3. Units of Work The SI unit of work is the Joule, J. 1 J = 1 Nm
We should always use J for work and energy units, the notation Nm will be used for moments which as we will see are a vector quantity.

4. Calculation of Work
During a finite movement of the particle the force does an amount of work given by:

5. Calculation of Work
In order to carry out this integral we must know the relationship between the force components and their respective component displacements, or the relationship between Ft and s.
For an analytical solution an analytical expression of Ft(s) is required. This is not always available.

6. The work done during a finite movement from P1 to P2 is:
Let us substitute Newton’s 2nd Law:

7. Principle of Work and Kinetic Energy
Let us define the Kinetic Energy T of a particle as:
This is the total work that must be done on the particle to bring it from rest to a speed of v.
Kinetic Energy, like work, is a scalar quantity
It has units of Joules, J.
Kinetic Energy is always a +ive quantity (v2)

8. Work-Energy Equation for a Particle
We have:
This equation states that the total work done by all forces acting on a particle as it moves from point 1 to point 2 equals to the corresponding change in kinetic energy of the particle.
Although T is always +ive, the change T may be +ive, -ive, or 0.
Work-Energy Equation for a particle

9. The work energy equation may be rewritten as:
Work done on (or by) a particle always results in a change of its kinetic energy.
The work energy equation may be rewritten as:
This form emphasizes that the final kinetic energy of a particle is equal to its initial kinetic energy plus the work done on it.

10. Example Problem

11. Advantages of the Work-Energy Method
We do not have to compute the acceleration.
Leads directly to changes in velocity.
Only involves forces that do work, i.e. only those forces that give rise to changes in the magnitude of the velocity.
Consider the centripetal force of circular motion.

12. System of Interconnected Particles
Consider a system of 2 particles joined together by a frictionless undeformable connection.
The forces in the connection are equal and opposite.
Their points of application must have identical displacement components in the direction of the forces.
The net work done by these internal forces is Zero during any movement of the system.
The Work-Energy Equation can be applied to the system as a whole.
Where U12 is the total work done on the whole system and T is the total change in kinetic energy of the whole system.
- We can analyze the system of particles without dismembering it.

13. Power
The Capacity or Ability of a machine to do work is best measured by the time rate at which it can do work (or deliver energy).
Measuring the total work/energy output of a machine is not very meaningful since even a small machine can do a lot of work if we leave it long enough.

14. Power
A powerful machine can deliver more energy in a unit of time than a less powerful machine can in the same amount of time.
Power delivered by a machine is:
Power is a scalar quantity.
The units of power are the Watt, W 1W=1J/s 1 hp = 746 W

15. Efficiency
The ratio of the work done by a machine to the work done on the machine in the same time interval is the Mechanical Efficiency, em.
The efficiency of any machine is always < 1
There are always losses
In mechanical devices this loss is due to the –ive work done by frictional forces on the machine.
This work is mainly converted into thermal energy.