Conservation of Energy Consider the system shown below, which consistes of a cart of mass m on an angled track. If the cart is released from rest at Point 1 it will travel down the track, losing potential energy U = mgh 1 mgh 2 = mg h (1) It should be noted that generally, height measurements such as h 1 and h 2 are relative to the center of gravity of the body. However, the cart changes neither shape nor orientation in its motion from Point 1 to Point 2, so measurements to any point on the cart will produce the same h if it is the same at each point. In the process, the cart will gain kinetic energy K = 1 2 mv 2 2 1 2 mv 1 2 = 1 2 mv 2 2 0 = 1 2 mv 2 2 (2) If energy is conserved (expected), then these quantities will be equivalent. That is what you will test in this experiment. Apparatus Dynamics track, Cart, Load mass, Masking tape, Meter stick, Photogate, Fence, Pasco interface, Computer. Procedure Setup 1. Open the Capstone software on the Windows desktop; within it, open the Conservation of Energy activity in the 151 folder. 1
2. Measure the mass of the cart and the load mass (separately); record the masses on the Data Sheet. 3. Raise one end of the track so that it is about 15cm above the table. Place an end stop at the bottom of the track with a foam pad in front of it to cushion the impact of the cart. 4. Put a small piece of tape on the edge of the track about 15cm up from the end stop; put a second piece about 80cm up from this. Do not write on the track! 5. Set up the photogate near your lower point; make sure the cable extending from it is connected to Digital Channel 1 of the interface. 6. The fence (what will block the signal from the photogate) in his case is the pice of cardboard sticking up from one of the long sides of the plastic plate. Attach the plate to the top of the cart so that the carboard is sticking up at the front of the cart. Place the cart on the track. 7. Adjust the location and height of the photogate. The beam should be at the center of the cardboard piece (only) when the bottom front of the cart is at your first piece of tape. 8. The assembled apparatus is shown below, minus the foam pad so you can see more of the track. Data Collection 1. The first set of trials uses an empty cart. Record its mass as m total. 2. Determine h. A convenient set of points for your measurements of h 1 and h 2 would be your pieces of tape. 3. Calculate the potential energy U that will be lost by the cart. 4. Position the cart so that bottom front of the cart is at your upper piece of tape. Click the Record button and release the cart; v 2 will be displayed after the cardboard travels through the photogate. No need to click Stop; from this point on, the photogate will only collect data if its beam is blocked and unblocked. Repeat 4 more times and calculate the average v 2. 2
5. Calculate the kinetic energy K gained by the cart. 6. Calculate the percent difference between U and K. 7. Place the load mass in the cart and repeat the procedure - keep h the same. 8. Remove the load mass from the cart and repeat the procedure with a different h. 3
Data Sheet Cart mass (kg) Load mass (kg) m total (kg) h 1 (m) h 2 (m) h (m) U (J) v 2 (m/s) v 2 (m/s) K (J) % difference 4
Analysis 1. Based on your percentages, do you believe that energy was conserved? What do you think is the largest source of error in the experiment? 2. When you increased the mass, what happened to the measured velocity? What about the calculated kinetic energy? Why is this? 5
Pre-Lab: Conservation of Energy Name Section Answer the questions at the bottom of this sheet, below the line (only) - continue on the back if you need more room. Any calculations should be shown in full. 1. Read the lab thoroughly; check the lab manual for any additional information. 2. What is the SI (mks) unit of energy? What is this in terms of other SI units? 3. If m = 250g, h 1 = 15.2cm, and h 2 = 8.6cm, what is U? 4. What must v 2 be in order for energy to be conserved? 5. What cushions the cart impact in this experiment? 6