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Lab 8: Real-world applications of physics Pysics 193 Fall 2006 Lab 8: Real-world application of physics I. Introduction Today’s lab involves the application of the conservation of momentum and the conservation of energy principles to solve a five-part problem. II. Theory Generalized impulse-momentum principle The momentum of an object of mass m moving with velocity v equals mv. For a one- or more-particle system, the initial momentum of the particles at time ti (initial momentum of the system) plus the net average impulse Fexternal (tf – ti) that external objects exert on the system objects during the time interval (tf – ti) equals the final momentum of the system at later time tf. (m1 v i1 + m2 v i2 + …) + external (tf – ti) = (m1 v f1 + m2 v f2 + …). F Note: If the external impulse is zero, then the momentum of the system is conserved. Generalized Work-Energy Principle The initial energy in the system Ui plus any work W done on objects in the system by objects outside the system equals the final energy Uf in the system. Ui + W = Uf or (Ki + Ug i + Us i + …) + W = (Kf + Ug f + Us f + Uint +…) The energy can take many different forms: kinetic K = (1/2)mv2, gravitational potential Ug = mgy, elastic potential Us = (1/2)kx2, internal energy change due to friction ∆Uint = +fks and other forms of energy introduced in later chapters. The unit of energy is the joule (J), where 1 J = 1 N•m. III. The problem The Forensics Lab of the New York City Police Department is interested in learning how to determine the coefficient of friction between two surfaces – the tires and the road. They need this information to help them relate the length of vehicle skid marks to the speed of a vehicle before it starts skidding. Your lab group, as a part of an interview process for a lucrative contract with the NYPD, is asked to devise a procedure to determine the coefficient of friction between the tire rubber and the asphalt using a collision process. They also asked you to write a detailed report about the experiment so they can replicate it. The following experiment should help you answer this question. 1 Lab 8: Real-world applications of physics Pysics 193 Fall 2006 IV. The experiment The experiment involves the following inexpensive materials. A pendulum bob swings down from a horizontal starting position and hits a box. The box slides across the table and eventually stops. This process resembles a car collision, and the length of the slide of the box on the table is similar to the skidding car after the collision. You will make measurements concerning the above process and use your physics knowledge to determine the coefficient of kinetic friction between the box and the tabletop. You have the following equipment: cardboard box, pendulum with sand-filled balloon bob, guide rails (meter sticks) for the box, protractor, duct tape, spring scale, and a mass measuring scale. An additional resource (a video of the experiment) may be found at http://paer.rutgers.edu/pt3/experiment.php?topicid=13&exptid=136 y a) Measure the mass of the pendulum bob vo = 0 and the mass of the box. Then, make yo (a) the setup as shown at the right. Vo = 0 0 b) With the pendulum bob hanging straight y down and at rest, be sure its length is (b) adjusted so it will hit the box in the middle of its smallest side—when hit, the box will slide between two meter V1 = 0 sticks. Place the box so its backside is v1 > 0 0 just touching the bob when hanging straight down. y c) Place the guide rail meter sticks so their (c) 0.0-cm marks are on each side of the backside of the box (the backside is the side hit by the pendulum bob). The meter sticks will guide the box as it V2 > 0 0 v2 > 0 slides and should be about 3 mm away from the sides of the box—so there is negligible rubbing as the box slides. y (d) 2 v3 = 0 y3 0 Lab 8: Real-world applications of physics Pysics 193 Fall 2006 d) When you start the experiment, hold the pendulum bob so the string is horizontal and taut (see (a)). When you release the bob, it should swing down, hit the box, and the box will slide until it stops due to the opposing friction force. y e) Practice doing the experiment several (e) times. Note that the bob does not stop after it hits the box (see (c) and (d)). Thus, it has some final momentum just after the V=0 collision. Practice noting the distance the s 0 pendulum bob swings forward after hitting the box (the distance from the bob position in (c) to that in (d)). Then do the s, distance Distance that experiment five times and for each box travels pendulum bob moves experiment record the distance s that the after hit forward after hit— box slides after the pendulum bob hits it from (c) to (d). and the distance the pendulum bob moves from the straight down position in (c) to the place it stops in (d) after hitting the box. A table is provided to record your measurements. f) Measure the vertical distance yo that the bob traveled while swinging downward. This will be the distance from the center of the rod holding the string to the middle of the pendulum bob. g) Calculate the average distance the box slid and