Problem Solving Strategy 37.2: Length Contraction Learning Goal: To practice Pro

Question

Problem Solving Strategy 37.2: Length Contraction Learning Goal: To practice Problem-Solving Strategy 37.2 Length IDENTIFY the relevant concepts: The concept of length contraction is used whenever the length of an object measured by observers in different inertial frames of reference is compared SET UP the problem using the following steps A support crossbeam on a high speed train is made from a titanium rod that has a length of 0.650 m when measured by an observer on the train. The beam is positioned such that the observer on the train measures an angle of 19 degrees between the crossbeam and the floor of the train. (Figure 1) At what speed u would the train have to be traveling in order for an observer standing outside the train to measure the angle as 49 degrees? In the figure, S indicates the reference frame of the observer standing outside the train and S"indicates the reference frame of the observer on the train. 1. Decide what defines the length in question. If the problem statement describes an object such as a ruler, it is just the distance between the ends of the object. 2. Determine what the target variable is EXECUTE the solution as follows: 1. Determine the reference frame in which the object in question is at rest. In this frame, the length of the object is its proper length 2. Keep in mind that length contraction occurs only for lengths parallel to the direction of relative motion of the two frames. Any length that is perpendicular to the relative motion is the same in both frames. 3. Use the equation Figure 1 of 1> to relate l and lp, and then solve for the target variable. EVALUATE your answer: Check that your answers make sense: l is never larger than lo and u is never greater than the speed of lightc3.00x108 m/s IDENTIFY the relevant concepts You are asked to find the speed of the train at which the angle between two objects on the moving train would appear to have a different value to an observer standing outside the train. One observer will see a contracted length for the rod which will affect the angle at which it meets the floor of the train. Since the size of the angle is related to the length of the crossbeam through trigonometry, the above strategy is appropriate. SET UP the problem using the following steps

Explanation / Answer

u=c > u=0.9c > u=0

as the speed increase angle increases  

------------------------------------------------------------------------

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.