3Objectives•To determine the relationship between kinetic,potential, and total mechanical energy for a cart on an incline.•Todetermine the work done by friction on a sliding cart.•To show thatenergy is not conserved when a non-conservative force, likefriction, is acting.Procedure: Energy of a cart withoutf riction Inthis experiment, we will assume that friction is negligible, andthat there are no non-conservative forces at work.The motion of acart rolling down an incline will be examined using real-timevelocity and position values from a motion sensor. Examining theposition and velocity of the cart as it rolls down the track allowsus to also determine the energy of the cart. In this experiment youwill examine the transition between gravitation potential energyand kinetic energy as the cart rolls down an incline.1.Figure 1 wasset up in real time, where the ramp was inclined at an angle of8.5°, and the mass of the cart is 0.250 kg. A Motion Detector wasattached to the upper end of the track.As the cart slides down thetrack, the motion detector ispre-programmed to measure the distance(position) of the cart from the bottom of the ramp –see (d)infigure 1.2.Gravitational potential energy depends on position,and kinetic energy depends on velocity. The cart was released,andthe position and velocity of the cart were measured with the motionsensor software.Time(seconds)Position(meters)Velocity(meters/second )

0.866658 1.273902 0.265542

0.899991 1.256238 0.471058

0.933324 1.239259 0.557238

0.966657 1.219022 0.618978

0.99999 1.197756 0.667428

1.033323 1.174775 0.720021

1.066656 1.14905 0.752035

1.099989 1.124183 0.771615

1.133322 1.098115 0.802199

1.166655 1.070846 0.8365

1.199988 1.042034 0.866512

1.233321 1.013222 0.901099

1.266654 0.982867 0.959695

1.299987 0.948738 1.006286

1.33332 0.915639   1.046589

1.366653 0.878766 1.080032

1.399986 0.842923 1.094753

1.433319 0.806908 1.141773

1.466652 0.766777 1.191794

1.499985 0.728361 1.266254

1.533318 0.682056 1.33071
43.Now, it’s time to plot the PE, KE, and total ME of the cart asit rolls down the track.To do this, let’s first convert eachposition, d, to a height so we can calculate the potential energyof the cart. Open the data above in excel and create a new columnlabeled height. Using equation 7,convert every position measurementto the vertical height of the cart. In excel, make sure you use0.1500983 (radians) for your angle, θ,Instead of 8.5°(degrees).

4.Create another new column titled Kinetic Energy. Create aformula which grabs each velocity value and, using your measuredmass, calculates the kinetic energy of the cart(equation1).

5.Next, create another new column that calculates GravitationalPotential Energy as the cart rolls down the incline. Create aformula which multiplies the height by the mass of the cart andgravitational acceleration(equation 2).

6.Finally, create a third new column titled Mechanical Energy,which is just be the sum of your two columns, Kinetic Energy andGravitational Kinetic Energy.

7.Create a line graph of kinetic energy versus time, potentialenergy versus time,and mechanical energy vs time on the same graph.Under your graph options, be sure to show a legend, so whoeverreads your report will have no trouble determining which line iswhich.Attach the graph with your lab submission.

8.What is the approximately slope of your kinetic energy graph?What does this suggest about your cart’s kinetic energy as afunction of time?

9.What is the approximately slope of your potential energygraph? What does this suggest about your cart’s kinetic energy as afunction of time?
10.Analyze your graph carefully. What is the approximate slope ofyour mechanical energy graph? What does this suggest about yourcart’s total mechanical energy?