FMO1 Final Kress

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Iowa State University *

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131L

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Physics

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Apr 3, 2024

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Lab FMO1 - Forces and motion Equipment  Motion detector  Force probe  A cart that rolls on an aluminum track. The cart has an adjustable friction pad, and is equipped with a wooden fixture for mounting the force probe horizontally on the cart.  Spirit level  Various masses, string and a pulley, to apply a force to the cart.  A scale (one or two in the room) Lab FMO1 – Page 1

Experimental setup The main apparatus is depicted below. The string should be 162-164 cm long , including the loop at each end. Check its length by stretching it gently on the measuring jig, or use a meter stick. Adjust or replace it if necessary; string and scissors are available. The cart and track  Handle and push the carts gently .  The two stops on the track (near the 20 cm mark and the 170 cm mark) prevent the cart from getting too close or too far from the motion detector.  The track should not wobble and should be leveled .  Check now and several times during today’s lab that the track’s feet are not too close to the end of the table. The track tends to slide about. The motion detector The motion detector system measures the distance to the nearest object in front of the detector. It emits short bursts of sound of ultrasonic frequency and detects any reflections of this sound that come back. It measures the time between the emission of the burst and the first reflected sound (above some threshold level), and transmits this time information to the computer. From this, the computer software calculates the distance to the reflecting surface by using the known speed of sound (in air at room temperature). This process is similar to that used by some auto-focus cameras, as well as the echo- location process that bats use. Lab FMO1 – Page 2

The motion detector fills a cone-shaped region with sound. The motion detector will measure the distance to the closest object within that cone. The object that should reflect the first sound received by the motion detector is the plate on the cart; when you are pushing the cart, be sure that you and your hand are farther from the motion detector than the plate. "Bad" data points often are the result of an unwanted object being in the "cone" of sound. Preparation of the force probe We are now ready to incorporate force into the picture. Reattach the string and weight to the force probe as shown in figure 1. Check that the probe switch is set to 10 N. Download and open Forces and motion.cmbl Calibration of the probe Before any real measurement, it is necessary to calibrate the force probe: we need to provide two reference points to the computer so that the software can compute the relation between the voltage measured by the probe and the force it represents. At the other end of the string, we will hang two different hooked weights.  Go to Experiment > Calibrate  Choose the Dual Range Force probe.  In the Calibrate tab, click Calibrate Now.  Carefully hang the smallest available weight at the end of the string. Make sure that the probe and cart are not moving, and that the weight does not oscillate at the end of the string. In the provided space, enter in the weight of the hooked mass, and then click Keep.  Repeat the procedure with the largest available hooked mass  At the end, click Done. Your force probe is now calibrated. Check the calibration by taking a data run. Hang different weights from the hook and collect some data. (Results should be within a few percents of the theoretical value). You can also push and pull the hook manually to check that negative/positive values make sense. Zeroing the probe You should not have to recalibrate the probe again. However, the probe should be zeroed each time before making a measurement.  Check that no force is applied to the hook of the probe (nothing should be attached to it)  Set the probe in the orientation in which it will be used.  Click Zero on the toolbar or in Experiments > Zero. Lab FMO1 – Page 3

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Background The figure below shows the forces acting on the cart+probe system (of total mass M ), and on the hanging weight at the end of the string (of mass m ). When the cart is released, both objects move with acceleration a . Which of these forces does the force probe measure? The tension force, T. Prediction What is the expected relationship between the measured force and the acceleration of the cart? Describe it in terms of an equation and with a graph. As Tension increases, the acceleration must increase because we are keeping the mass of the cart constant within the equation T = Ma + F(fr). Lab FMO1 – Page 4

Experiment Each hanging weight at the end of the string results in a different tension T and different acceleration a in the system. Your goal is to verify the predicted relationship between tension and acceleration. Data collection Friction The cart has a friction pad underneath it to produce friction if desired. Using the plastic screw behind the cart’s reflective plate, lower the friction pad of the cart until it touches the track. We want enough friction to be noticeable, but not so much that the cart has trouble moving. Please do not turn the screw all the way out. Test run For the first data run, use a relatively small hanging weight to pull the system. Hold the cart at rest on the track, as far away as possible from the pulley. Start data collection on Logger Pro, wait about 1 second, and release the cart. The acceleration of the cart should be more or less constant while the cart is moving freely. The average acceleration can be obtained in two ways: you can either use the Statistics tool in the a vs. t graph, or the Slope tool in the v vs. t graph. Record your measurement below. 0.0619 m/s 2 Use the Statistics tool to obtain the value of the average force acting on the cart while the cart is moving freely. -0.0047 N Compare the value of the force while the cart was at rest to the force during the time when the cart was accelerating. (You may want to expand the vertical scale of your force graph to compare these regions more carefully.) Explain. While the cart was at rest in the first part of the graph, the force was zero and then when the cart was accelerating, the force was negative. Insert a screenshot of the LoggerPro window showing the graphs and measurement boxes for this first run. Lab FMO1 – Page 5

Lab FMO1 – Page 6

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Data Collect data for the tension and the acceleration for at least 10 different hanging weights. Collect the data in a table, with appropriate units and labels. Insert the table below. Data analysis and conclusions Plot T vs. a. Does the plot match your prediction? Explain. Yes! Our prediction was that the tension and acceleration would increase proportionally. Use the plot to estimate the mass of the cart+probe system. Show your calculation below. Our mass of the cart+probe is the slope of our graph because the slope is N/m/s 2 , which is kilograms. The value that we found from the linear fit is 1.040 ± 0.0343 kg. Weigh the cart+probe system with one of scales in the room and record the measurement below. 771 g or 0.771 kg. Lab FMO1 – Page 7

Use the plot to obtain an estimation of the frictional force between the cart+probe system and the track. According to our linear fit, the b value is our frictional force because T = Ma + F(fr) and T is equal to y, a is equal to x, M is our slope so that means that b is equal to our frictional force. This value is 0.05471 ± 0.0347 N. Insert your plot below. Lab FMO1 – Page 8

FMO1 Final Kress

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