Download Work and Kinetic Energy Script

Work and Kinetic Energy Script
Slide One: Click Here Button
Slide Two: Work and Energy
Slide Three: Work and Kinetic Energy
Slide Four: Work is a measurement of energy transfer. For work to be done on an
object, a force must be applied in the direction of the motion of the object. If there is no
motion, no work is done on the object. If the motion is opposite to the direction of force,
negative work is done on the object. In the equation, the angle is used to determine the
component of the force that is in the axis of motion.
Slide Five: In our free body diagram, the normal and the weight, m g, do not have any
components in the direction of motion. They do no work. Only the x component of the
applied force is in the axis of motion.
Slide Six: The x component of the force is F cosine theta if theta is measured between
the axis of motion and the direction of the applied force.
Slide Seven: Work is a transfer of energy, so if energy is a scalar quantity, work must be
a scalar quantity. However, Force is a vector, and displacement is a vector. The scalar
product of two vectors is called the dot product. The result is always the product of the
two vectors multiplied times the cosine of the angle between them.
Slide Eight: Work done by a varying force.
Slide Nine: Often, the force applied to an object is not constant. The work done on the
object is the area under the curve of a graph of the x component of force versus
displacement. If the slope is constant then we can use geometry to determine the area
under the line. If it is a curved function, then we must use calculus.
Slide Ten: Using a small period of time, delta t, the area can be approximated using the
area of a rectangle.
Slide Eleven: The sum of all these rectangles would be the total area under the curve.
So we need to integrate between the starting and ending points.
Slide Twelve: We apply calculus by letting the size of delta x approach zero.
Slide Thirteen: If more than one force is applied to the object we can calculate the total
work using the equation provided. However, if the object cannot be treated as a particle,
then the integrand is not valid.
Slide Fourteen: The integral is of the path of the particle, so we need an equation for the
force as a function of the displacement.
Slide Fifteen: The Work Kinetic energy theorem
Slide Sixteen: The equation for kinetic energy is derived from the value of the work
done on an object.
Slide Seventeen: First we replace the F with the relationship mass times acceleration. In
the second equation acceleration is replaced with its definition which is d v over d t.
Then d v over d t equals d v over d x times d x over d t.
Slide Eighteen: So the energy due to the motion of a particle is given as one half mass
times velocity squared. This becomes our definition of kinetic energy.
Slide Nineteen: The work kinetic energy theorem states that the work done on an object
is equal to the change in kinetic energy of that object if no other form of energy change
takes place.