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

Question

Learning Goal: Problem Solving Strategy 37.2: Length Contraction To practice Problem-Solving Strategy 37.2 Length Contraction. 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. 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 tu 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. SET UP the problem using the following steps: 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 ength 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 lo, and then solve for the target variable. LUATE your answer: The figure shows a train moving horizontally to the right at a speed u. A crossbeam is placed in ck that your answers make sense: l is never larger than lo and u is never greater than the speed of light c 3.00x108 m/s the middie of the train, making an acute angle with the horizontal. There is an observer outside the train, with coordinate system S, consisting of horizontal axis x and vertical axis y and a passenger in the train with coordinate system S with accent, consisting of horizontal axis x with 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 accent and vertical axis y with accent. crossbearn NTIFY the relevant concepts 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 of the train. Since the size of the angle is related to the length of the crossbeam through trigonometry, the above strategy is appropriate

Explanation / Answer

Length contraction is a direct result of relative velocity.

The train is moving horizontally with respect to the observer on the platform so the only relative motion is between the observer on the platform and the train. As the train is not moving vertically there is no relative verticle motion between the train and any of the observer.

Now as there is no relative verticle motion the height of the rod remains same for both the observers.There is also no relative motion between the observer on the train and the train so for him there is no height or width contraction.

But there is horizontal relative motion between the train and the observer on the platform so the width of the rod appears to be contracted for the observer on the platform.

So the only first statement is applicable which is: The crossbeam is moving relative to the observer on the platform so the width appears contracted.

Other three statements are not applicable.

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