Physics 250 Laboratory:

Transcription

1 Physics 250 Laboratory: Score: Section #: Name: Name: Name: Lab-Specific Goals: To examine the conservation of energy during transformations among gravitational potential, elastic potential and kinetic energy. Equipment List: Photogate timer Air Track with one glider Flag on glider Spring launcher at one end of track to launch glider Ruler Block for setting air track at an angle Introduction and Pre-Lab Questions: Energy can take numerous different forms. In this course you have learned about gravitational potential, elastic potential, kinetic, rotational kinetic and thermal. While energy can change forms, the total energy in a closed system never changes. This concept of the conservation of energy was not a single discovery, but rather was an idea that developed during the late 18 th and first half of the 19 th centuries. The unit for energy, Joules, is named after one of the important experimenters in this area, James Prescott Joule, who in 1843 showed that the decrease in gravitational potential energy in a system was equal to the increase in its thermal energy. In this lab, you will explore energy transformations among gravitational potential (U G = mgh), elastic potential (U E = ½ kδl 2 ) and kinetic (K= ½ mv 2 ) energy and whether the total energy (T E = U G + U E + K) in a system remains constant. We will be assuming negligible energy transformation to thermal energy (i.e., friction between the glider and track is negligible). One visual way of representing energy and energy transformations is with energy bar charts. For example, consider a pop-up toy with a compressed (massless) spring that releases launching the toy vertically. Here are sample energy bar charts for four different points: before the spring releases, immediately after the spring has completely released, halfway to the top, and at the top of its trajectory.

2 U E K U G T E U E K U G T E U E K U G T E U E K U G T E U E K U G T E Activity 1: Launch Speed and Spring Compression 1. Set up the airtrack so that it is level, with one photogate somewhere near the launcher (but far enough away so that the launcher will have completely released before the glider passes through the photogate). 2. Set the photogate in GATE mode. 3. Measure the glider s speed as a function of ΔL, how much the spring in the launcher was compressed. Collect four speeds for each ΔL and find the average value. NOTE: Record the individual photogate times for each run and then calculate the average speed from the average time. Experimental notes: (1) Make sure your track is level before beginning. (2) Make sure your glider is touching the spring mechanism when the spring releases. When the track is level, you may need to exert a very tiny force on the glider with your finger to keep it in contact with the spring mechanism before you release the spring.

3 (3) The spring mechanism can be set so that it locks at the same setting (ΔL) every time. Your instructor will show you how to set this lock. (4) Make sure the spring mechanism hits the glider straight on at not at an angle. Position the launcher to hit the glider as low as possible (while still being able to release the spring). Run 1 Run 2 Run 3 Run 4 Average time (s) Average speed (m/s) ΔL = m ΔL = m ΔL = m ΔL = m ΔL = m Mass of glider = kg 4. Graph your data (average v versus ΔL) on the graph paper on the following page. Draw a line of best fit that goes through the origin. Why does it have to go through the origin? 5. From conservation of energy (½ kδl 2 = ½ mv 2 ), how is k related to the slope of this graph? What value for k (in N/m) do you get?

4 Graph for Activity 1

5 Activity 2: Max Height and Spring Compression You will be launching the glider again, but this time it will be up an airtrack at an angle. Explain in words what is happening in your experiment in terms of energy. On the diagram below, draw energy bar charts for before you launch the object (at the bottom right), after you launch the object, and when the object is at its peak height. 1. Set up the airtrack so that it is up at an angle by putting a block under one of the legs. 2. You will not need the photogate in this activity. 3. Be sure to determine the angle θ you use since you will need it later. (You can determine θ from the height of the block and the space between the sets of legs.) 4. Measure the glider s peak height as a function of ΔL, how much the spring in the launcher was compressed. Collect four maximum heights for each ΔL and find the average value. Don t forget that when you compress the spring you change the initial height of the glider. (Note: find the average distance along the track and then use trig to find the average Δy for that ΔL.) 5. Use the data tables below to organize your data. Do four runs for each ΔL, measuring the distance the glider moves along the track, and then take the average value. Then calculate the average height the glider rose from the distance it moved along the track. Below the table show your calculations for how you got height from distance the glider moved. θ = degrees (note: tanθ = height of block / distance between legs) Run 1 Run 2 Run 3 Run 4 Average distance along track Average Δy of glider ΔL = m ΔL = m ΔL = m ΔL = m ΔL = m 6. Graph your data (average Δy versus ΔL 2 ) on the graph paper on the following page. Draw a line of best fit that goes through the origin. (Why does it have to go through the origin?)

6 Graph for Experiment 2

7 7. From the conservation of energy condition (½ kδl 2 = mgδy), how is the spring constant related to the slope of your best fit line? 8. What is the spring constant of your spring according to this experiment? 9. What is the % difference between your two k values? Is there good agreement (< 10% percent difference) between your values? 10. What is the average spring constant k for your spring (from your two experiments)?

8 Activity 3: All Three Kinds of Energy (Gravitational, Elastic, Kinetic) 1. Prediction time: With your glider track still at an angle, pick a ΔL for the spring and position your photogate about halfway up the track from the maximum height that the glider went for that ΔL. Predict what the speed of the glider will be using conservation of energy: Distance along track from starting position to photogate m Δy from starting position to photogate position: m Predicted speed = m/s (show your calculations below) BEFORE YOU DO THE EXPERIMENT, WRITE YOUR PREDICTION ON THE BOARD (with your first names) or get your instructor to come over to your station if he/she is available. 2. Now test your prediction (do 5 runs and take the average): Average speed = m/s 3. How did it compare? (e.g., what was the % difference between your prediction and your measured value?)