PHYS 101 Lab Report, Spring 2008

ROTATIONAL INERTIA 1. Object: The purpose of this experiment is to measure the rotational inertia of a disk and a ring experimentally and compare it with the theoretical value and to experimentally test the parallel axis theorem. 2. Equipment: Science workshop interface, PC, Smart pulley, rotational apparatus, mass set and hanger, balance, caliper, string. 3. Theory: The rotational inertia of a homogenous disk of radius R and mass M about an axis perpendicular to its surface and passing through the center of the disk is given by: (1) The rotational inertia of a ring of mass M and radiuses R1 and R2 is given by: (2) To find the rotational inertia of the disk (or ring) experimentally, a known torque is applied to the disk and the resulting angular acceleration is measured : R1 R2 Ring of radiuses R1, R2 and mass M. R Disk of radius R and mass M. Perpendicular rotational axis Parralel rotational axis (3) Where,  is the angular acceleration in (rd/s2) and  is the torque in (N.m). (4) By definition the torque is equal to: (5) Where r is the distance from the center of the ring to the point where the force is applied. If and are perpendicular, then: (6) In our experiment, the force is the tension T in a string that is tied to a step pulley that is part of the rotational apparatus. The string is pulled by a hanging mass m. The value of r is the radius of the step pulley on the apparatus (See figure 1). The radius is perpendicular to the tension. Therefore, the torque is: (7) Figure 1. Rotational inertia apparatus. Applying Newton’s second law for a hanging mass result in: (8) 2 mg T ? Ring Step pulley Smart pulley Object of Known Mass To Digital Channel 1 Where a is the tangential acceleration of the rotating apparatus and m is the hanging mass. (9) thus, Using Equations (3), (8) and (9) we obtain: (10) 4. Procedure and Analysis: For this activity, the smart pulley measures the motion of a hanging mass that is connected by a string to a step pulley on the rotational apparatus. The Science Workshop program calculates and displays velocity versus time, the slope of this curve is the acceleration. 1. Set up the rotational accessory, first mount the disk only. 2. Connect the science workshop interface to the computer and turn it on. 3. Connect the stereo phone plug of the smart pulley to Digital Channel 1 on the interface. 4. Open the file titled P26_ROTA.SWS, found in the hard disk c:/Phys105. The document opens with a graph display of Velocity (m/s) versus time. 5. Measure the diameter of the smallest step pulley on the main plotter of the rotational apparatus measure the radius of the disk. 6. Use a string that is about 10cm longer than the distance needed to reach from the spindle of the rotational apparatus over the smart pulley and down to the floor. Tie one end of the string to the edge of the smallest step pulley of the rotational apparatus. Then put the string in the groove of smart pulley adjust leveling. 7. Attach 500g to the string and wind the string around the step pulley of the disk by rotating the disk until the mass hanger is raised almost to the smart pulley. Hold the system in this position. 8. Click the REC bottom to begin recording data and then release the disk. 9. Click STOP bottom just before the mass hanger reaches the floor. Note RUN#1 will appear in the DATA list in the experiment set up window. 10. Repeat steps 7 to 10 for the acceleration of the disk. RUN#2 will appear in the DATA list in the experiment set up windows. 11. Record in both cases the value of slope by opening the statistic mode. 3 12. Determine the rotational inertia of the disk and compare it with the theoretical value. 