To find the magnitude of the force that a concrete support exerts on the bridge, we need to analyze the forces acting on the bridge and apply the principles of equilibrium.
Let's start with the forces acting on the bridge:
1. The weight of the hiker (976 N) acts vertically downward.
2. The weight of the bridge itself (4350 N) also acts vertically downward.
3. The reaction forces from the concrete supports act upwards from each end of the bridge.
Now, let's break it down into two scenarios: one for each end of the bridge.
(a) At the near end:
Since the hiker is 1/3 of the way along the bridge, only 1/3 of the hiker's weight is acting on the near end. Therefore, the hiker's weight that acts on the near end is (1/3) * 976 N = 325.33 N.
To find the magnitude of the force that the concrete support exerts on the near end, we need to balance the forces vertically. At equilibrium, the sum of the vertical forces is zero.
So, the equation will be:
Reaction force at the near end - 325.33 N (hiker's weight) - 4350 N (bridge's weight) = 0
Simplifying the equation:
Reaction force at the near end = 325.33 N + 4350 N
Therefore, the magnitude of the force that the concrete support exerts on the near end is 325.33 N + 4350 N = 4675.33 N.
(b) At the far end:
Since the hiker is 1/3 of the way along the bridge, 2/3 of the hiker's weight is acting on the far end. Therefore, the hiker's weight that acts on the far end is (2/3) * 976 N = 650.67 N.
Applying the same equilibrium principle:
Reaction force at the far end - 650.67 N (hiker's weight) - 4350 N (bridge's weight) = 0
Simplifying the equation:
Reaction force at the far end = 650.67 N + 4350 N
Hence, the magnitude of the force that the concrete support exerts on the far end is 650.67 N + 4350 N = 5000.67 N.