Answer Happy

P04.04 W-KE Theorem Problems You have the opportunity to make infinite attempts on the lab activity immediately preceding this problems set. It will be assumed you have obtained 100% on that assessment before attempting this one. These depend on those, so please return to that assessment and get help if you need it before attempting this one. For these problems, report more digits than are significant to ensure correct answers are not marked incorrect and do not recycle rounded numbers. Specifically, you will run into trouble with #7 and #9 if you are rounding intermediate results. 1) Calculate the kinetic translational energy at the instant I release the cart from rest. Remember that all numeric answer fields expect a numerical answer in the standard units for that quantity without letters indicating units or directions etc. 2) Calculate the translational kinetic energy of the cart just before it hits the end of the track. Remember that all numeric answer fields expect a numerical answer in the standard units for that quantity without letters indicating units or directions etc. 3) Calculate the change in the cart's translational kinetic energy from the time the cart is released until the time just before it hits the end of the track. Remember that all numeric answer fields expect a numerical answer in the standard units for that quantity without letters indicating units or directions etc. 4) According to the work-kinetic energy theorem then, what is the net work done on the cart from the time the cart is released until the time just before it hits the end of the track? Because the normal force from the track and the gravitational force on the cart are equal and opposite here (it does not accelerate up or down), assuming friction is negligible, we can say the net work done on the cart is performed by the tension in the cord. This force acts constantly from the time I released the cart until it hits the end of the track. Using the definition of work, you can calculate the tension in the cord assuming there is no other force acting in the horizontal direction. This is an assumption we'll explore later, so do not simply read the tension from the force sensor display in the video-calculate the tension as requested. To motivate this, first inspect the displacement vector for the cart during the

experiment as well as the direction in which the tension force acts. 5) What is the angle between the tension acting on the cart and the cart's displacement vector? Report your answer in degrees, but of course do not include the unit in the answer field 6) What is the cosine of this angle? The result of a trigonometric function is dimensionless, so there is no unit to remind you not to report in this field. Just the number will do. 7) Using the definition of work, calculate the apparent tension in the cord. The cord between the cart and the hanging mass on the far side of the pulley at the end of the track provides a tension. As we saw in the Newton's Laws module, such a cord provides tension parallel to its length and when strung over a pulley, simply changes the direction of the tension. Thus, the tension in the cord pulling on the cart has the same magnitude as the tension pulling up on the hanging mass. Also, the acceleration of the cart to the right is the same as the acceleration of the hanging mass down- ward. Finally, the distance the cart moves to the right must also be the same distance the hanging mass moves downward. You have already observed the distance the cart travels and the correspond- ing distance the hanging mass falls. We now endeavor to determine the amount of mass that's hang- ing. We have no way to know (from the video at least) what the initial and final heights of the hanging mass are, but we know the difference. We also know the acceleration due to gravity is 9.81 5. Thus, we can calculate the mass that hangs from the apparatus. There are several ways to find it based on the content we have learned. One way is available from the Newton's second law analysis. Analyzing forces that act on the hanging mass and knowing its accelera- tion permit calculation of the unknown mass, however you need to first calculate the acceleration of the system. Another way, using energy methods, is to recognize that the amount of work the tension does on the cart is equal and opposite to the amount of work the tension does on the hanging mass, so the work done by gravity on the hanging mass is responsible for the change in the kinetic energy of the entire system of cart plus hanging mass. Yet another way is to use the conservation of energy, which is indistinct from the W-KE theorem approach just described in practice but offers a slightly different way to think about the problem. 8) What amount of energy is transferred to the cart system from the hanging mass system? Remember that all numeric answer fields expect a numerical answer in the standard units for that quantity without letters indicating units or

P04.04.nb | 3 directions etc.. Again, energy changes do not depend on what you call "zero" for your coordinate system. What is the change in energy for the cart during the experiment? 9) Calculate what must have been the mass hung on the end of the cord. Remember that all numeric answer fields expect a numerical answer in the standard units for that quantity without letters indicating units or directions etc. It is true that this problem could be done using the Module 02 content. You could calculate the accelera- tion of the system from the plots' data and represent the net force acting on the hanging mass symboli- cally, then solve Newton's second for the unknown mass. The problem with this method is that it is too difficult to read off the time points from the plots. Intelligent people can disagree exactly where the "good" data begins and ends and even if one agrees with me on what the "good" data is, the instrumen- tal resolution is poor for the time axis. Solve this problem using the work-energy theorem (as the title suggests).

Mass of Cart + Sensor + 500g cylinder system = 0.82904 Time that experiment begins = 0.17 Speed of cart before it hits apparatus = 0.80 m/s Distance from the sensor to the cart at the beginning of the experiment = 0.17m Distance from the sensor to the cart at the point just before it hits the end of the track = 0.94m Distance the cart travels during this experiment from the time it is released until it runs into the end of the track = 0.77m Distance the hanging mass travels during this experiment from the time the cart is released until it runs into the end of the track = 0.77m