13.Add the ring on the top of the disk and repeat 7,8,9,10, 11. Deduce finally the value of rotational inertia of the ring and compare it to the theoretical value using Equation (2). Note that the rotational inertia of the system disk plus ring is : Itotal = Idisk +Iring 14. Perform the same experiment using the disk, but this time change the rotation axis to be passing through the plane of the disk. 4 Physics 105 Rotational Inertia Radius (m) Radius of Step pulley (r) 0.01875 m R1 inner radius of the ring 0.05375 m R2 outer radius of the ring 0.0635 m R radius of the disk 0.115 m Rotational inertia of a disk about a axis perpendicular to its surface and pasing through its center: Hanging mass m = 0.5 Kg Mass of the disk MD = 1.407 Kg Acceleration a (m/s2) IExperimental = mr2 Itheoretical = % Error Run #1 0.232 m/s2 0.00726 Kg.m2 0.00930 Kg.m2 21.9 % Run #2 0.233 m/s2 0.00723 Kg.m2 0.00930 Kg.m2 22.2 % Run #3 0.231 m/s2 0.00729 Kg.m2 0.00930 Kg.m2 21.6 % Run #4 0.230 m/s2 0.00732 Kg.m2 0.00930 Kg.m2 21.3 % Calculate the average experimental rotational inertia of the disk, and determine I. How can you reduce friction in order to obtain better result, explain. Average Experimental Rotational Inertia = 0.00728 ± 0.00002 Kg.m2 The best way to reduce friction is to use smoother objects or to use lubricants such as oil or cream. Rotational inertia of the system disk plus ring: Hanging mass m = 0.5 Kg Mass of the ring MR = 1.436 Kg Run Acceleration (m/s2) IExperimental = mr2 Itheoretical = % Error #1 0.152 m/s2 0.0112 Kg.m2 0.0143 Kg.m2 21.7 % #2 0.151 m/s2 0.0112 Kg.m2 0.0143 Kg.m2 21.7 % #3 0.153 m/s2 0.0111 Kg.m2 0.0143 Kg.m2 22.4 % #4 0.152 m/s2 0.0112 Kg.m2 0.0143 Kg.m2 21.7 % Deduce the experimental rotational inertia of the ring and compare it with the theoretical value. Comment. Theoretical Rotational Inertia = 0.00497 Kg.m2 Experimental Rotational Inertia = 0.00392 Kg.m2 Error = 21.1 % Our values are very precise but the accuracy isn’t that great, but acceptable. Rotational inertia of a disk about a axis passing along its surface: Hanging mass m = 0.5 Kg Mass of the disk MD = 1.407 Kg Acceleration a (m/s2) IExperimental = mr2 Itheoretical = % Error Run #1 0.416 m/s2 0.00397 Kg.m2 0.00465 Kg.m2 17.1 % Run #2 0.415 m/s2 0.00398 Kg.m2 0.00465 Kg.m2 17.1 % Run #3 0.415 m/s2 0.00398 Kg.m2 0.00465 Kg.m2 17.1 % Run #4 0.414 m/s2 0.00399 Kg.m2 0.00465 Kg.m2 17.0 % Calculate the average experimental rotational inertia of the disk, and determine I. How can you reduce friction in order to obtain better result, explain. Average Experimental Rotational Inertia = 0.003980 ± 0.000004 Kg.m2 Same as before you should use smoother objects and lubricants to reduce friction as much as possible. Physics 105 Rotational Inertia Name:_________________________ Section:______________________ Partner's name:__________________ Instructor:____________________ Radius (m) Radius of Step pulley (r) R1 inner radius of the ring R2 outer radius of the ring R radius of the disk Rotational inertia of a disk about a axis perpendicular to its surface and pasing through its center: Hanging mass m = Kg Mass of the disk MD = Kg Acceleration a (m/s2) IExperimental = mr2 Itheoretical = % Error Run #1 Run #2 Run #3 Run #4 Calculate the average experimental rotational inertia of the disk, and determine I. How can you reduce friction in order to obtain better result, explain. Rotational inertia of the system disk plus ring: Hanging mass m = ____ Kg Mass of the ring MR = Kg Run Acceleration (m/s2) IExperimental = mr2 Itheoretical = % Error #1 #2 #3 #4 Deduce the experimental rotational inertia of the ring and compare it with the theoretical value. Comment. Rotational inertia of a disk about a axis passing along its surface: Hanging mass m = Kg Mass of the disk MD = Kg Acceleration a (m/s2) IExperimental = mr2 Itheoretical = % Error Run #1 Run #2 Run #3 Run #4 Calculate the average experimental rotational inertia of the disk, and determine I. How can you reduce friction in order to obtain better result, explain. CONSERVATION OF MECHANICAL ENERGY 1. Object: The purpose of this experiment is to test the conservation of energy of a system by using a falling object and rotational system. 2. Equipment: Science workshop interface, Smart pulley, Balance, Masses and hangers set, Meter stick, Rotational apparatus, PC, and Vernier caliper. 