ME 101: Forces & Moments (Continued) Chapter 4 ME-101 1
Particle/Rigid Body Particle – A very small amount of matter assumed to occupy a single point in space Rigid Body – A combination of a large number of particles that are fixed relative to one another ME-101 2
Newton’s 3 Fundamental Laws First Law – If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion) Second Law: Third Law – The forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense ME-101 3
Equilibrium ME-101 4
Equilibrium (in 2-D) ME-101 Particle is in equilibrium if forces balance (zero resultant) Rigid body is in equilibrium if forces and moments balance 5
Free Body Diagram (FBD) Forces and moments acting on a body are applied to a simplified version of the body ME-101 W F chair W 6
How to Draw a FBD 1.Isolate the body from its surroundings and draw a simplified version of it 2.Use an appropriate coordinate system (Usually Cartesian) and include it with your FBD 3.Add the loads to the body in appropriate locations with proper direction and magnitude 4.Label all known quantities ME-101 7
T Example ME-101 WBWB T WAWA NANA A B F app Pulley θ Assume surface is smooth – no friction What is FBD of Block A? Block B? F app Use the free body diagram to evaluate the system y x θ
Example The mass center G of the 1400 kg rear engine car is located as shown in the figure Determine the normal force under each tire when the car is in equilibrium ME-101 9
Example ME
Example Determine the pull P on the rope exerted by the man to hold the crate in the position shown Also find the tension T in the upper rope ME
Example Compute the moment about point O ME
Example Compute the moment about point B ME-101 θ F 13
Example Calculate the moment of the 400 N force about point O ME
Design Applications ME
Hyatt Regency Hotel in Kansas City July 17, 1981 Killing 114 Injuring 200+ Worst structural disaster in U.S. history The engineering firm that approved the final plans was stripped of its license ppcases/texindex/hyatt_walkway.aspx ME
Why? ME
The initial plan and final deviation ME
Beam Failure ME
Design Application: Bearings Two types of bearings –Rolling-Element Balls or rollers between inner and outer race Very common –Journal Shaft in lubricated sleeve Rotates on film of oil Examples – Engine crankshafts, pumps, and compressors ME
Radial Ball Bearing ME
Ball and Roller Contact Stress ME-101 Max shear stress occurs below the surface, failure appears as cracks, pits, or flakes 22
Roller Bearings Higher Loads – Axial or Radial ME
How to Size Component Create FBD Determine loads acting on component Determine size of component –Consider Non-Traditional Solutions –Factor of Safety –Consider Dimensional Constraints –Cost –Manufacturability –Ease of Assembly ME
Bearing Selection ME