The work energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body.
Work done and kinetic energy formula.
The units are the same as for work i e.
It needs to be emphasized that the work energy equation only applies to work done by the net force in a mechanical system the work done by just any old force may or may not show up as kinetic energy but the work done by the net force always shows up as kinetic energy.
Kinetic energy is a form of energy that an object or a particle has by reason of its motion.
Kinetic energy is a scalar.
This version of the work energy equation was derived for one dimensional motion and is valid.
So we can define work done by a force as energy given or taken from the system of objects.
The energy an object has by reason of its motion equal to latex frac 1 2 text mv 2 latex for the translational i e non rotational motion of an object of mass m moving at speed v.
Where v stands for an object s velocity.
Kinetic energy is a property of a moving object or particle and depends not only on its motion but also on its mass.
The result based on newton s laws that the net work done on an object is equal to its change in kinetic energy kinetic energy.
This is known as work done by force.
Thus we define the kinetic energy as the capacity of an object to do work by virtue of its motion.
Now suppose a ball is moving with velocity v.
The kinetic energy of an object is denoted by ke and its si unit is joules j.
The principle of work and kinetic energy also known as the work energy theorem states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.
Where ke stands for kinetic energy.
But are they interchangeable.
By now we have started to sense that work and kinetic energy are closely related.
The unit for kinetic energy is the same unit for work the joule.
In other words the change in kinetic energy of a body is equal to the amount of work done on that body.
Note that the work in this equation is the work done by the net force rather than the work done by an individual force.
We apply some force in the opposite direction now the velocity becomes less than v or in other words the body loses kinetic energy so where has that energy gone.
Ke 1 2 kg v 2.
If work which transfers energy is done on an object by applying a net force the object speeds up and thereby gains kinetic energy.
The work done on an object by a net force equals the change in kinetic energy of the object.
Very important fine print.
This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy.
Conversely a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force.
Hence it can do work.
