A hiker, who weighs 990 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 3550 N, and rests on two concrete supports, one at each end. He stops one-fifth of the way along the bridge. What is the magnitude of the force that a concrete support exerts on the bridge at the near end?
To find the magnitude of the force that a concrete support exerts on the bridge at the near end, we can consider the forces acting on the bridge.
The weight of the hiker, acting vertically downward, is 990 N. The weight of the bridge, acting vertically downward, is 3550 N. Since the bridge is uniform, we can assume that the weight is evenly distributed along the length of the bridge.
Since the hiker is one-fifth of the way along the bridge, the length of the bridge from the near end to the hiker is four-fifths of the total length.
To find the force at the near end of the bridge, we need to consider the upward force needed to balance the downward forces of the hiker and the bridge. This upward force is exerted by the concrete support.
Using the principle of equilibrium, the sum of the upward forces should equal the sum of the downward forces.
The hiker's weight is 990 N, and since the hiker is one-fifth of the way along the bridge, the length of the bridge from the hiker to the near end is four-fifths of the total length. Hence, the force exerted by the hiker on the bridge at the near end is (990 N) * (4/5) = 792 N.
The weight of the bridge is 3550 N, which is distributed evenly along the length of the bridge. Therefore, the force exerted by the bridge on the bridge at the near end is (3550 N) * (4/5) = 2840 N.
To find the force exerted by the concrete support at the near end, we need to sum the forces exerted by the hiker and the bridge at the near end. Hence, the magnitude of the force that the concrete support exerts on the bridge at the near end is 792 N + 2840 N = 3632 N.