The document summarizes work, energy, and Newton's second law. It defines work as a force applied over a distance, and discusses how work can be positive, negative, or zero depending on the direction of force and distance. It also introduces the work-energy theorem, which states that the work done on an object equals its change in kinetic energy. Potential energy stored can also be converted to kinetic energy. The document distinguishes between different types of potential and kinetic energy.

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

3. • NEWTONS SECOND LAW
• WORK
• ENERGY
• WORK-ENERGY THEOREM

4. Force equals mass times acceleration.
F = ma
Acceleration: a measurement of how quickly an
object is changing velocity.

5. Acceleration is inversely
proportional to mass
 Acceleration is directly
proportional to force

6. Large Force = Large Acceleration
F
a

7. F Small acceleration
Large Mass a
Large acceleration
F a
Small Mass

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

10. W = Fd
 W (Joules) = F (N) Δx
(m)
 Work is measured in
Newton-meters (Nm),
more commonly called
joules (J).
1 J = 1 Nm

11. Is there working being done?

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

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

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

15. 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

16. 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.

17. WORK DONE BY A CONSTANT FORCE

18. 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.

19. 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).

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 KE0 to a final
value of KEf, the difference between the two
values being equal to the work:
1 2 1 2
W KE f KE0 mv f mv0
2 2
20

21. 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.

22. 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.

23. 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
W + Q = ∆E

24. So for mechanics neglecting Q
W = ∆Ek + ∆Eg + ∆Eel+
∆Echem+∆Eint

26. All Energy
Potential Kinetic
Energy Energy
Gravitation Elastic Chemical
Potential Potential Potential
Energy Energy Energy

27. o Energy that is
stored and waiting
to be used later

28. o Energy an object has due
to its motion
o K.E. = .5(mass x speed2)

29. Energy Storage Mode Equations:
1) EK = ½mv2
2) Eg = mgh
3) Eel = ½kx2