A hiker, who weighs 1120 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 3775 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 each end?

Question

A hiker, who weighs 1120 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 3775 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 each end?

Answer 1

Let F1 and F2 be the forces on the two ends of the bridge.

The sum of the forces in the y direction is 0:

F1 + F2 - 1120 - 3775 = 0

The sum of the torques about each support is zero:

1120*(L/5) + 3775*(L/2) - F2*L = 0
Dividing by L:

1120/5 + 3775/2 - F2 = 0

Solve for F2, then solve for F1

Answer 2

To determine the magnitude of the force that a concrete support exerts on the bridge at each end, we can use the concept of equilibrium. Since the bridge is uniform and at rest, the sum of the forces acting on it must be zero in both the horizontal and vertical directions.

Let's break down the problem step by step:

Step 1: Calculate the total weight of the bridge.
The weight of the bridge is given as 3775 N.

Step 2: Determine the weight of the hiker.
The weight of the hiker is given as 1120 N.

Step 3: Calculate the distance of the hiker from one end of the bridge.
The hiker is one-fifth (1/5) of the way along the bridge. Since the bridge is horizontal, the hiker's position does not affect the vertical forces acting on the bridge.

Step 4: Determine the total downward force on the bridge.
The total downward force on the bridge is the sum of the bridge's weight and the hiker's weight.
Total downward force = Weight of the bridge + Weight of the hiker

Step 5: Divide the total downward force by the number of supports.
Since there are two concrete supports, we need to divide the total downward force by 2 to find the magnitude of the force that each support exerts on the bridge.
Force exerted by each support = Total downward force / Number of supports

Let's plug in the values and calculate:

Total downward force = 3775 N + 1120 N = 4895 N
Force exerted by each support = 4895 N / 2 = 2447.5 N

Therefore, the magnitude of the force that each concrete support exerts on the bridge at each end is approximately 2447.5 N.