Trial 1 2 3 Investigation A: Energy of a Rolling Cart Purpose: To observe the motion of a cart on an incline and verify

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Trial 1 2 3 Investigation A: Energy of a Rolling Cart Purpose: To observe the motion of a cart on an incline and verify that mechanical energy is conserved as it moves down the incline. Materials: Ramp, cart, motion detector, books to prop up the ramp Procedure: 1) Set up your station as shown in the diagram below. 2) Hold the cart about 10 cm from the motion detector. Using a meter stick, measure the initial vertical distance from the desk to the center of the cart (this is htop in the diagram). Record this value in the data table for trial 1 below. Cart mass= hf (m) h, (m) 0.15 0.155 0.145 0.255 kg vf (m/s) E. (J) Ef (J) 0.1 1.056 0.375 J 0.382 J 0.095 1.478 0.387 J 0.516 J 0.105 2.006 0.362 J 0.775 J 3) Hit the collect button to begin recording data. Let the cart go, then catch it at the bottom of the ramp. After you catch the cart, don't move it! Hold the cart in place and measure the final vertical distance from the desk to the center of the cart (this is hbottom in the diagram). Record this value in the data table. 4) Look at your velocity vs. time graph. Try to identify the time just before you caught the cart at the bottom of the ramp. Read the speed off of the graph (this is vf), and record your value in the data table 0 m/s 5) Measure the mass of your cart. Record this value in the data table 6) You let your cart go at the top of the ramp, without giving it an initial push in either direction. This means your initial speed is % difference between initial and final energy 1.75% 0.399% 1.995%
7) Calculate the initial potential energy of your cart using the formula PEi= mghi. Here, hi is the initial height of the cart measured relative to the desk and g = 9.8 m/s2. Show your calculation below. Trial 1) hi = 0.15m PEi= mghi => PEi= (0.255kg)(9.8m/s^2)(0.150m) => PEi = 0.375 J Trial 2) hi 0.155m PEi= mghi => PEi= => PEI=0.387 J (0.255kg)(9.8m/s^2)(0.155m) Trial 3) hi- 0.145m PEi= mghi => PEi = (0.255kg)(9.8m/s^2)(0.145m) => PEI=0.362 J 8) You let your cart go at the top of the ramp, without giving it an initial push in either direction. This means your initial kinetic energy is KE, 0J 9) Calculate the initial mechanical energy of your cart E, PE,+ KE.. Show your calculation below. Record your result in the data table. Ei= PEi + KEI Trial 1) PEi 0.375J, KEi=OJ => Ei=0.375 +0=0.375 J Trial 2) PEi=0.387J, KEi=OJ => Ei= 0.387 +0=0.387 J Trial 3) PEi 0.362J, KEi=OJ ->Ei 0.362 +0 -0.362 J 10) Calculate the final potential energy of your cart using the formula PE(f) = mgh(f). Here, hf is the final height of the cart measured relative to the desk. Show your calculation below. Record your result in the data table Trial 1) hf 0.1 PEf=mghf = (0.255)(9.8)(0.1)=0.240 J Trial 2) hf 0.095 PEf=mghf=(0.255)(9.8)(0.095)=0.237 J Trial 3) hf 0.105 PEf mghf (0.255)(9.8)(0.105)=0.262 J
11) Calculate the final kinetic energy of your cart using the formula KE(f) = (1/2)mv(f)². Here, v(f) is the final speed of the cart, just before you caught it at the bottom. Show your calculation below. Record your result in the data table. Trial 1) vf = 1.056 KEf= 1/2mv^2f = 1/2(0.255)(1.056)^2=0.142 J Trial 2) vf = 1.478 KEf = 1/2mv^2f = 1/2(0.255(1.478)^2 = 0.279 J Trial 3) vf=2.006 KEf = 1/2mv^2f = 1/2(0.255)(2.006)^2=0.513 J 12) Calculate the final mechanical energy of your cart E(f) = PE(f) + KE(f). Show your calculation below. Record your result in the data table. Trial 1) PEf = 0.240 J; KEf = 0.142 J Ef=PEf + KEf=0.240 +0.142 = 0.382 J Trial 2) PEf=0.237 J; KEf=0.279 J Ef=PEf + KEf=0.237 +0.279=0.516 J Trial 3) PEf=0.262 J; KEf = 0.513 J Ef=PEf+KEf=0.262 +0.513=0.775 J 13) Calculate the percent difference between E(i) and E(f). Show your work calculation in the space below and record your result in the data table. Was mechanical energy conserved as the cart rolled down the ramp? What might have caused a loss of mechanical energy? Explain below. %diff = E(f) - E(i)/EV Eav = [E(f) - E(i)]/2 Trial 1) Eav = (0.382 -0.3750)/2=0.004J % diff=(0.007)/(0.004) = 1.75% Trial 2) Eav (0.516-0.387)/2=0.323J % diff=(0.219)/(0.323) = 0.399% Trial 3) Eav (0.775 -0.362)/2=0.207J % diff=(0.413)/(0.207) = 1.995 % Mechanical energy is not conserved in this case because there is a friction force acting opposite to the motion of the cart. Because of this friction force, some energy is lost as heat.
14) We will now change the setup for trial # 2. Increase the angle of your incline by adding another book at the detector end of the track. Repeat steps 2-13 for your new setup. Show all of your calculations in the space below. 15) We will now change the setup for trial # 3. Increase the angle of your incline by adding another book at the detector end of the track. Repeat steps 2-13 for your new setup. Show all of your calculations in the space below.
Investigation B: Free Falling Purpose: To observe the motion of a free falling object and verify that mechanical energy is conserved as it falls to the ground. Materials: motion detector, wire basket, ball Procedure: Set the wire basket on top of the motion detector as shown below. Set the motion detector to ball/walk mode. Motion Detector CHE 1) Measure and record the mass of the ball you plan to use in this experiment m kg 2) Hold the ball 1 meter above the surface of the table, right above the motion detector. Use a meter stick to verify the height. Hit collect to begin recording data, then drop the ball. 3) Take a look at your graphs, and identify a time just after the ball was dropped. From the graphs, determine the speed of the ball and the height above the detector at this time. 0.015 m/s v= h= 0.985 m Using these values, calculate the total energy of the ball. Remember, E = PE +KE. Show your calculation below.
4) Take a look at your graphs again, and identify a time just before the ball landed on the basket. From the graphs, determine the speed of the ball and the height above the detector at this time. 4.27 m/s v= 0.025 m Using these values, calculate the total energy of the ball. Remember, E = PE +KE. Show your calculation below. 5) Take a look at your graphs again, and identify a time about halfway between when the ball was dropped and the ball landed on the basket. From the graphs, determine the speed of the ball and the height above the detector at this time. 2.49 m/s h= 0.653 m Using these values, calculate the total energy of the ball. Remember, E = PE +KE. Show your calculation below. 6) You should have obtained roughly the same value of the total energy in steps 3-5. How close were your measured total energies? What effects might cause the total energy to change as the ball falls towards the ground?