statics refers to the bodies in equilibrium

Statics refers to the bodies in equilibrium. Equilibrium deals with the absence of a net force.

First Condition of Static Equilibrium: If the sum of all forces acting concurrently on a body at rest is equal to zero, then the body must be in: Translational Equilibrium Mathematically:

ΣFup = ΣFdown

Second Condition of Static Equilibrium: If the sum of the clockwise torques equals the sums of the counterclockwise torques about a point. This is called: Rotational Equilibrium Mathematically: Σtcw = Σtccw

The net torque = 0:

The net force = 0:

A system is in static equilibrium if:

This means that the system is not accelerating and its rotation (if any) is constant.

A bridge is a classic example of a system in static equilibrium. The bridge undergoes neither translational nor rotational motion!

¡  A torque is an action that causes objects to rotate

¡  Torque is not the same thing as force

¡  For rotational motion, the torque is what is most directly related to the motion, not the force

¡  Torque is created when the line of action of a force does not pass through the center of rotation.

¡  The line of action is an imaginary line that follows the direction of a force and passes though its point of application.

¡  To get the maximum torque, the force should be applied in a direction that creates the greatest lever or torque arm.

¡  The torque arm is the perpendicular distance between the force and the center of rotation or fulcrum

The greater the distance from the axis to the point where we apply the force, the greater the torque. Maximum torque occurs when the direction of the applied force is perpendicular to a line drawn between the axis and the point where the force is applied. When the line and the force are in the same direction, so that the force acts directly toward or away from the axis of rotation, there is no torque.

•  t = torque

•  F = force (N)

•  l = torque arm or lever arm (m)

t = F x l

Pivot Point, Fulcrum or Axis of Rotation: The point around which an object is free to rotate.

Torque is measured in: •  Newton-Meters (N·m) •  Foot-Pounds (ft·lbs)

All static equilibrium problems are solved the same way: 1.  Find all forces (free body diagram) 2.  Apply translational equilibrium formula:

•  ΣFup = ΣFdown

3.  Apply rotational equilibrium formula: •  Σtcw = Σtccw

4.  Choose a fulcrum or pivot point 5.  Solve for unknown variable

NOTE: Step 2 and 3 can be changed and possibly not needed

It is generally simpler to choose the pivot (fulcrum) at the point of application of the force for which you have the least information

Example #1 A force of 50 N is applied to a wrench that is 30 cm long. Calculate the torque if the force is applied perpendicular to the wrench.

t = 15 N·m

Example #2 What are the forces (FA, FB) holding the uniform bridge up at either end?

FA = 850 N FB = 400 N

Example #3 A boy and his cat sit on a uniform seesaw. The cat has a mass of 4 kg and sits 2 m from the center of rotation (fulcrum). If the boy has a mass of 50 kg, where should he sit from the fulcrum so that the see-saw will balance?

Lb = 0.16 m from the fulcrum

Example #4: What force is needed in both the left hand (FL) and the right hand (FR) to support a weight of the pole for the situation shown in figure below? The pole is uniform and has a mass of 5.00 kg. The hands are 0.900 m apart, and the COG of the pole is 0.600 m from the left hand.

FR = 32.7 N FL = 81.75 N

Work Problem #1 A 5.8 kg uniform ladder, 1.80 meters in length, rests on two sawhorses. Sawhorse “A” (FA) is 0.60 meters from the left end of the ladder, and sawhorse “B” (FB) is 0.15 meters from the right end of the ladder. What force does each sawhorse exert on the ladder? (FA = 40.64 N; FB = 16.26 N)