MECE 701 Fundamentals of Mechanical Engineering

1. MECE 701Fundamentals of Mechanical Engineering

2. MECE 701 Engineering Mechanics Mechanics of Materials MECE701 Machine Elements & Machine Design Materials Science

3. Fundamental Concepts • Idealizations: • Particle: • A particle has a mass but its size can be neglected. • Rigid Body: • A rigid body is a combination of a large number of particles in which all the particles remain at a fixed distance from one another both before and after applying a load

4. Fundamental Concepts Concentrated Force: A concentrated force represents the effect of a loading which is assumed to act at a point on a body

5. Newton’s Laws of Motion • First Law: A particle originally at rest, or moving in a straight line with constant velocity, will remain in this state provided that the particle is not subjected to an unbalanced force.

6. Newton’s Laws of Motion • Second Law A particle acted upon by an unbalanced force F experiences an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force. F=ma

7. Newton’s Laws of Motion • Third Law The mutual forces of action and reaction between two particles are equal, opposite, and collinear.

8. Newton’s Laws of Motion • Law of Gravitational Attraction F=G(m1m2)/r2 F =force of gravitation btw two particles G =Universal constant of gravitation 66.73(10-12)m3/(kg.s2) m1,m2 =mass of each of the two particles r = distance between two particles

9. Newton’s Laws of Motion • Weight W=weight m2=mass of earth r = distance btw earth’s center and the particle g=gravitational acceleration g=Gm2/r2 W=mg

10. Scalars and Vectors • Scalar: A quantity characterized by a positive or negative number is called a scalar. (mass, volume, length) • Vector: A vector is a quantity that has both a magnitude and direction. (position, force, momentum)

11. Basic Vector Operations • Multiplication and Division of a Vector by a Scalar: The product of vector A and a scalar a yields a vector having a magnitude of |aA| 2A -1.5A A

12. Basic Vector Operations • Vector Addition Resultant (R)= A+B = B+A (commutative) Parallelogram Law Triangle Construction B R=A+B A A R=A+B A A R=A+B B B B

13. Basic Vector Operations • Vector Subtraction R= A-B = A+(-B) • Resolution of a Vector a R A B b

14. Trigonometry • Sine Law A B c a b • Cosine Law C

15. Cartesian Vectors Right Handed Coordinate System A=Ax+Ay+Az

16. Cartesian Vectors • Unit Vector A unit vector is a vector having a magnitude of 1. Unit vector is dimensionless.

17. Cartesian Vectors • Cartesian Unit Vectors A= Axi+Ayj+Azk

18. Cartesian Vectors • Magnitude of a Cartesian Vector • Direction of a Cartesian Vector DIRECTION COSINES

19. Cartesian Vectors • Unit vector of A

20. Cartesian Vectors • Addition and Subtraction of Cartesian Vectors R=A+B=(Ax+Bx)i+(Ay+By)j+(Az+Bz)k R=A-B=(Ax-Bx)i+(Ay-By)j+(Az-Bz)k

21. Dot Product Result is a scalar. Result is the magnitude of the projection vector of A on B.

22. Dot Product • Laws of Operation Commutative law: Multiplication by a scalar: Distributive law:

23. Cross Product The cross product of two vectors A and B yields the vector C C = A x B Magnitude: C = ABsinθ

24. Cross Product • Laws of Operation Commutative law is not valid: Multiplication by a scalar: a(AxB) = (aA)xB = Ax(aB) = (AxB)a Distributive law: Ax(B+D) = (AxB) + (AxD)

25. Cross Product

26. Cross Product