a. In the demonstration, a row of paper cups was placed a distance from the spring that was just larger than the amplitude of the incident pulse, as shown in the diagram below. TOP VIEW Cups o O Incident pulse i. On the diagram, indicate which cup(s) were knocked away in the demonstration. ii. On the basis of this observation, did the free end of spring have 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 your reasoning. In tutorial, we developed a model that we can use to predict the shape and orientation of a pulse reflected from a fixed-end of a spring. Recall that the boundary condition in the case of fixed-end reflection is that the end of the spring never moves. We chose the shape, orientation, and location of the imagined pulse so that as it passes the incident pulse, the end of the spring remained fixed. The imagined pulse was travelling on the opposite side of the spring with the same leading edge as the incident pulse. A similar model exists for the case of free-end reflection. We first imagine that the spring extends past the free end. We then imagine sending a pulse on this imaginary portion of spring toward the incident pulse so that, as the two pulses pass each other, the appropriate shape of the spring is given by the superposition of the incident pulse with the imagined pulse. In this case in contrast to the fixed end), however, the imagined pulse will be travelling on the same side of the spring as the incident pulse with the same leading edge as the incident pulse. The corresponding boundary condition for the free end is that the spring very near the ring (and hence the tension force) must be perpendicular to the rod. In the exercises below, you will apply this model to find the shape of the spring upon reflection from the free end and confirm that this model indeed describes the above demonstration. b. (1 square = 10 cm) _t = 0.0 The figure at right illustrates a pulse incident on a free end of a spring with a speed of 1.0 m/s. i. Free end On the basis of your results in part a, would the reflected pulse be on the same side of the spring as the incident pulse or on the opposite side? L(1 1 square = 10 cm) t = 0.2 s. Would you expect the incident and reflected pulses to have the same leading edge or different leading edges? (1 square = 10 cm). t = 0.4 s. ii. Use your results above to determine the shape of the spring at t = 0.2 s, 0.4 s, and 0.6 s. Are your answers consistent with the fact that the cup(s) closest to the rod got knocked away in the demonstration? If, so explain how you can tell. If not, check your drawings of the shape of the spring and resolve the inconsistencies. |(1 square = 10 cm) t = 0.6 s. 4. The figure shown below has several errors. How many can you find? 5591777 577733 a. In the demonstration, a row of paper cups was placed a distance from the spring that was just larger than the amplitude of the incident pulse, as shown in the diagram below. TOP VIEW Cups o O Incident pulse i. On the diagram, indicate which cup(s) were knocked away in the demonstration. ii. On the basis of this observation, did the free end of spring have 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 your reasoning. In tutorial, we developed a model that we can use to predict the shape and orientation of a pulse reflected from a fixed-end of a spring. Recall that the boundary condition in the case of fixed-end reflection is that the end of the spring never moves. We chose the shape, orientation, and location of the imagined pulse so that as it passes the incident pulse, the end of the spring remained fixed. The imagined pulse was travelling on the opposite side of the spring with the same leading edge as the incident pulse. A similar model exists for the case of free-end reflection. We first imagine that the spring extends past the free end. We then imagine sending a pulse on this imaginary portion of spring toward the incident pulse so that, as the two pulses pass each other, the appropriate shape of the spring is given by the superposition of the incident pulse with the imagined pulse. In this case in contrast to the fixed end), however, the imagined pulse will be travelling on the same side of the spring as the incident pulse with the same leading edge as the incident pulse. The corresponding boundary condition for the free end is that the spring very near the ring (and hence the tension force) must be perpendicular to the rod. In the exercises below, you will apply this model to find the shape of the spring upon reflection from the free end and confirm that this model indeed describes the above demonstration. b. (1 square = 10 cm) _t = 0.0 The figure at right illustrates a pulse incident on a free end of a spring with a speed of 1.0 m/s. i. Free end On the basis of your results in part a, would the reflected pulse be on the same side of the spring as the incident pulse or on the opposite side? L(1 1 square = 10 cm) t = 0.2 s. Would you expect the incident and reflected pulses to have the same leading edge or different leading edges? (1 square = 10 cm). t = 0.4 s. ii. Use your results above to determine the shape of the spring at t = 0.2 s, 0.4 s, and 0.6 s. Are your answers consistent with the fact that the cup(s) closest to the rod got knocked away in the demonstration? If, so explain how you can tell. If not, check your drawings of the shape of the spring and resolve the inconsistencies. |(1 square = 10 cm) t = 0.6 s. 4. The figure shown below has several errors. How many can you find? 5591777 577733