1. Two pulses on opposite sides of a spring are moving toward each other. The diagrams below show the pulse locations at four successive instants. On each diagramsketch the shape of the spring for the instant shown. 2. A pulse is moving toward the end of a spring that is attached to a wall. The diagram at right shows the pulse at r = 0.0 s. The leading edge of the ' " pulse reaches the wall at t = 0.4 s. ' mgi4i a. In the spaces provided below right, carefully draw the shape of the spring at I: 0.8 s and l= 1.2 s. (Note: The pulse is in the process of being reflected at r: 03 s.) 3. In this problem. you will detennine and apply.r the appropriate boundary condition for reection from a freevend of a spring (i.s.. an end that is free to move in a direction transverse to the length of the spring}. a. We begin by considering the forces exerted on a ring that is connected to a spring and that is free to slide along a rod. [See the top view diagram at right.) I Top view i .5 Assume that the ring is omriess and that the rod is tistioniess. i. What is the net force on the ring? (Hint: Consider what happens to the net force on an object as its mass approaches zero.} Explain. Does the net force on a rnassless ring depend on the acceleration of the ring? Explain. What is the mgnitttde of the gravitational force exerted on the ring? (Recall that the ring is rnassless] ii. Does the force exerted on the ring by the rod have a component that is parsiiei to the rod? Explain. (Hint: Recall the assumptions made above.) iii. In the space at right. draw and label a free-body diagram for the ring at the instant when it is farthest from its equilibrium position. (Hint: Which objects are in contact with the ring'!} Freetbody diagram for rnassless ring Check that your Free-benetr diagram is consistent with your answers to parts i and ii. iv. For the instant shown in your free-body diagram, does the force exerted on the ring by the spring have a component that is parallel to the rod? Explain. Would your answer above differ if you considered an instant when the free end was nor at its farthest point from its equilibrium position? Explain. v. What do your results in part iv suggest about the shape of the spring very near the ring? In particular, which of the diagrams at right best represents the "slope" of the spring at the point where the spring is connected to the ring? (The correct answer to part v is the boundary condition for a free-end reflection.) b. At the end of the tutorial Superposition and reflection of pulses, you observed a demonstration of a pulse reflected from the free end of a spring. A row of paper cups was placed near a spring as shown in the top view diagram below. A pulse with an amplitude slightly less than the cup-spring distance was sent down the spring. On the diagram, indicate which Top view Cups cup(s) were hit by the spring O O O O O during the demonstration. On the basis of your observation, did the free end of the spring have Incident pulse a maximum displacement that was greater than, less than, or equal to the amplitude of the incident pulse? On the basis of your answer above, were the incident and reflected pulses on the same side of the spring or on opposite sides of the spring? Explain.In the tutorial Superposition and reflection of pulses, we developed a model that we can use to predict the shape and orientation of a pulse reflected from the fixed end of a spring. We can develop a similar model for free-end reflection. In this case as well, we imagine that the spring extends past the free end. We then imagine sending a pulse with the appropriate shape and location on this imaginary portion of spring toward the incident pulse so that, as the pulses pass each other, the appropriate boundary condition at the free-end is satisfied. c. Consider a pulse incident on the free end of a spring as shown. i. Would the reflected and incident pulses be on the Before- same side of the spring or on opposite sides? Free end Would you expect the incident and reflected pulses to have the same leading edge or different -After leading edges? Explain. Free end ii. Sketch your prediction for the shape of the reflected pulse on the diagram at right. d. At/ = 0.0s a pulse with speed 1.0 m/s is incident on the free end of a spring as shown. i. Predict the shape of the spring at / = 0.2 s,0.4 s, and 0.6 s. / = 0.0 s (1 square = 10 cm) /= 0.2 s (I square = 10 cm) Free end 1=04s (1 square = 10 cm) 1= 0.6 s (1 square = 10 cm) ii. Are your diagrams consistent with the boundary condition that you determined in part a for a free end of a spring? If so, explain how you can tell. If not, check your answers to part c and resolve any inconsistencies