3. Theory: The gravitational potential energy of an object of mass m and a distance h from the floor is given by: PE = mgh (1) where g is the acceleration due to gravity. The Kinetic energy of a rotating object depends on its rotational inertia I and its angular speed ω. The rotational kinetic energy is given by: (2) A falling object has also translational Kinetic energy given by: KET = (3) Where m is the mass of the falling object and v its velocity. Conservation of Mechanical Energy between the initial and final position gives: mgh = (4) Main plotter Step pulley Smart pulley h Initial position (h1) Final position (h2) 4. Procedure: For this activity, the rotational inertia of the main plotter of the rotational apparatus should first be calculated. We will use the same method as in the previous experiment where the smart pulley measures the motion of the plotter as it is accelerated by a net torque. The science workshop program calculate and displays the speed of the system versus time, and the tangential acceleration could be determined from the slope. To find the rotational inertia of the main plotter, a known torque is applied to the main plotter and the resulting motion is measured. From the previous experiment we know that: (4) Make necessary measurements and determine the rotational inertia of the main plotter Iplotter. After finding Iplotter hang a mass attached to the step pulley on the main plotter using a string and allow the mass to fell. The smart pulley measures the motion of the main plotter and that of falling object. The science workshop program calculate and displays the speed V of the falling mass also used to calculate the angular speed of rotating plotter and change in rotational kinetic energy. 1- Connect science workshop interface. 2- Connect the smart pulley’s stereoplane plug into digital channel 1 of the interface. Open file titled P29_GRAV.SWS, found in the hard drive directory C:/PHYS105, The document will open with a graph display and a table display of velocity. The velocity isufy tells you how fast the falling object is dropping. The velocity will be used to determine angular speed of plotter and the object translational K.E. 3- Put the rotational apparatus box near the edge of the table and place main plotter on the spindle. 4- Mount the smart pulley’s rod vertically in the table clamp. 5- Use a piece of string about 50 cm longer than the distance from the top of the smart pulley to the floor. Put one end of the string through the hole in the edge of the smallest step pulley on the main plotter and thread the string upward through the hole. Then tie the string around the round head screw on the step pulley. 6- Attach mass hanger to other end of the string. (Use 200 g). 7- Wind the string around the plotter’s step pulley by rotating the plotter until the mass hanger is raised almost to the smart pulley. Hold the plotter. 8- Click REC button to high recording data and release the plotter. Click the STOP button just before the falling mass reach floor. 9- Run#1 will appear. Measure the diameter of the step pulley using caliper. 10- Adjust the position of the mass hanger on the string. Attach the hanger so it is high enough on the string that it will not hit the floor at its lowest position. Measure h2 and h1. 11- Click REC and release the plotter allow the mass to reach lower position and then click stop. Repeat several time keeping h1 constant using different mass:100, 150, 200g. 12- Click experiment menu in the menu bar and select RUN#1 data and graph now can be displayed. 13- The maximum speed corresponds to the point whose gravitational potential energy of the falling object reached a minimum and rotational kinetic energy of the plotter reached maximum. 14- Calculate the rotational kinetic energy of the main plotter. Remember that =v/r where r is the radius of step pulley. 15- Record the maximum linear speed V and maximum rotational kinetic energy for RUN#1. 16- Repeat analysis for all data run by selecting each run from the experiment menu, and fill in the data sheet. Calculate total K.E, the sum of maximum rotational K.E and maximum linear kinetic energy. Calculate PE of falling object. 