Equilibrium and Free-body Diagrams

Source: Ketron Mitchell-Wynne, PhD, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA

Equilibrium is a special case in mechanics that is very important in everyday life. It occurs when the net force and the net torque on an object or system are both zero. This means that both the linear and angular accelerations are zero. Thus, the object is at rest, or its center of mass is moving at a constant velocity. However, this does not mean that no forces are acting on the objects within the system. In fact, there are very few scenarios on Earth in which no forces are acting upon any given object. If a person walks across a bridge, they exert a downward force on the bridge proportional to their mass, and the bridge exerts an equal and opposite upward force on the person. In some cases, the bridge may flex in response to the downward force of the person, and in extreme cases, when the forces are great enough, the bridge may become seriously deformed or may even fracture. The study of this flexing of objects in equilibrium is called elasticity and becomes extremely important when engineers are designing buildings and structures that we use every day.

1. Observe equilibrium in a static system and verify that the sum of the forces and torques is zero. Confirm the spring constants k used in the system.

Obtain a meter stick, two spring scales with known spring constants, two stands to suspend the springs from, two weights of different masses, and a mechanism to suspend the weights from the meter stick.
Secure the two stands to the table, 1 m apart.
Attach the springs to the stands.
Attach the spring to each end of the me

The representative results for the experiment can be found in Table 1. The force exerted on the two springs by the hanging mass are denoted by their locations: left and right, denoted by subscripts L and R. Since there are two unknowns in this experiment, F_Land F_R, two equations are required to solve for them. Thus, Equations 1 and <

All bridges are under some amount of stress, from both their own weight and the weight of the loads moving across. Suspension bridges, like the Golden Gate, are a complex system of objects under very heavy forces and in equilibrium. The cables that hold the bridge up are elastic, and their elasticity was considered when the structural engineers designed the bridge. Similarly, skyscrapers have a complex system of steel beams under tremendous forces, which altogether compose a rigid system in static equilibrium. Elasticity

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