Next: About this document ... Up: PHYSICS 123: Solutions for Previous: Question 2B Question 3. [25 points]

1. Two students are performing an experiment. Two springs are connected at a point J that is equidistant from the students? hands, as shown in the top view diagram below. Student 2 creates a pulse having a displacement on only one side of the spring. A short time later, students 1 and 2 receive pulses on opposite sides of the spring.

i. [5 points] Is the tension in spring A greater than, less than or equal to the tension in spring B? Explain your reasoning.

The tensions are equal. The force exerted on point J by spring B must be equal and opposite to the force exerted on point J by spring A since point J is not accelerated to the left or right.

 

ii. [5 points] For this experiment, is the reflection at point J like that at a fixed end or a free end? If there is not enough information to tell, state so explicitly. Explain. A transmitted pulse is always on the same side of the spring as the incident pulse, therefore student 1 receives the pulse on the same side of the spring as it was sent by student 2. Since student 2 receives a reflected pulse on the opposite side of the spring, the reflection at point J is like that at a fixed end.

 

iii. [8 points] Who received a pulse first, student 1 or student 2? If there is not enough information to tell, state so explicitly. Explain your reasoning.

 

Student 2 receives the reflected pulse on the opposite side of the spring from which it was sent, which is like a fixed end reflection. In order for a fixed end type of reflection to occur, spring A must have a greater linear mass density than spring B. So the pulse velocity in spring B is greater than in spring A. The transmitted pulse and the reflected pulse leave point J at the same time, therefore student 2 receives the reflected pulse first. `

 

B. [7 points] A pulse moves toward one end of a spring at a speed of 80 cm/s. It is not known whether the end of the spring is fixed to a rod or free to slide along it. The diagrams at right show the shape of the spring at t = 0.0 s and at t = 1.0 s.

 

Is the end of the spring fixed or free? Explain how you can tell.

After 1.0 s the leading edge of the pulse will have reflected from the rod, but the trailing edge will not have. The shape of the spring in the second diagram is a superposition of the reflected leading edge and the incident trailing edge. The reflected leading edge must be on the opposite side of the spring to give this shape, therefore it is a free end reflection.

 

 

  
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