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CE 201 - Statics

CE 201 - Statics. Lecture 7. EQUILIBRIUM OF A PARTICLE. CONDITION FOR THE EQUILIBRIUM OF A PARTICLE A particle is in EQUILIBRIUM if: it is at rest, OR it is moving with constant velocity

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CE 201 - Statics

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  1. CE 201 - Statics Lecture 7

  2. EQUILIBRIUM OF A PARTICLE CONDITION FOR THE EQUILIBRIUM OF A PARTICLE A particle is in EQUILIBRIUM if: • it is at rest, OR • it is moving with constant velocity The term "EQUILIBRIUM" is often used to describe a particle at rest. For a particle to be in EQUILIBRIUM, Newton's First Law of Motion must be satisfied.

  3. Newton's First Law of Motion "IF THE RESULTANT FORCE ACTING ON A PARTICLE IS ZERO, THEN THE PARTICLE IS IN EQUILIBRIUM".  F = 0

  4. Newton's Second Law of Motion F = m × a Applying the condition for equilibrium  F = m × a then, m × a = 0 since m ≠ o then, a = 0 this means that the particle acceleration is equal to zero, therefore the particle is moving at constant velocity.

  5. THE FREE-BODY DIAGRAM To apply the equilibrium equation ( F = 0), all known and unknown forces must be included in the equation. The equilibrium equation will best be applied when a free-body diagram of the particle is drawn. What is a free-body diagram?

  6. F = 50 N 30 F = 50 N 30 R W Example Suppose that we have a ball supported on a surface with force F is applied. How can we draw a free-body diagram of the ball? • Isolate the ball from all surroundings • Indicate all known and unknown forces acting on the ball.

  7. F = 50 N 30 F = 50 N 30 R W In this case, we have the following forces acting on the particle: F = 50 N Ball weight, W = ? Surface reaction, R = ?

  8. F F   R1 R2 W Example Draw a free-body diagram of the following system: Tips • Label known forces: should be labeled with their magnitude and direction • Label unknown forces: should be labeled using letters • Assume +ve magnitude of unknown forces. If magnitude of an unknown force was obtained –ve, then the direction of the force is opposite to the direction assumed. • Apply equilibrium equation

  9. Connections Two types of connections will be discussed: • Springs • Cables and Pulleys

  10. Springs If a spring is subjected to a force, the length of the spring will change in direct proportion to the force acting on it (if it is a linear elastic spring).

  11. L0 s (-ve) L -F +F L0 s (+ve) L Example In this case, the following equation can be used: F = k  s F = acting force k = spring constant or stiffness s = deformed distance measured from its unloaded position (elongated or compressed) If ( s ) is +ve, then ( F ) pulls on the spring, while if ( s ) is –ve, then ( F ) pushes on the spring. s = L – L0

  12. T T Cables and Pulleys • All cables are assumed to have negligible weight and can not be stretched • Cables can support only tension or pulling forces

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