Physics Lab #14

 

Work-Energy Virtual Lab

Theory

See Lab #7 for the theory behind motion on a ramp.  You should take a look at what you did for lab 7 and compare it to what you do in this lab to see the advantages and disadvantages of the work-energy approach.

 

The work done by a force is calculated by using

 

Work = W = F∙s  = Fscosθ

 

where work is a scalar quantity measured in Joules (J) and F is the force in Newtons, s is the displacement in meters and θ is the angle between F and s.  Note that for F in the same direction as s, θ is 0º so W=Fs.  For F opposite to s, θ is 180º so W=-Fs.  For F perpendicular to s, θ is ±90º so W=0 J.  (I gave a formula in class yesterday that showed a shortcut for calculating the work done by gravity.  It showed that the work done by gravity was equal to the change in height times g times mass. )

 

The net work on an object then is simply found by calculating the work done by the net force (found by vectorial addition) OR by adding up the work done by all the forces (scalar addition).  (For the frictionless ramp the net work is simply the work done by gravity because the normal force is by definition perpendicular to the motion.)

 

Kinetic energy, E_K (in Joules), of an object of mass m (in kg) with speed v (in m/s) is given by:

 

E_K = ½mv²

 

Work-Energy Theorem: The theorem relates the net work done on an object to the change in kinetic energy of the object:

 

W_net = ΔE_K = ½mv_f² - ½mv_i²

 

Use this and what you know for the ramp to find the algebraic relationship between the height a block falls through and the speed it will have.  Assume no friction and zero initial speed.

 

 

Procedure

The virtual lab equipment you will be using is here.

1. Start by making sure the initial speed and the friction are set to zero, and that rebound is off.
2. Using various ramp heights let the block do a run.  Devise a method to find the final speed of the block at the bottom of the ramp (hint: the speed at the bottom of the ramp is the same as the speed along the flat). Make a data table of the height the block falls and the speed it reaches at the bottom of the ramp for various ramp heights. 
3. Graph the data available to confirm the work-energy theorem prediction for the relationship between height and speed that you were asked to find in the theory section.  Compare the experimental and known values for the acceleration due to gravity.
4. Set the ramp so that you can get as long a horizontal run as possible.  Choose a non-zero initial speed and coefficient of friction.  Start the block down on the flat and play with things until you can get the block to run as far as possible along the flat but still come to a stop.  Do a free body diagram for the block and calculate the net work done on it.  By using the work-energy theorem you will find a relationship between the coefficient of friction, the initial speed and the distance traveled.  Use the data to confirm the relationship.