A hiker who weighs 834N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 3520N, 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?

b). What is the magnitude of the force at the far 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.

Let's break it down step by step:

Step 1: Calculate the weight of the bridge
The weight of the bridge is given as 3520N.

Step 2: Calculate the weight of the hiker
The weight of the hiker is given as 834N.

Step 3: Calculate the total weight supported by the bridge
The total weight supported by the bridge is the sum of the weight of the bridge and the weight of the hiker:
Total weight = weight of bridge + weight of hiker = 3520N + 834N = 4354N.

Step 4: Determine the distance of the hiker from the near end of the bridge
The hiker is stopped one-fifth of the way along the bridge. Since the bridge is uniform, dividing it into fifths means the hiker is 1/5 * length of the bridge away from the near end.

Step 5: Calculate the forces
Since the bridge is in equilibrium, the force exerted by the concrete support at the near end must balance the total weight supported by the bridge.

Let's call the magnitude of the force at the near end F_near and the magnitude of the force at the far end F_far.

Forces acting at the near end:
- Force exerted by the concrete support at the near end (F_near)
- Force due to the weight of the bridge (3520N)
Force equation at the near end:
F_near + 3520N = 4354N.

Forces acting at the far end:
- Force exerted by the concrete support at the far end (F_far)
- Force due to the weight of the bridge (3520N)
Force equation at the far end:
F_far + 3520N = 4354N.

Step 6: Solve the force equations
Solving the force equations from Step 5, we get:
F_near + 3520N = 4354N.
F_far + 3520N = 4354N.

Subtracting 3520N from both sides of each equation gives us:
F_near = 4354N - 3520N = 834N.
F_far = 4354N - 3520N = 834N.

Therefore, the magnitude of the force that a concrete support exerts on the bridge at the near end is 834N, and the magnitude of the force at the far end is also 834N.