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 need to consider the forces acting on the bridge.

The weight of the hiker (W_hiker) is acting vertically downward with a magnitude of 990 N. The weight of the bridge (W_bridge) is also acting vertically downward with a magnitude of 3550 N. Since the hiker is one-fifth of the way along the bridge, his weight is distributed along that portion of the bridge.

Let's denote the length of the entire bridge as L. Since the hiker is one-fifth of the way along the bridge, his distance from the near end of the bridge is (1/5) * L. Therefore, the length of the bridge from the near end to where the hiker is standing is (4/5) * L.

Now, let's consider the forces acting on the bridge. At the near end of the bridge, there are two forces: the force exerted by the concrete support (F_support) and the weight of the bridge (W_bridge).

According to Newton's third law, the force exerted by the concrete support on the bridge is equal in magnitude and opposite in direction to the force exerted by the bridge on the concrete support. So, we have F_support = -W_bridge.

To find the magnitude of the force exerted by the concrete support, we first need to find the weight of the bridge that is resting on the near end. Since the hiker is one-fifth of the way along the bridge, the weight of the bridge resting on the near end is (4/5) * W_bridge.

So, the magnitude of the force exerted by the concrete support at the near end is:

F_support = -[(4/5) * W_bridge]

Substituting the value of W_bridge (3550 N), we get:

F_support = -[(4/5) * 3550]

F_support = -2840 N

Note that the negative sign indicates that the force exerted by the concrete support is in the opposite direction as the weight of the bridge. So, the magnitude of the force exerted by the concrete support at the near end is 2840 N.