Union College Mechanical Engineering ESC020: Rigid Body Mechanics1 Kinetics of Particles  Free Body Diagrams  Newton’s Laws  Euler’s Laws

Union College Mechanical Engineering ESC020: Rigid Body Mechanics2 Free Body Disgrams  The basic, graphical, force accounting tool for the analyst  Drawing FREE BODY DIAGRAMS A right handed Cartesian Coordinate system must be attached to a point on the structure All geometric points necessary to a force analysis must be clearly marked  Triplet of ordered numbers referenced to the coordinate system  Dimensions referenced from the origin

Union College Mechanical Engineering ESC020: Rigid Body Mechanics3 Free Body Diagrams Continued  Unit Vectors MUST be shown in the figure  Isolate the structure or element from it’s surroundings  Sketch all forces that act on the structure or element Known forces should be labeled with their proper magnitude and direction Unknown forces magnitude and direction will be assumed

Union College Mechanical Engineering ESC020: Rigid Body Mechanics4 Newton’s Laws of Motion  Basis for entire subject of rigid body mechanics  Based on experimental observation  Apply to the motion of particles as measured from a non-accelerating reference frame

Union College Mechanical Engineering ESC020: Rigid Body Mechanics5 Newton’s FIRST LAW A particle remains at rest or continues to move in a straight line with uniform velocity if there is no unbalanced force acting on it.

Union College Mechanical Engineering ESC020: Rigid Body Mechanics6 Newton’s SECOND LAW The acceleration of a particle is propositional to the resultant force acting on it and is in the direction of the resultant force

Union College Mechanical Engineering ESC020: Rigid Body Mechanics7 Newton’s THIRD LAW The forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear.

Union College Mechanical Engineering ESC020: Rigid Body Mechanics8 Euler’s Laws  Important extension of Newton’s laws  Restated laws in terms of force, mass, and absolute acceleration

Union College Mechanical Engineering ESC020: Rigid Body Mechanics9 Euler’s FIRST LAW The resultant of the external forces on a body is at all times equal to the time derivative of its momentum

Union College Mechanical Engineering ESC020: Rigid Body Mechanics10 Euler’s SECOND LAW The resultant moment of these external forces about a fixed point is equal to the time derivative of the body’s moment of momentum about the point.

Union College Mechanical Engineering ESC020: Rigid Body Mechanics11 Archimedean Versus Newtonian Equilibrium  Archimede’s concept of Equilibrium The fundamental principle of physics that applies to all force systems that act on bodies that are at rest, remain at rest, relative to the surface of the earth  Newon’s concept of Equilibrium A body is in equilibrium only if it is at rest relative to the “Fixed Set of Start” or it travels at a constant speed  This course is based on the Archimedean concept of equilibrium.

Union College Mechanical Engineering ESC020: Rigid Body Mechanics12 Example 1 The 10lb block has an initial velocity of 10ft/s on the smooth plane. If a force F=(2.5t) lb, where t is in seconds, acts on the block for 3s, determine the final velocity of the block and the distance the block travels during this time.

Union College Mechanical Engineering ESC020: Rigid Body Mechanics13 Example 2 A particle falls under the force of gravity in a medium that exerts a resisting force proportional to the velocity of the particle. Develop equations for the velocity and displacement of the particle. The velocity and displacement of the particle are zero at time t=0.

Union College Mechanical Engineering ESC020: Rigid Body Mechanics14 Example 3 Each of the two blocks has a mass m. The coefficient of kinetic friction at all surfaces of contact is μ. If a horizontal force P moves the bottom block, determine the acceleration of the bottom block in each case

Union College Mechanical Engineering ESC020: Rigid Body Mechanics15 Example 4 A conical pendulum consists of a 10 lb sphere supported by a 6ft cord that revolves about a vertical axis with a constant angular velocity so that the string is inclined 30° to the vertical. Determine the tension T in the string and the linear velocity of the sphere.

Union College Mechanical Engineering ESC020: Rigid Body Mechanics16 Free Body – Mass Acceleration Diagrams