Question

3Objectives•To determine the relationship between kinetic, potential, and total mechanical energy for a cart on an incline.•To determine the work done by friction on a sliding cart.•To show that energy is not conserved when a non-conservative force, like friction, is acting.Procedure: Energy of a cart withoutf riction In this experiment, we will assume that friction is negligible, and that there are no non-conservative forces at work.The motion of a cart rolling down an incline will be examined using real-time velocity and position values from a motion sensor. Examining the position and velocity of the cart as it rolls down the track allows us to also determine the energy of the cart. In this experiment you will examine the transition between gravitation potential energy and kinetic energy as the cart rolls down an incline.1.Figure 1 was set up in real time, where the ramp was inclined at an angle of 8.5°, and the mass of the cart is 0.250 kg. A Motion Detector was attached to the upper end of the track.As the cart slides down the track, 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,and the position and velocity of the cart were measured with the motion sensor 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 as it rolls down the track.To do this, let’s first convert each position, d, to a height so we can calculate the potential energy of the cart. Open the data above in excel and create a new column labeled height. Using equation 7,convert every position measurement to the vertical height of the cart. In excel, make sure you use 0.1500983 (radians) for your angle, θ,Instead of 8.5°(degrees).

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

5.Next, create another new column that calculates Gravitational Potential Energy as the cart rolls down the incline. Create a formula which multiplies the height by the mass of the cart and gravitational 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 and Gravitational Kinetic Energy.

7.Create a line graph of kinetic energy versus time, potential energy versus time,and mechanical energy vs time on the same graph. Under your graph options, be sure to show a legend, so whoever reads your report will have no trouble determining which line is which.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 a function of time?

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

Answer 1