A BRIDGE IS CONSTRUCTED WITH LUMP OF WOOD 15M LONG ITS PIVOTED AT 2M FROM BOTH ENDS RESPECTIVELY, A THIN AND FAT MAN OF MASSES 30KG & 90KG RESPECTIVELY,STOOD AT POINT A & B,4.5M AND 10M,WHAT IS THE REACTION EXPERIENCED AT THE PIVOT THE BRIDGE
To find the reaction experienced at the pivot of the bridge, we need to consider the forces acting on the bridge.
Let's start by considering the forces acting on the thin man at Point A:
1. Weight of the thin man (30 kg): The weight of the thin man can be calculated by multiplying his mass (30 kg) by the acceleration due to gravity (9.8 m/s^2). Therefore, the weight of the thin man is 30 kg * 9.8 m/s^2 = 294 N.
Next, let's consider the forces acting on the fat man at Point B:
1. Weight of the fat man (90 kg): Similar to the thin man, the weight of the fat man can be calculated as 90 kg * 9.8 m/s^2 = 882 N.
Now, let's consider the reaction at the pivot of the bridge:
1. To balance the bridge, the sum of the moments about the pivot point must be zero. We can use the principle of moments to calculate the reaction.
2. The moment (torque) of the thin man can be calculated by multiplying the weight (294 N) by the distance from the pivot (4.5 m): 294 N * 4.5 m = 1323 Nm.
3. The moment of the fat man can be calculated by multiplying his weight (882 N) by the distance from the pivot (10 m): 882 N * 10 m = 8820 Nm.
4. Since the bridge is in equilibrium, the total sum of the moments on both sides of the pivot should be equal. Therefore, the reaction at the pivot can be calculated as the difference between the moments:
Reaction = Moment of fat man - Moment of thin man
= 8820 Nm - 1323 Nm
= 7497 Nm (or -7497 Nm, depending on the direction)
Hence, the reaction experienced at the pivot of the bridge is 7497 Nm (assuming it is in the upward direction).
Please note that the above calculation assumes a static scenario where both men are standing still. In reality, there might be additional forces and factors to consider, such as the distribution of weight across the bridge and the effect of any other loads or forces applied to the bridge.