the standard deviation of these five measurements. Do the same for the five measurements of the distance the bob traveled after hitting the box. Calculate the average of these distances. h) Place a ruler oriented vertically so that its end is on the table’s surface. Measure the distance that the center of the pendulum bob is above the tabletop when hanging straight down. Now, move the pendulum bob forward the average distance it traveled after hitting the box (calculated in the second part of g)). Measure the height of the bob above the table. Take the difference of this measurement and the distance above 3 Lab 8: Real-world applications of physics Pysics 193 Fall 2006 when hanging straight down. This will be the vertical distance the pendulum bob rose after hitting the box and will be used to determine its speed just after the collision. i) You are now ready to do the calculations. This involves five separate parts. • Part I: Use the conservation of energy principle to determine the speed of the pendulum bob just before it hit the box. The initial situation is the pendulum bob at its highest point (gravitational potential energy) and the final situation is when the bob is moving fast just before hitting the box (kinetic energy). Determine the bob’s speed v1 just before hitting the box. • Part II: Use the conservation of energy principle to determine the speed of the pendulum bob just after it hit the box (use the vertical distance the bob rose as determined in part h). The initial situation is the bob moving at speed v2 just after it hit the box (the bob has kinetic energy) and the final situation is the bob at rest having risen this vertical distance (it has gravitational potential energy). • Part III: Use the conservation of momentum principle to determine the speed of the box just after the pendulum bob hit it. In part I you calculated the bob’s speed before it hit the box and in part II you calculated its speed just after hitting the box. The box was initially at rest and you should now be able to use momentum conservation to find the speed of the box just after the pendulum bob hit it. To help, you might draw an initial-final sketch of this part of the whole process. Then, apply momentum conservation. • Part IV: Write an expression for the kinetic friction force that the tabletop exerts on the box. • Part V: Use energy conservation to determine the coefficient of kinetic friction between the box and the tabletop. The initial situation is the box moving just after the 4 Lab 8: Real-world applications of physics Pysics 193 Fall 2006 collision (it has kinetic energy) and the final situation is the box when it has stopped sliding (thermal energy has increased by ∆Uint = + fk s where s is the distance the box traveled on the surface after being hit by the pendulum bob). Set the two energies equal to each other and substitute the expression for the kinetic friction force. You should now be able to determine the coefficient of kinetic friction. j) Determine the uncertainty in the value of the coefficient of kinetic friction that you just determined. To do this, decide what quantity in your calculations had the greatest fractional uncertainty (∆value)/(value). The coefficient of kinetic friction should have at least as great a fractional uncertainty. Use this method to determine the uncertainty in the value of the coefficient of kinetic friction. k) Make an independent measurement of the coefficient of kinetic friction. To do this attached a string to the bottom of a spring scale. Attach the other end of the string to the middle of the front side of the box (use tape). Pull the box at constant speed and record the force that the spring scale exerts on the box while pulling it. Since the box is moving at constant speed, this forward force is balanced by and has the same magnitude as the resistive kinetic friction force. The normal force FN of the tabletop on the box is balanced by the downward gravitational force mg that the earth exerts on the box. Thus, the measured force needed to pull the box at constant speed equals fk which in turn equals µk FN = µk mg. Thus, you should now be able to independently determine µk. How does this value compare with that determined in Part V of i)? 5 Lab 8: Real-world applications of physics Pysics 193 Fall 2006 V. Homework In Lab IX, you will do experiments involving gases. The following problems will help you prepare for that lab. Please solve the problems before coming to lab and bring the solutions to turn in at the beginning of the lab. 1. The middle ear has a volume of about 60 cm3 when at a pressure of 1.0 atm = 1.0 x 105 N/m2. Determine the volume of that same air when the air pressure is 0.83 x 105 N/m2, as it is at an elevation of 1500 m above the sea level. (If the volume of the middle ear remains constant, some air will have to leave as the elevation increases. The ears are said to ―pop‖.) 2. Homemade beer is capped into a bottle at a temperature of 27 0C and a pressure of 1.2 x 105 N/m2. The cap will pop off if the pressure inside the bottle exceeds 1.5 x 105 N/m2. What temperature must the gas inside the bottle reach to pop the cap? 6