Lecture 4 Monday: 26 January 2004 Newton’s Laws of Motion

Commonly shortened to “F=ma”. Correctly, it is :  Only forces which act on that object affect the acceleration of the object.  Forces exert by the object on another object do not. Newton’s Second Law in One Dimension

Using Newton’s 2 nd Law to Solve Problems 1.Identify all forces acting on the object -Pushes or Pulls -Frictional forces -Tension in a string -Gravitational Force (or weight = mg where g is 9.8 m/s 2 ) - “Normal forces” (one object touching another). 2.Draw a “Freebody Diagram” -draw the object, show all forces acting on that object as vectors pointing in the correct direction. Show the direction of the acceleration. 3.Chose a coordinate system. 4.Translate the freebody diagram into an algebraic expression based on Newton’s second law.

Consider an elevator moving downward and speeding up with an acceleration of 2 m/s 2. The mass of the elevator is 100 kg. Ignore air resistance. What is the tension in the cable? v 1.Identify Forces: Tension in cable, weight of the elevator 2.Draw freebody diagram 3.Chose coordinate system: Let up be the +y direction and down –y. Then : 4.Translate the FBD into an algebraic expression. T- W = m(-a) so T-(100 kg)(9.8 m/s 2 ) = (100 kg)(-2 m/s 2 ) T W=F g earth  elevator. a Note: No negative sign

Newton’s Third Law Whenever one object (object A) exerts a force on another object (object B), the second object exerts a force back on the first object. These forces are ALWAYS equal in magnitude (but they point in opposite directions). Such forces are called “Newton’s third law force pairs”. Not all forces that are equal and opposite are third law force pairs. The forces are on different bodies, so do not add to zero.