17- Make percent error and comment on conservation of energy. Physics 101L CONSERVATION OF MECHANICAL ENERGY Rotational inertia of the main plotter: Hanging mass m = 0.200 Kg Mass of the main plotter Mplotter = 1.410 Kg Radius of Step pulley (r) = 0.01855 m Acceleration a (m/s2) IPlotter = mr2 Run #1 0.076 m/s2 0.0088 Kg.m2 Run #2 0.080 m/s2 0.0084 Kg.m2 Run #3 0.078 m/s2 0.0086 Kg.m2 Run #4 0.077 m/s2 0.0087 Kg.m2 What is the average value of the main plotter’s rotational inertia? I average = 0.0086 ± 0.0001 Kg.m2 Conservation of Mechanical Energy: Run Mass m (Kg) h =h2-h1 Vmax (m/s) (J) Total K.E. (J) mgh (J) % diff. 1 0.300 Kg 0.9375 m 0.449 m/s 2.52 J 0.020 J 2.54 J 2.76 J 7.97 % 2 0.250 Kg 0.9375 m 0.411 m/s 2.12 J 0.017 J 2.14 J 2.30 J 6.96 % 3 0.200 Kg 0.9375 m 0.369 m/s 1.70 J 0.014 J 1.71 J 1.84 J 7.07 % 4 0.150 Kg 0.9375 m 0.320 m/s 1.29 J 0.010 J 1.30 J 1.38 J 5.80 % 5 0.100 Kg 0.9375 m 0.258 m/s 0.831 J 0.0067 J 0.838 J 0.92 J 8.9 % 6 0.050 Kg 0.9375 m 0.179 m/s 0.400 J 0.0032 J 0.403 J 0.46 J 12 % 1. Is the rotational Kinetic energy equal to the gravitational potential energy of the falling object? No they are not equal, since there are other factors that contribute to the overall Mechanical Energy. 2. How does the total kinetic energy compare to the gravitational potential energy of the falling object? They have to be equal. Physics 101L CONSERVATION OF MECHANICAL ENERGY Rotational inertia of the main plotter: Hanging mass m = Kg Mass of the main plotter Mplotter = Kg Radius of Step pulley (r) =_______________ m Acceleration a (m/s2) IPlotter = mr2 Run #1 Run #2 Run #3 Run #4 What is the average value of the main plotter’s rotational inertia? I average = ______________________________. Conservation of Mechanical Energy: Run Mass m (Kg) h =h2-h1 Vmax (m/s) (J) Total K.E. (J) mgh (J) % diff. 1 2 3 4 5 6 1. Is the rotational Kinetic energy equal to the gravitational potential energy of the falling object? 2. How does the total kinetic energy compare to the gravitational potential energy of the falling object? XI. Simple Harmonic motion 1. Object: To study the simple Harmonic motion of an oscillating spring and a torsional pendulum. 2. Apparatus: Spring, masses, torsion wire, Wheel with ball bearing, metal disk, metal ring, meter-stick, and stopwatch. 3. Experiment: When metals are subjected to a external stress, that is not too large so that the body is deformed completely, the deformation or strain is generally proportional to the stress. The metal body, in its attempt to return to its original shape exerts a restoring stress. Systems where restoring stress is proportional to the strain are said to obey Hooke’s law. A. Oscillating spring: When a mass m is hung from a massless spring, the gravitational force (stress) stretches the spring (strain) from its unloaded length L0 to a new length L1. If the spring obeys Hooke’s law then, F = - k(L1-L0) = -mg (1) Where F is the restoring force that is equal and opposite to the gravitational force mg, when the system is in equilibrium, and k is the spring constant in N/m. If the spring is stretched further and released, then at any length L the spring exerts a force –k(L -L0) on the mass and the net force on m is: F = -k (L-L1) = -kx (2) Where x represents the displacement of the mass from its equilibrium position at a spring length L1. The Equation of motion of m subject to this force is: (3) Equation (3) predicts that m will undergo simple harmonique motion according to: x = A sin(t +) (4) where A is the amplitude of the motion and w is the angular frequency. The period of the motion T is given by: (5) and is independent of the amplitude. B. Torsional pendulum: When a torque (stress) is applied to the torsion wire is twisted through an angle  (strain). In its attempt to return to its undistorted condition the wire exerts a restoring torque  that is proportional to the angular displacement from equilibrium . If the wire obey Hooke’s law, then  = -C (6) where C is the torsional constant of the wire in N.m/rad. If a rigid body is attached to this wire and the wire is twisted and released, the body undergoes simple harmonic rotational motion. The motion is purely rotational about a fixed axis, namely the wire, and the equation of motion of the body is: (7) where I is the rotational momentum of inertia of the body about the axis of rotation. The period of the motion that is again independent of the amplitude is given by: (8) 4. Procedures: A. Oscillating spring: 1. Hang different masses (up to 1000 g) on the spring and measure (L1 – L0). Plot a graph of mg against (L1 – L0) and find k using Eq. (1). Comment. 2. Hang masses (up to 1000 g in steps of 200 g) on the spring and set them into oscillation. Measure the period T by timing a few oscillations using the stopwatch. Plot T2 versus m. 3. Find k from the slope of the second graph and compare with the value obtained in part 1. 