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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 without friction 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 is pre-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

1.366655 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)

I need help with getting the height not sure if I am doing it right

Answer 1

Given angle of incline is 0.1500983 radians
so, from the given data, we calculate height as h = y*sin(0.1500983) radians , where y is location
KE is calculated as 0.5mv^2, where m = 0.25 kg , v is speed
Pe is calculated as mgh, m = 0.25 kg, g = 9.81 m/s/s
total ME = KE + PE

so following is the the completed table

Time (s)	Position (m)	Velocity (m/s)	Height (H)	KE (J)	PE (J)	T.M.E
0.86666	1.273902	0.265542	0.19049335	0.008814	0.467185	0.475999
0.89999	1.256238	0.471058	0.18785196	0.027737	0.460707	0.488444
0.93332	1.239259	0.557238	0.185313	0.038814	0.45448	0.493294
0.96666	1.219022	0.618978	0.18228685	0.047892	0.447059	0.49495
0.99999	1.197756	0.667428	0.17910684	0.055683	0.43926	0.494942
1.03332	1.174775	0.720021	0.17567036	0.064804	0.430832	0.495635
1.06666	1.14905	0.752035	0.17182357	0.070695	0.421397	0.492092
1.09999	1.124183	0.771615	0.16810507	0.074424	0.412278	0.486701
1.13332	1.098115	0.802199	0.16420699	0.08044	0.402718	0.483158
1.16666	1.070846	0.8365	0.16012931	0.087467	0.392717	0.480184
1.19999	1.042034	0.866512	0.1558209	0.093855	0.382151	0.476006
1.23332	1.013222	0.901099	0.15151248	0.101497	0.371584	0.473082
1.26665	0.982867	0.959695	0.14697334	0.115127	0.360452	0.475579
1.29999	0.948738	1.006286	0.14186985	0.126576	0.347936	0.474512
1.33332	0.915639	1.046589	0.13692038	0.136919	0.335797	0.472716
1.36666	0.878766	1.080032	0.13140656	0.145809	0.322275	0.468083
1.39999	0.842923	1.094753	0.12604677	0.149811	0.30913	0.45894
1.43332	0.806908	1.141773	0.12066125	0.162956	0.295922	0.458877
1.46665	0.766777	1.191794	0.11466025	0.177547	0.281204	0.458751
1.49999	0.728361	1.266254	0.1089157	0.200425	0.267116	0.467541
1.53332	0.682056	1.33071	0.10199147	0.221349	0.250134	0.471483

following are graphs
1. PE vs time
2. KE vs time
3. total ME vs time