A hiker, who weighs 811 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 3350 N, and rests on two concrete supports, one on each end. He stops 1/6 of the way along the bridge. What is the magnitude of the force that a concrete support exerts on the bridge (a) at the near end and (b) at the far end?

Question

A hiker, who weighs 811 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 3350 N, and rests on two concrete supports, one on each end. He stops 1/6 of the way along the bridge. What is the magnitude of the force that a concrete support exerts on the bridge (a) at the near end and (b) at the far end?

Answer 1

fnear+ffar=3350+811 N

now sum moments around any point, lets do it from the near end.
811*1/6-ffar*1=0
solve for ffar, then use the first equation for fnear

Answer 2

To determine the magnitude of the force that a concrete support exerts on the bridge, we can use the principle of equilibrium. In this case, the sum of the forces acting on the bridge in the vertical direction must be zero.

Let's start by calculating the weight of the hiker. The given weight of the hiker is 811 N, which acts downwards.

Now, let's calculate the weight of the bridge. The given weight of the bridge is 3350 N, which acts downwards.

Since the hiker stops 1/6 of the way along the bridge, we can assume that the bridge is 6 parts. So, the weight of each part of the bridge is 3350 N / 6 = 558.33 N.

To find the force exerted by the concrete supports, we can consider the forces acting on each end of the bridge.

(a) At the near end:
To find the force exerted by the concrete support at the near end, we need to consider the forces acting at this point.

There are two forces acting at the near end:
1. Weight of the hiker = 811 N, acting downwards.
2. Weight of the first 5 parts of the bridge = 558.33 N * 5 = 2791.65 N, acting downwards.

To find the force exerted by the concrete support at the near end, we need to add up these vertical forces that act downwards:
Force at the near end = 811 N + 2791.65 N = 3602.65 N (downwards).

(b) At the far end:
To find the force exerted by the concrete support at the far end, we need to consider the forces acting at this point.

There is only one force acting at the far end:
1. Weight of the last part of the bridge = 558.33 N, acting downwards.

Therefore, the force exerted by the concrete support at the far end is equal to the weight of the last part of the bridge, which is 558.33 N.

To summarize:
(a) The magnitude of the force that the concrete support exerts on the bridge at the near end is 3602.65 N (downwards).
(b) The magnitude of the force that the concrete support exerts on the bridge at the far end is 558.33 N (downwards).