4. If the mass of the spring ms is not negligible then the Equation of motion is modified and Eq. (5) becomes (without proof): (9) the system behaves as if a larger effective mass (m + ms/3) is attached to a massless spring. When ms << m Eq. (5) can be used safely. From the intercepts of the second graph evaluate ms. Measure ms and compare. B. Torsional pendulum: 1. Mount the wire on the hub of the wheel and clamp the other end. Using a set of weights, apply torques to the wire and measure the angular displacement . Plot  versus and find C. 2. Mount the metal disk on the wire and hang it vertically using the provided clamps. Twist the wire and release it. Measure the period of the resulting motion. 3. Measure the mass and radius of the disk and find its moment of inertia. Calculate T using Equation (8). Compare with part 2. 4. Add the metal ring to the disk and repeat steps 2 and 3. Comment. PHYSICS 105 Exp. XI Simple Harmonique Motion Object: To study the simple Harmonic motion of an oscillating spring and a torsion pendulum A. Oscillating spring masses 200g 400 500 800 1000 L = L - Lo 0.200 m 0.405 m 0.513 m 0.837 m 1.033 m t(10 oscillation) 10.47 s 13.99 s 15.44 s 19.04 s 21.35 s T 1.047 s 1.399 s 1.544 s 1.904 s 2.135 s I. Plot mg against L - Lo and find k. K= 9.35 Comment: The graph of these two quantities is a straight line suggesting that they are directly proportional. II. Plot T2 against m and find k from the slope of the graph. Compare with the previous value. K= 9.19 This value is equal to the other K but there is a difference since there is an experimental error which we expect. Evaluate the mass ms of the spring from the graph and compare with the measured value. ms= 0.163 Kg B. Torsional pendulum a) Determination of C mass (Kg) 0.200 Kg 0.400 Kg 0.500 Kg 0.800 Kg 1.00 Kg  0.14 0.28 0.35 0.56 0.70  (degrees) 5.5 10 12.5 19 24 Plot  vs.  and find C C= 0.0304 b) metal disk hung vertically measure the period T1= 1.155 s for  r twisting angles T2= 1.172 s mass of disk M= 6.500 Kg radius of disk R= 0.142 m rotational inertial I= 0.0655 Kg.m2 Calculate T and compare with the previous experimental value. T= 9.213 s It should be equal with the experimental T but it isn’t and I am not sure why. c) Repeat the previous experiment after adding the metal ring. T1= 1.408 s T2= 1.424 s M of Disk= 6.500 Kg M of ring= 1.985 Kg R1= 0.121 m R2= 0.127 m I= 0.0961 Kg.m2 T= 11.2s Since C is a constant that doesn’t change, then the Rotational Inertia is the factor that can change the period. Now the Inertia is increasing in experiment (c). So the Period also increases since they are directly proportional. Also in this case the period should also be equal to the experimental value but it isn’t and I am not sure why. PHYSICS 105 Exp. XI Simple Harmonique Motion NAME: ____________________________ SECTION: ________ P_NAME: __________________________ INSTRUCTOR: __________ Object: A. Oscillating spring masses 200g 400 500 800 1000 L = L - Lo t(10 oscillation) T I. Plot mg against L - Lo and find k. Comment. II. Plot T2 against m and find k from the slope of the graph. Compare with the previous value. Evaluate the mass ms of the spring from the graph and compare with the measured value. B. Torsional pendulum a) Determination of C mass   Plot  vs  and find C b) metal disk hung vertically measure the period T1 = . . . . . . . . . . . . . . . . . for  r twisting angles T2 = . . . . . . . . . . . . . . . . . mass of disk M = . . . . . . . . . . . . . . . . . radius of disk R = . . . . . . . . . . . . . . . . . rotational inertial I = . . . . . . . . . . . . . . . . . Calculate T and compare with the previous experimental value. c) Repeat the previous experiment after adding the metal ring. Comment. Physics 101 L Exp. 1 Measurement A. Time Measurement 1. Stop watch Group 1 2 3 4 5 6 X   Beats/s 87 76 80 81 77 1.4 0.080 0.036 1.5 1.3 1.3 1.4 1.3 2. Vibrator : Calibration of the tick. Length of tape L = 2.00 meters Number of dots N = 176 dots Measured Time T = 5.0 seconds One tick = 0.028 seconds 3. Stroboscope The frequency (RPM): 1500 RPM The frequency (RPS): 25 Hz The time for 1 tick: 0.040 seconds Find the