Therefore we have proved the work energy theorem.
Work energy theorem graph.
The quantity latex frac 1 2 mv 2 latex in the work energy theorem is defined to be the translational kinetic energy ke of a mass m moving at a speed v translational kinetic energy is distinct from rotational kinetic energy which is considered later in equation form the translational kinetic energy latex text ke frac 1 2 mv 2 latex is the energy associated with.
General derivation of the work energy theorem for a particle.
A pretty similar problem so great idea to pause and see if you can try yourself first.
This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy.
Workdone under a variable force.
The work energy theorem is useful however for solving problems in which the net work is done on a particle by external forces is easily computed and in which we are interested in finding the particles speed at certain positions of even more significance is the work energy theorem as a starting point for a broad generalization of the concept.
And so this is how even velocities are given we can accurately use work energy theorem to calculate the work done.
Review the key concepts equations and skills for the work energy theorem.
Work energy theorem suppose that an object of mass is moving along a straight line.
This is the derivation of work energy theorem.
Understand how the work energy theorem only applies to the net work not the work done by a single source.
Proving the work energy theorem for a variable force is a little tricky.
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All right right lets try one more.
A variable force is what we encounter in our daily life.
All right lets see a 500 kilogram tempo traveling at 30 meters per second brakes and comes to a stop.
The force that we come across everyday is usually variable forces.
For any net force acting on a particle moving along any curvilinear path it can be demonstrated that its work equals the change in the kinetic energy of the particle by a simple derivation analogous to the equation above.
Deriving the work energy formula for variable force is a bit hectic.
Thus we can say that the work done on an object is equal to the change in the kinetic energy of the object.
If and are the the starting and ending positions and are the the starting and ending velocities and is the force acting on the object for any given position then.
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.
