Question

Consider the work-energy theorem relating work done on an object and its change in kinetic energy. What is the formula? Explain in your own words what this formula gives you. Create an example. Include a graphical or picture representation that illustrates what all the variables are. Then exemplify the use of the formula with a simple problem of your own creation. The problem should be stated in words first. Every variable should have a well defined value with appropriate units. Finally, solve your problem.
( please show image and explain clearly)

Answer 1

Work energy Theorem stats that the work done on an object is equal to the change in kinetic energy of the object

Suppose the work done on an object = W = F*x

F = Force applied on the object

x = displacement of the object

W = change in kinetic energy = Kf - Ki

Kf = final kinetic energy, Kf = 1/2 m v^2

Ki = initial kinetic energy, Ki = 1/2 m u^2

where m = mass of the object

u = initial velocity of the object

v= final velocity of the object

Consider an example

Force F is applied on the object with mass m at rest which displaces x meter.find the final velocity of the object? note: surface is friction less

solution

According to the work energy theorem

W = Kf-Ki

Kf = 1/2 m v^2

Ki = 0 since the object was at rest

Work done W = F*x

therefore,F*x= 1/2 m v^2 - 0

you can calculate velocity from this equation

Now consider a value of F = 10 N , x = 5 meter and mass of the object to be 1 kg

so 10*5 = 1/2 (1) v^2

so v = 10 m /s

so the final velocity of the object is 10 m/s