.4 N × 2 m)
= 39.2 N + 156.8 N
= 196 N.
5. Calculate the moment about support Q: Similar to the previous step, the moment about support Q is the sum of the moments of the beam and the mass near P. It can be calculated as follows:
Moment about Q = (Weight of the beam × Distance from Q) + (Weight of the mass near P × Distance from Q to the CG of the beam)
= (39.2 N × 1 m) + (98 N × 2 m)
= 39.2 N + 196 N
= 235.2 N.
6. Use the principle of moments: According to the principle of moments, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point for the object to be in equilibrium. Since the beam is in equilibrium, the sum of the clockwise moments about P must be equal to the sum of the anticlockwise moments about P, and similarly for Q.
7. Calculate the reactions at P and Q: The sum of the clockwise moments about P is calculated as -196 N (since it is in the opposite direction), and the sum of the anticlockwise moments about P is zero (as there are no other forces acting on that side). The reaction at support Q can be calculated in a similar manner, using the moments around Q.
Therefore, the reaction at support P is +196 N (upwards), and the reaction at support Q is -235.2 N (downwards).