Experiment 09

WORK AND ENERGY-Practical

PRELAB

PURPOSE

To demonstrate the validity of the work-energy theorem, and to use energy principles to measure the acceleration of gravity, g.

EQUIPMENT linear air track, electronic timer, glider, two photogates, pulley and weights, and shim.
 
 

RELEVANT EQUATIONS

DISCUSSION

The work-energy theorem states that the total work W done on an object moving from point A to point B is equal to the difference in the kinetic energies of the object at A and B. The work done on the object is defined as:

where Fx is the magnitude of the component of the force parallel to the direction of motion of the object, and dis the distance the object is moved. The kinetic energy of an object is defined as:

where m is the mass of the object and v is its speed. In terms of these equations, the work-energy theorem can be written:
 
 

                                                                    (1)


In this experiment, you will study this relationship on the air-track.
 
 



 

Figure 9-1: Glider on an Inclined Air Track

Figure 9-1 shows an object of mass m sitting on an inclined plane. If the plane is frictionless, the magnitude of the total force parallel to the plane is:

so the work done on m in moving it from A to B, a distance d along the incline, is:

                             W  =  Fx d  =  (m g sin q) d = m g h                                                                        ( 2)
where h = d sin q  is the vertical distance between points A and B. From Equation (1) we have:
 
 

or:

                                                                                                              ( 3)


 This equation says that the difference in the square of the speeds of an object at two fixed points on a frictionless inclined plane is the same regardless of the object's initial speed.