� MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.01T Fall Term 2004 Experiment 06: Work, Energy and the Harmonic Oscillator Purpose of the Experiment: In this experiment you allow a cart to roll down an inclined ramp and run into a spring that is attached to a force sensor. You will measure the position and velocity of the cart and the force exerted by the spring while it is compressed. Then you will attach the cart to the force sensor by a spring and make a harmonic oscillator. Finally, you will replace the spring by a rubber band and see the effect of a non-ideal spring. You will do the following things in this experiment: • You will investigate experimentally the work–kinetic energy theorem, how potential energy in a gravity field converts to kinetic energy which is then converted into the potential energy of a compressed spring. • You will observe and quantify the effect of non-conservative forces and estimate the work done by these forces at various stages of the cart’s motion up and down the ramp. • You will measure how well a harmonic oscillator spring obeys Hooke’s Law, test the formula for the resonant frequency of a simple harmonic oscillator, ω = k/m, and explore the idea of lissajous patterns to study the relationship between variables. • You will observe that a rubber band does not obey Hooke’s Law, and the significant energy loss when a rubber band is stretched and released. Setting Up the Experiment: Refer to the photo to the right and the figure at the top of the next page. A force sensor should be mounted at the end of the track that has an adjustable support sc rew—which should be screwed in enough that the end of the track can lie flat on the table. Clip the motion sensor to the other end of the track and raise it by placing a short piece of 2 × 4 under the motion se nsor where it clips onto the track, as you can see in the photo to the right. This should raise the end of the track 4.2 cm above the table (measure it); you can find the slope θ as the track is 122 cm long. The heavier of the two springs available should be screwed into the force sensor. Experiment 06 1 October 20, 2004yx4.2 cmθPlace a cart on the track with the end having the VelcroTM patches facing the motion sensor. Put two 250 gm weights in the cart, which will bring its total mass to 750 gm. (The extra mass reduces vibrations and gives less noisy measurements.) Place the cart about half way up the track from the force sensor and release it. It will roll down the track, bounce most of the way back up, and repeat that several times. You may notice the track slides when the cart runs into the spring. This is an example of conservation of momentum. To prevent the track from sliding, place your thumb on the end of the track resting on the table and press it firmly against the table. Setting Up DataStudio: Connect the motion sensor (yellow plug into jack 1) and the force sensor to the 750 interface. The slide switch on top of the motion sensor should be set to the narrow beam position. Drag the appropriate icons to the 750 in the experiment Setup window. Double-click the force sensor icon to open the Sensor Properties window. Experiment 06 2 October 20, 2004You don’t need to calibrate the force sensor, but set it to Low Sensitivity under the Calibration tab and be sure to tare it before making measurements. Under the General tab set the force sensor Sample Rate to 500 Hz and click OK. Return to the Experiment Setup window and double-click the motion sensor icon. Under the Measurement tab, check the boxes so that position, velocity and acceleration will be measured. You should calibrate the motion sensor because the speed of sound varies slightly from day to day. Rest the cart against the spring on the force sensor and measure the distance between the motion sensor and the end of the cart closest to it. The motion sensor works best if it is angled up slightly rather than pointing directly at the cart. (That reduces the effect of sound waves that bounce off the track before hitting the cart.) Select the Motion Sensor tab and type the distance you measured into the Calibration Distance window and click the Calibrate button. This will be the point x0 where the cart and relaxed spring make contact. Set the Trigger Rate to 60 Hz and click OK. Next, set the start and stop conditions. Click the Options button. None of the boxes under the Manual Sampling tab should be checked. In the experiment you will let the cart roll into the spring starting from res t about 30 cm up the track from the point x0 where it first touches the spring. A convenient way to start the experiment is to hold the car on the track about 30 cm above the spring and measure the position with the motion sensor. (In my e xperiment that was 0.52 m.) Set the Automatic Start condition to begin measurements when the distance from the motion sensor first rises above this distance (see next page). To make a measurement, you can hold the cart 1 or 2 cm up the track from this position, click the Start button, and release the cart. Experiment 06 3 October 20, 2004Under the Delayed Start tab click the radio button for Data Measurement, choose “Position, Ch 1&2 (m)” from the pull-down list, set the start condition to Rise Above 0.52 m (or the appropriate number for your experiment), and keep data from 0.5 s before the start condition. Then under the Automatic Stop tab click the Time radio button and type in 10 s. Prepare to plot your measurements by dragging the Force and Position entries from the Data window onto the Graph icon in the Displays window. That will make two graphs. Tare the force sensor, hold the cart at a position 1 to 2 cm above the point you chose for the Delayed Start condition, click the Start button, and when you see yellow numbers in the counter window release the cart. You should see the position and force plotted on your graphs as the cart bounces up and down the track. These graphs contain a wealth of information. The position graph shows the sharp reversal of direction that occurs when the cart collides with the spring (and the force graph shows a corresponding spike in the force). You can see the slower reversal of direction as the cart coasts to high turning points on the track (the first two are marked by
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