PHYSICS LAB Experiment 6 Fall 2004 WORK AND ENERGY GRAVITY

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Piers Day
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1 PHYSICS LAB Experiment 6 Fall 004 WORK AND ENERGY GRAVITY In this experiment we will study the effects of the work-energy theorem, which states that the change in the kinetic energy (1/Mv ) of an object is equal to the work done on the object by all external forces: (1) We will study the work done by the gravitational force. This work equals the gravitational force times the displacement,. () nd This can also be understood in terms of Newton s Law. THE THEORY Consider a small mass m is suspended from a string which passes over a pulley to a glider of mass M. The mass m is held in place and then released. After it falls a distance y (during which time the glider also moves a distance y) it will have a velocity, v. Because they are attached by the string, both masses will have the same velocity, v. The initial kinetic energy, K i, of the system consisting of the two masses is zero (they are at rest). The kinetic energy of the system when they have moved a distance y is given by K f = ½(M+m)v. So, from this plus equations (1) and () above, we have nd [Note that we get the same result by applying Newton s Law to this system. The acceleration of the system is a = mg/(m+m). Then using v = ay, we get (3) above] If we plot v as a function of the ratio m/(m+m), we expect to obtain a single straight line with slope equal to gy. (3) 1

2 PHYSICS LAB Experiment 6 Fall 004 DATA COLLECTION The apparatus consists of a glider of mass M which travels on a frictionless air track, and a light source and photocell supported above the air track. The photocell controls an electric stopclock, which measures the time interval T during which the light beam is interrupted as the glider travels the length L of the attached flag. Measurement of T with this phototimer allows the velocity of the glider to be determined as v = L/T. (4) The glider is attached by a string over a pulley to a small mass m hanging down from the pulley. 1. Remove the mass m and the string from the glider.. Record the mass M of the glider. 3. In order to accurately measure L move the glider slowly into the light beam. Record the position of the glider when the phototimer starts counting (where the flag begins to obscure the photocell) and the position where the phototimer stops counting (so the flag is just out of the light beam incident on the phototimer). The difference in these two positions is the effective length of the flag. 4. Reattach the mass m to the glider with the string over the pulley. 5. Choose a reasonably small distance upstream of where the middle of the flag intercepts the photocell (see 3.), e.g. 30 cm. This distance will be y in equations () and (3) above. Use this same starting position for all measurements. 5. Measure the velocity of the system for several values of m and fill out the data table. As usual, record several (e.g.4) trials for each value of m in order to obtain a reliable average measurement. Make sure the hanging mass, m, is not swinging when the system is released from rest. DATA ANALYSIS 1. Plot v vs. m/(m+m) [Make sure to include the point (0,0)]. Draw the best straight line through your data points. 3. Answer the questions on the worksheet.

3 PHYSICS LAB Expt 6 Worksheet Fall 004 WORK AND ENERGY GRAVITY STUDENT NAME DATE PARTNER S NAME LAB SECT Mass of the glider M = gm Glider flag: position 1: cm position : cm Total length L = cm Distance of starting position from photocell y = cm Table 1: Suspende d mass m (grams) Flag fly-by time T (seconds) trial 1 trial trial 3 trial 4 Avg. Velocity v units = v units = (~5) (~10) (~15) (~0) (~5) 1

4 PHYSICS LAB Expt 6 Worksheet Fall 004 QUESTIONS 1. From you graph of v as a function of m/(m+m), determine the value of the slope for the best fit line through your data points. Show your work (on your graph). (a) What is the expected value for the slope extracted from your graph? (b) What is the difference between measured and expected values in terms of a percentage difference. Show your work. (c) State two possible mechanisms by which the experiment could bias the measured slope. Explain briefly how the slope would be affected (Answer this question whether your measured value is close to the expected value or not.)

5 PHYSICS LAB Expt 6 Worksheet Fall 004 nd 3. Write down Newton s Law for the system consisting of the glider and the suspended mass. (Write it in the form F = ma) 4. If the force is expressed in terms of units, what are the corresponding units for work? Provide an answer in terms of kg, m, and s, as applicable. 5. In this experiment, we neglect the frictional force f (remember that f>0) between the glider and the track. However, if friction were not negligible, how would you modify the expression for the work done by all external forces? Write the new expression for the work W as would apply to the experiment. 3

6 PHYSICS LAB Expt 6 Worksheet Fall 004 At the end of the lab, turn in your worksheet with the data and answered questions as well as your graph. 4

PHYSICS LAB Experiment 3 Fall 2004 CENTRIPETAL FORCE & UNIFORM CIRCULAR MOTION

PHYSICS LAB Experiment 3 Fall 2004 CENTRIPETAL FORCE & UNIFORM CIRCULAR MOTION CENTRIPETAL FORCE & UNIFORM CIRCULAR MOTION In this experiment we will explore the relationship between force and acceleration for the case of uniform circular motion. An object which experiences a constant