A hiker who weighs 889 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 3690 N, and rests on two concrete supports 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?

what is L?

Sum moments about either end. I will do it from the far end.

weightbridge*1/2 L+ 4/5L*889-force*L=0

solve for force.

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.

First, let's consider the weight of the hiker. The weight of the hiker is given as 889 N. This force is acting vertically downward and exerts a downward force on the bridge.

Next, let's consider the weight of the bridge itself. The weight of the bridge is given as 3690 N. This force is acting vertically downward and is distributed evenly across the entire length of the bridge.

Since the hiker has stopped one-fifth of the way along the bridge, we know that four-fifths of the bridge is still on the near end of the bridge. Therefore, the portion of the bridge that is on the near end is (4/5) * 3690 N.

Now, let's calculate the total downward force on the near end of the bridge. This is the sum of the hiker's weight and the weight of the portion of the bridge on the near end.

Total downward force on the near end of the bridge = hiker's weight + weight of the portion of the bridge on the near end
= 889 N + (4/5) * 3690 N

Now, we can calculate the magnitude of the force that a concrete support exerts on the bridge at the near end. This force is equal in magnitude but opposite in direction to the total downward force on the near end of the bridge.

Magnitude of the force that a concrete support exerts on the near end of the bridge = Total downward force on the near end of the bridge

Therefore, to get the final answer, we substitute the values:

Magnitude of the force that a concrete support exerts on the bridge at the near end = 889 N + (4/5) * 3690 N