Archive:In statics, the sum of the forces is equal to zero

2007-06-17T02:35:32Z

70.121.98.26:

Lesson:In Statics the Sum of the Forces is Equal to Zero

The term statics refers to an object or system in static equilibrium. The object or system is motionless because all of the forces balance to zero.

Newton's Second Law:

Σ<math>F = ma</math>

The sum of the forces is equal to the mass times the acceleration. The 2nd law tells us that if the object or system is motionless, the acceleration is equal to zero. Therefore the sum of the vector forces must be equal to zero.

Example: Consider a table with four legs and a 200kg object resting motionless in the center of the table.

Object 200
______________
| | Weight of table = 100kg
| |
| | What is the force acting up on each table leg?

Then the force upward on the legs is found by balancing these forces in the equation given by Newton's Law:

sum F=MA = 0 = - (200kg X 9.81 m/s2) - (100kg X 9.81 m/s2) + (Forceleg X 4)

Gravity is acting down on the 200kg object and the 100kg table.

Forceleg = ((200kg X 9.81 m/s2) + (100kg X 9.81 m/s2)) / 4

The units kg•m/s2 are equivalent to the units N/kg. Thus when multiplying through, the kilograms cancel out.

Forceleg = (1962 N + 981 N) / 4

Forceleg = 735.75 N

Notice that it is critical that a consisent sign convention is followed throughout an entire analysis effort. The sign convention is typically chosen in more complex problems to ease the total amount of algebra necessary to analyze the equations in the x, y, and z axis.

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[[Category:Statics]]

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Archive:In statics, the sum of the forces is equal to zero