percentage error: 43% error B. Length Measurements : 1. Meter stick Area (A) = Length (L)  width ( W) L=2.0220  0.0005 ; W = 0.6100  0.0005 ; A =1.233 m2 ; A +0.001 A = (1.233  0.001) m2 2. Vernier Calipers Inner radius Outer radius 1 0.62 cm 0.73 cm 2 0.54 cm 0.66 cm 3 0.39 cm 0.48 cm Micrometer calipers Wire 1 Wire 2 Wire 3 0.83 mm 0.89 mm 1.00 mm C. Mass and Density Measurement : 1. Steel balls You will be given 3 different steel balls. Mass (g) Diameter (d) (d3) 1 27.7  0.05 g 1.89  0.01 cm 6.75  0.11 cm3 2 7.99  0.05 g 1.28  0.01 cm 2.10  0.05 cm3 3 5.40  0.05 g 1.09  0.01 cm 1.30  0.04 cm3 Using the table , plot the (mass) versus (d3) . Calculate the slope. Determine the density () from the slope. Find . Express as :  = (7.91  1.2) g/cm3 Physics 101 L Exp. 1 Measurement NAMES: ____________________________ I.D#: ______________ ____________________________ _______________ Section: __________________________ Date: ______________ A. Time Measurement 1. Stop watch Group 1 2 3 4 5 6 X   Beats/s 2. Vibrator : Calibration of the tick. Length of tape L = Number of dots N = Measured Time T = One tick = 3. Stroboscope The frequency (RPM): The frequency (RPS): The time for 1 tick: Find the percentage error: B. Length Measurements : 1. Meter stick Area (A) = Length (L)  width ( W) L= ; W = ; A = ; A + A = (  ) 2. Vernier Calipers Inner radius Outer radius 1 2 3 3. Micrometer calipers Wire 1 Wire 2 Wire 3 C. Mass and Density Measurement : 1. Steel balls You will be given 3 different steel balls. Mass (g) Diameter (d) (d3) 1 2 3 Using the table , plot the (mass) versus (d3) . Calculate the slope. Determine the density () from the slope. Find . Express as :  = (  ). I. MEASUREMENT 1. Object: To familiarize the student with some basic measuring instruments. 2. Apparatus: Stopwatch, Timer-vibrator, paper tape, stroboscope, meter stick, vernier calipers and micrometer calipers. 3. Experiment: A. Time measurements: Stopwatch. Use the stopwatch to measure your heart rate. Record the value on the black board, and when the rates of all students are recorded calculate the mean rate, the average deviation and standard deviation. Vibrator. Anything that performs steady oscillatory motion can be used as a clock. The time for one oscillation is a natural unit for making measurements. We shall call this unit a “tick”. If one wants to know how long is this natural unit of time is compared to a second then “Calibration has to be performed using a absolute standard such as a stop watch. To calibrate the vibrator we must find how much time it takes for one oscillation. Since this time is short we must measure the time for many vibrations. The vibrator is built as to print a dot on a paper tape every vibration. Your instructor will show you how. Cut a piece of tape approximately one to two meters long and pass it under the carbon paper. Start the vibrator and pull the tape at a uniform rate for about 5 seconds. The time of movement of the tape should be measured with the stopwatch. Count the number of dot, which is the number of oscillations and calculate the length of your “tick” in seconds. Repeat several times. Stroboscope. Your instructor will use a stroboscope to measure the time for an oscillation of your vibrator. B. Distance measurements: Meter stick. Use the meter stick to measure the length of your table. Calculate the area and estimates the uncertainties. Verniers Calipers. Use the verniers calipers to measure the inner and outer diameters of the provided tubes. The instructor will help you. Micrometer calipers. Use the micrometer calipers to measure the diameters of the provided wires. C. Mass and density: The density of a substance is defined as: (1) where m is the mass of the object and V its volume. The instructor will show you how to use the balance to determine the mass of the object. Steel balls: The volume of a sphere is given by, (2) where d is the diameter of the sphere and, (3) Measure the mass and diameters of three steel balls. Plot m against d3. The resulting graph is a straight line. Calculate  from the slope of this line. II. POSITION, SPEED AND ACCELERATION 1. Object: The purpose of this activity is to introduce the relationships between the motion of an object and a graph of position, velocity and time and to determine the acceleration due to gravity by measuring the time of fall of a “picket fence” dropped through a photogate. 