Engineering Mechanics – deals with the state of a body at rest or motion of a body caused by the action of forces. Statics – deals with the action of forces on bodies at rest. Net force acting on the body is zero Dynamics – deals with the motion of bodies under the action of forces. Net force acting on a body is not zero.  Kinematics – study of motion without reference to the forces which cause the motion. Deals with position, velocity, and acceleration in terms of time  Kinetics – relates the action of forces on bodies to their resulting motions Ken Youssefi 1 Mechanical Engineering Department

A body, not necessarily small, where it’s motion can be characterized without considering its size and orientation. Rotation of the body about its own axis is neglected. Particle Rigid body The body is called a rigid body If its rotation about its own axis cannot be neglected. Ken Youssefi 2 Mechanical Engineering Department

Problem Solving Technique 1.Identify all given data (known parameters) 2.Identify the goal (unknown parameters) 3.Draw diagrams needed to solve the problem: Free Body Diagram (FBD), Motion Diagram (inertial Response Diagram), Geometry Diagram 4.Identify the dynamics principles applied to the problem 5.Clearly state all assumptions Ken Youssefi 3 Mechanical Engineering Department

Ken Youssefi Mechanical Engineering Department 4 6.Use your technical judgment (common sense) to determine if the answer is reasonable 7.Report the answer with the same accuracy as the given data 8.Careless solutions that cannot be read easily are of little or no value. Problem Solving Technique

Consider the Bat-Sled as shown. At time zero its rocket engine is fired, producing a thrust of T = 43,000 N. The mass of the sled is m = 1600 kg and the coefficient of friction between the sled and snow is 0.2. Determine the sled’s acceleration. Example 1.Known parameters: Total mass ( m ), thrust ( T ) and coefficient of friction (  ) 2.Goal (unknown): Acceleration of the sled, a 3.Draw diagrams: FBD = MD (IRD) FBDMD Ken Youssefi Mechanical Engineering Department 5

4.Dynamics principles (formulate equations): Summation of forces in the x direction Summation of forces in the y direction 5.Assumptions 6.Solve Acceleration = 2.54 g 7.Check Check assumption, is the answer reasonable? Ken Youssefi Mechanical Engineering Department 6 b)There is no motion of the Bat-Sled in the vertical direction. c)The Bat-Sled will not flip over. a)For the sled to move, the thrust has to overcome the friction between the snow and the sled. We have to check this assumption later. F =  N T > F =  N ?

Ken YoussefiMechanical Engineering Department. 7 Some Reference Values Acceleration, SI system (English system) Fast car 3 m/s 2 (118 in/ s 2 ) Hard braking car7 m/s 2 (275 in/ s 2 ) Earth gravity at sea level9.81 m/s 2 (32.2 ft/ s 2 ) Humans blackout40 m/s 2 (4 g-force) Belly flopping in water from 10 m diving board, causing broken bones 100 m/s 2 (10 g-force) Head-on car collision occupant acceleration 10,000 m/s 2 (2730 ft/ s 2 ) Bullet fired from a rifle60,000 m/s 2 (16,400 ft/ s 2 ) Centrifugal acceleration of light trapped in a black hole 2 x m/s 2 (550 x ft/s 2 )

Ken YoussefiMechanical Engineering Department. 8 Some Reference Values Force, SI system (English system) Attraction between electron and proton in hydrogen 0.08 μ N (.018 μ lb.) Weight of a piece of paper0.04 N (.14 ounce) Weight of a small apple1 N (.22 lb.) Finger force for appliance7 N (1.6 lb.) Weight of bag of potatoes100 N (22.5 lb.) Weight of two small people 1.5 kN (337 lb.) Thrust of Boeing MN (224, 820 lb.) Space shuttle thrust0.2 GN (45 million lbs.)

Geometry diagram FBD = MD (IRD) Ken Youssefi Mechanical Engineering Department 9