Physics Notes Ch 9

Statics Statics – The study of forces in equilibrium. The net force and the net torque on an object (or on a system) are zero. The object is either at rest or its center of mass is moving at constant velocity.

Equilibrium  F x = 0  F y = 0  F z = 0 Any force acting in the negative x, y or z direction will have a negative sign. This is the first condition for equilibrium.

Torque (Chapter 8, section 4) Torque is equal to the product of force times the moment arm.  = r  F  (Greek lowercase letter tau) is the symbol for torque. Moment arm (r  ) is the perpendicular distance from the axis of rotation to the line along which the force acts. F is any force. May also be written as:  = rF 

Equilibrium For a body to remain at rest, the net torque acting on it must be zero.   = 0 This is the second condition for equilibrium.  F x = 0,  F y = 0,  F z = 0 &   = 0 These are the only requirements for a body to be in equilibrium.

Elasticity Any object changes shape under the action of applied forces. The change in length of an object is directly related to the force applied: F Hooke’s law (F = k  L) applies to almost any solid (iron to bone) up to a point called the proportional limit.

Elasticity The change in length is also directly related to the original length: L 0 The change in length is inversely proportional to the cross-sectional area: A The change in length is also inversely proportional to a measure of its elasticity called the Elastic modulus (Young’s Modulus): E. (There is a table of the Elastic Moduli of various materials on page 254.  L = F L 0 / EA

Elasticity If a greater force is applied the object will continue to stretch and the object will return to its original length if stretched up to the elastic limit. If the force continues to increase, the object will continue to stretch (but not return to its original length when the force is removed) until its maximum elongation is reached at the breaking point. The maximum force that can be applied prior to breaking is called the ultimate strength.

Stress & Strain Stress is the force per unit area. Stress = force/area = F /A Strain is the ratio of the change in length to the original length. Strain=change in length/Original Length =  L/L 0

Elastic Modulus