2. Apparatus: Motion sensor, base and support rod, computer, PASCO Science workshop interface, photogate or smart pulley, picket fence, spring-loaded clothes pin, ruler. 3. Experiment: When describing the motion of an object, knowing where it is relative to a reference point, how fast and in what direction it is moving, and how it is accelerating is essential. In this experiment a sonar ranging device “PASCO motion sensor” uses pulses of ultrasound that reflect from object to determine the position of the object. As the object moves, the change in its position is measured many times in each second. The change in position from moment to moment is expressed as a velocity (meters per second). The change in velocity from moment to moment is expressed as acceleration (meters per second per second). The position of an object at a particular time can be plotted on a graph, (a graph is a mathematical picture of the motion of an object). For this reason it is important to understand how to interpret a graph of position, velocity, or acceleration versus time. A) Position versus time: For this activity, you will be the object in motion. The motion sensor will measure your position and your velocity as you move in a straight line. The challenge in this activity is to move in such a way that a plot of your motion on the same graph will much the line that is already there. B) Velocity versus time: As in part A), you will be the object in motion. The motion sensor will measure your velocity as you move in a straight line at different speeds. The science Workshop program plots your motion on a graph of velocity and time. The challenge in this activity is to move in such a way that a plot of your motion on the same graph will match the line that is already there. C) Acceleration due to gravity: Under the effect of gravitational attraction, falling bodies move with a constant acceleration of approximately 9.8 m.s-2 near sea level. To study the motion of a falling object, and thus be able to determine its velocity and acceleration we have to make a record of its position at different times. If air resistance is neglected, and speed of the object is measured over several short consecutive intervals of time as it falls, the difference in the speed can be used to determine the acceleration due to gravity. In this activity, a “picket fence” (a clear plastic strip with uniformly spaced opaque bands) drops through a photogate (Fig. 1). The photogate beam is blocked by each opaque band and the time from one blockage to the next becomes increasingly shorter. Knowing the distance between the leading edge of each opaque band, the science workshop program calculates the average speed of the picket fence from one band to the next. The slope of the graph of average speed versus time gives the acceleration of the falling object. Fig. 1 To Interface Photogate Base & Support rod Picket fence 4. Procedure: A) Position versus time. 1. Connect the science workshop interface to the computer, turn on the interface and turn on the computer. 2. Connect the motion sensor’s phone plugs to digital channels 1 and 2 on the interface. (The yellow taped plug to digital channel 1). 3. Open the file titled P01_MOT1.SWS located in the directory c:\phys105. 4. Set up the sampling option of your experiment as follow: a) Periodic samples = fast 10 Hz b) Condition = time at 10 seconds e. g. after 10 seconds the program will stop collecting data. 5. Mount the motion on a support road so that it is aimed at your midsection when you are setting in front of the sensor. Make sure that you can move at least two meters away from the motion sensor. Position the computer monitor so you can see the screen while you are moving away from the sensor. 6. From the existing graph on your screen determine the following: a) How close should you be to the motion sensor at the beginning? b) How far away should you move? c) How long your motion last? 7. Click REC button to begin recording data. (Data recording will begin almost immediately. The motion sensor will make a faint clicking noise. 8. Watch the plot of your motion on the gr