A hiker, who weighs 985 N, is strolling through the woods...

A hiker, who weighs $985 \mathrm{N}$, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs $3610 \mathrm{N}$, 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 (a) at the near end and (b) at the far end?

Key Concepts

Statics

Statics is the branch of mechanics that deals with analyzing forces and moments on bodies at rest. In problems like the bridge scenario, the principles of statics are used to ensure that both the sum of forces and the sum of moments (torques) acting on the system are zero, which is necessary for equilibrium.

Force Equilibrium

Force equilibrium refers to the condition where all the forces acting on a system balance each other out, such that the net force is zero. In the context of the bridge problem, the total downward forces due to the weights of the bridge and the hiker are exactly counteracted by the upward reaction forces from the supports.

Torque and Rotational Equilibrium

Torque (or moment) is a measure of the tendency of a force to cause rotation about an axis. Rotational equilibrium means that the sum of all torques acting on a body is zero. In the bridge problem, taking moments about a selected pivot point allows us to determine the individual support forces by ensuring that clockwise and counterclockwise torques cancel.

Center of Mass

The center of mass is the point in a body or system where the mass is evenly distributed or can be considered to act. For a uniform bridge, the weight can be assumed to act at its midpoint, which simplifies the analysis by providing a single point where the gravitational force is concentrated.

Distributed Load

A distributed load is one that is spread out along the length or area of a structure rather than concentrated at one point. In this problem, the bridge’s weight is uniformly distributed, meaning it can be replaced by an equivalent point load acting at the center of mass, which aids in the calculation of moments.

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