Ekins P7A Lab 3

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Physics

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Apr 3, 2024

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Physics 7A Dynamics Lab, v.5.0 p-1 Lab 3: Dynamics Introduction This lab has two purposes. First, starting in the prelab, you'll address increasingly difficult versions of a standard exam-level force problem about a cart and pulley. Then in lab you'll test your answers experimentally. In addition, you'll do experiments and answer questions designed to highlight some of the subtle conceptual aspects of Newton’s laws, and how these relate to common-sense force intuitions. Prelab Questions: An exam-level force problem [Complete these questions before coming to lab! Your GSI will discuss them at the beginning of the lab.] Consider the lab set-up below. A cart of mass m_,,, is connected to a vertically hanging mass, of mass my,,.. The cart moves with negligible friction. Inlab, you will give the cart a brief push away from the pulley, and then let it go. —— 1 —_— adjustable end stop Figure 7.1 Equipment Setup A. Draw separate free-body diagrams (FBDs) for the cart and for the hanging mass. Your diagrams should describe those objects after you finish pushing the cart, but while it's still traveling away from the pulley. Label each force acting on each object. T F(n) F(9) Flg) B. After you finish pushing the cart, what force (if any) is making the cart slide away from the pulley? Explain. After the initial push, the acceleration caused by the applied force makes the cart continue to slide away from the pulley. There is no applied force currently present though. Even though the applied force is no longer acting upon the object, the object will remain moving in the direction of the acceleration until the point at which the tension of the pulley overcomes the initially applied force.

Physics 7A Dynamics Lab, v.5.0 p.2 C. Interms of m,, My, and g, find the cart’s acceleration. Show your work here. (During the lab, you will plug in the relevant numbers, to make a numerical prediction.) Horizontal Mass: F =m2a =T - m2g Cart: F =m1a =T (left is positive in the horizontal direction) m2a = (m1a) - m2g a(m2-mil) =-m2g a=-m2g/(m2-m1) D. Consider the time after the cart reverses direction and starts moving back towards the pulley. (i) Inwhat ways, if any, must we modify the free-body diagrams from question A? Explain, and draw the correct FBDs here. The free-body diagrams will be changed to have a tension that is smaller than the force of gravity for the hanging mass FBD. The cart's FBD will need to have no applied force, making the tension the sole horizontal force. T T F(n) Fo F@ (ii) Is the new acceleration bigger than, smaller than, or the same as the cart’s acceleration when it was traveling away from the pulley? Relate your answer to (i). The new acceleration is in the opposite direction, so the new acceleration will be less than the original. In (Di), the tension of the cart FBD is equal to the net force as the acceleration will only be in the negative horizontal direction at this interval of time. End of pre-lab questions. The lab starts on the next page GSI's Initials:

Physics 7A Dynamics Lab, v.5.0 p.3 Cart & hanging mass 1. In this first experiment, you'll test your prelab prediction about the acceleration. ¢ Remove the brake from the cart, if it's attached. ¢ Usea scale to measure m,,,, and .. Don't forget to include the mass of the “hook” in . With these values, predict the cart’s acceleration, using your answer to prelab question C. My =_5509 Mygng =59 Predicted acceleration = _0-089 m/s"2 4 If the track is currently set up as a ramp, lay it flat on the lab bench, and make sure it’s level. 4 Using the computer software "7A_MotionDetector.mbl" from our earlier labs, set up the screen to show an acceleration graph—and no other graphs. 4 Set up the motion detector, and run the experiment. To determine the value of the acceleration as accurately as possible, adjust the acceleration axis. A Measured acceleration = 01 mis"2 2. By what percentage does the measured acceleration differ from the predicted acceleration? Show your work. Measured value - expected value / expected value x 100% (0.1-0.089) /0.089 = 0.1235 = 12.35% 3. List some reasons why your predicted and measured acceleration disagree. How could the experiment be improved? The predicted acceleration differs from the measured acceleration because there are other forces that we considered negligible in our calculations. For example, the track had friction and the string moving over the pulley had friction so these forces were unaccounted for in our expected value. Additionally, the string has a mass that was not taken into consideration. The experiment could be improved by utilizing materials with smaller amounts of friction and mass (in regards to the string).

Physics 7A Dynamics Lab, v.5.0 p-4 4.* After you let the cart go, as it moves back and forth across the track, is the tension in the string more than my,, g, equal to my,. g, less than m,, ¢? Explain, both mathematically and conceptually. As the cart moves back and forth, the tension of the string changes and oscillates among being less than, equal to, and greater than m(hang) g. As the cart moves away from the pulley, the hanging mass moves upwards. The only forces acting on the hanging mass are tension in the upwards direction and the force of gravity, which is constant. In order for the hanging mass to move upwards as the cart moves away from the pulley, the tension must be greater than m2g. When the cart moves towards the pulley, the hanging mass moves in the downward direction, so the tension must be less than the force of gravity. There is a point in time when the tension value is changing that it will equal m2g because it cannot achieve a value of + - m2g without being equal to m2g at a point. Horizontal Mass: F =m2a =T - m2g Cart: F =m1a =T (left is positive in the horizontal direction) T =m2g + m2a when cart is moving in the positive horizontal direction T>m2g T =m2g - m2a when cart is moving in the negative horizontal direction T<m2g 5. (Prediction) What will the position, velocity, and acceleration graphs of the cart look like if you repeat the above experiment, but with the following twist: after the cart has reversed direction and traveled about half way back towards the pulley, you'll catch the hanging mass, allowing the string to go slack. In other words, you'll “turn off” the tension force. As usual, draw your predictions before doing the experiment. Let “towards the pulley” be the positive direction, and neglect friction. The actual graphs were very close to the predictions N T art hanging @t hanging ant hanging direction caught direction caught direction caught ¢ Before running the experiment, pull down the View menu, select Graph Layout and choose “Three panes”. Make sure one of the graphs shows position, another shows velocity, and a third shows acceleration. As usual, you can change graphs by double clicking them. Make sure they all have the same time scale. Set the time scale onall three graphs equal to 4 sec. (You can change this setting if needed; but all three graphs must have the same time scale.) ¢ Make sure the motion detector is at the other end of the track from the pulley. ¢ Run the experiment. Change the scale of the graphs, if needed, to see the results more clearly. # If the actual graphs disagree with your predictions, sketch them on the above axes, using a different color or a dashed line. Omit the beginning segment of the graph when your hand was still pushing the cart.

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