Bridge Force Calculations for Hiker's Weight

[playboy2006]

A hiker, who weighs 696 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 4440 N, and rests on two concrete supports, one on each end. He stops 1/4 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?

 

[Maxwell]

1) This is the wrong section for homework problems.

2) What work have you done so far?

 

[quicknote]

I would approach this problem by first considering the forces acting on the bridge. The hiker's weight and the weight of the bridge itself are both downward forces, while the two concrete supports provide upward forces to balance the weight. We can use the principle of equilibrium, which states that the sum of all forces acting on an object must equal zero, to solve for the magnitude of the forces at each end of the bridge.

To start, we can calculate the total weight of the bridge and the hiker combined, which is 4440 N + 696 N = 5136 N. Since the hiker is stopped at 1/4 of the way along the bridge, we can assume that the weight is evenly distributed along the length of the bridge.

(a) To find the force exerted by the near end support, we can set up an equation using the principle of equilibrium:

ΣF = 0

Where ΣF represents the sum of all forces acting on the bridge. We can then rewrite this equation as:

Fsupport + Fhiker = Fbridge

Where Fsupport is the force exerted by the near end support, Fhiker is the weight of the hiker, and Fbridge is the total weight of the bridge and the hiker. Plugging in the values, we get:

Fsupport + 696 N = 5136 N

Solving for Fsupport, we get Fsupport = 4440 N. This means that the force exerted by the near end support is equal to the weight of the bridge itself, indicating that the support is carrying the entire weight of the bridge at this point.

(b) To find the force exerted by the far end support, we can use the same equation as above, but this time the distance between the support and the hiker is 3/4 of the length of the bridge. This means that the force exerted by the far end support is equal to 3/4 of the total weight of the bridge and the hiker, or (3/4)(5136 N) = 3852 N.

In conclusion, the magnitude of the force exerted by the near end support is 4440 N, while the magnitude of the force exerted by the far end support is 3852 N. These calculations show that the supports are effectively distributing the weight of the bridge and the hiker, ensuring that the bridge remains stable and safe for