Work energy and second law

PRESENTATION MADE BY FAROOQ MUSTAFA JOYIA,MOHTASIM AND ADIL ZAHOOR (students of Departement of Mechanical Engineering,International Islamic University Islamabad)

1. WORK, ENERGY AND SECOND LAW PRESENTED BY: FAROOQ MUSTAFA (169) ADIL ZAHOOR (176) DAIYAL ZAHEER (182) M.BILAL ARSHAD (183) MOHTASIM NAWAZ (187)

2. AGENDA:- NEWTONS SECOND LAW WORK ENERGY WORK-ENERGY THEOREM

3. Newton’s Second Law Force equals mass times acceleration. F = ma Acceleration : a measurement of how quickly an object is changing velocity.

4. What does F = ma mean? Acceleration is inversely proportional to mass Acceleration is directly proportional to for ce

5. In other words…. Large Force = Large Acceleration F a

6. In other words…..using the same amount of force…. F Large Mass a Small acceleration F Small Mass Large acceleration a

7. WORK

8. DEFINATION When a force “F” is applied to a body and it covers some distance “d” than a work is done on a body.

9. Work = Force x distance W (Joules) = F (N)  Δ x (m) Work is measured in Newton-meters (Nm), more commonly called joules (J). 1 J = 1 Nm W = Fd

10. Is there working being done?

11. This is great! I’m getting paid for doing no work!

12. Force and distance in same direction = + work Force and distance in opposite directions = - work CAN YOU DO NEGATIVE WORKING ?

13. W = Fd(cos ө ) …so when the applied force is perpendicular to the distance, you end up with zero work!

14. CALCULATION OF WORK Just as velocities may be integrated over time to obtain a total distance, by the fundamental theorem of calculus, the total work along a path is similarly the time-integral of instantaneous power applied along the trajectory of the point of application. Work is the result of a force on a point that moves through a distance. As the point moves it follows a curve X with a velocity v at each instant. The small amount of work δW that occurs over an instant of time δt is given by

15. where the F.v is the power over the instant δt . The sum of these small amounts of work over the trajectory of the point yields the work.

16. WORK DONE BY A CONSTANT FORCE

17. WORK DONE BY A SPRING A horizontal spring exerts a force F=( kx , 0, 0) that is proportional to its deflection in the x direction. The work of this spring on a body moving along the space curve X(t) = (x(t), y(t), z(t)), is calculated using its velocity, V=( vx , vy , vz ), to obtain For convenience, consider contact with the spring occurs at t=0, then the integral of the product of the distance x and the x-velocity, xvx , is (1/2)x2.

18. WORK DONE BY A GRAVITY Gravity exerts a constant downward force F=(0, 0, W) on the center of mass of a body moving near the surface of the earth. The work of gravity on a body moving along a trajectory X(t) = (x(t), y(t), z(t)), such as the track of a roller coaster is calculated using its velocity, V=( vx , vy , vz ), to obtain. where the integral of the vertical component of velocity is the vertical distance. Notice that the work of gravity depends only on the vertical movement of the curve X(t).

19. 20 THE WORK-ENERGY THEOREM When a net external force does work W on an object, the kinetic energy of the object changes from its initial value of KE to a final value of KE f , the difference between the two values being equal to the work :

20. The work done in lifting the mass gave the mass gravitational potential energy. Potential energy then becomes kinetic energy. Kinetic energy then does work to push stake into ground.

21. Mechanical Energy Mechanical energy is the energy which is possessed by an object due to its motion or its stored energy of position. Mechanical energy can be either kinetic energy or potential energy .

22. The 1st Law of Thermodynamics and the Law of Conservation of Energy state that the algebraic sum of these energy changes and transfers must add up to zero, accounting for all changes relative to the system. W + Q = ∆E  E Q W

23. So for mechanics neglecting Q W = ∆E k + ∆E g + ∆E el + ∆ E chem +∆E int

24. Potential and Kinetic Energy

25. How is all energy divided? Potential Energy Kinetic Energy All Energy Gravitation Potential Energy Elastic Potential Energy Chemical Potential Energy

26. What is Potential Energy? Energy that is stored and waiting to be used later

27. What is Kinetic Energy? Energy an object has due to its motion K.E. = .5(mass x speed 2 )

28. Energy Storage Mode Equations : E K = ½mv 2 E g = mgh E el = ½ kx 2