Table 4: Shifted Values From the course text, Section 36-5, we connect the time in the...

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Table 4: Shifted Values From the course text, Section 36-5, we connect the time in the moving frame (t) and the stationary frame (t) as: At At = Eq. 36 1a Where is the speed of the rocket and c is the speed of light. Since we use this relationship constantly, it is useful to define the factor gamma (y) as: Y = Eq. 36-2 So now we can write the first equation at: At = ysto Eq 36 1b This is the time dilation equation. Similarly in the text, Section 36 - 6, we see the distance also contracts. So, relating the distance in the stationary frame to the moving frame I as: Or in gamma notation, we get: Eq 36-3a Eq 36-3b You are now tasked with proving the relations with the simulation and showing you can shift between frames. Procedure: Table 1: Ground Frame Speed of Light (c) Measured Time (ns) Path Length (m) 0.1 3.3524 1.0050 0.2 3.4044 1.0206 0.3 3.4967 1.0483 0.4 3.6394 1.0911 0.5 3.8516 1.1547 0.6 4.1695 1.2500 0.7 4.6708 1.4003 0.8 5.5593 1.6666 0.9 7.6524 2.2941 Table 2: Rocket Frame Speed of Light (c) Measured Time (ns) Path Length (m) 0.1 3.3356 1.0000 0.2 3.3356 1.0000 0.3 3.3356 1.0000 0.4 3.3356 1.0000 0.5 3.3356 1.0000 0.6 3.3356 1.0000 0.7 3.3356 1.0000 0.8 0.9 3.3356 3.3356 1.0000 1.0000 1. Using equation 36-2 find gamma (X) for each of the Speed of Light values and record it in Table 3. Table 3: Gamma Values Speed of Light (c) Gamma (X) 0.1 1.0050 0.2 1.0206 0.3 1.0483 0.4 1.0911 0.5 1.1547 0.6 1.2500 0.7 1.4003 0.8 1.6666 0.9 2.2941 2. Using Equations 36-1a and 36-1b, please transfer the times and distance from the Ground frame to the Rocks frame and then transfer the times and distance from the Rocket frame to the Ground frame. Record your values in Table 4 3. Find the percentage error for the Ground Frame and the values you got by shifting the Rocket values to the Ground frame. Record your values in Table 4 4. Find the percentage error for the Rocket Frame and the values you got by shifting the Ground values to the Rocket frame. Record your values in Table 4 Ground Frame Shifted to Rocket Frame Measured Path length Time (ns) |(m) Time Percent Error Distance Percent Error Measured Time (ns) (m) Error Rocket Frame Shifted to Ground Frame Path length Distance Percent Error Time Percent 3.3524 1.0050 3.3356 1.0000 3.4044 1.0206 3.3356 1.0000 3.4967 1.0483 3.3356 1.0000 3.6394 1.0911 3.3356 1.0000 3.8516 1.1547 3.3356 1.0000 4.1695 1.2500 3.3356 1.0000 4.6708 1.4003 3.3356 1.0000 5.5593 1.6666 3.3356 1.0000 7.6524 2.2941 3.3356 1.0000 Table 4: Shifted Values From the course text, Section 36-5, we connect the time in the moving frame (t) and the stationary frame (t) as: At At = Eq. 36 1a Where is the speed of the rocket and c is the speed of light. Since we use this relationship constantly, it is useful to define the factor gamma (y) as: Y = Eq. 36-2 So now we can write the first equation at: At = ysto Eq 36 1b This is the time dilation equation. Similarly in the text, Section 36 - 6, we see the distance also contracts. So, relating the distance in the stationary frame to the moving frame I as: Or in gamma notation, we get: Eq 36-3a Eq 36-3b You are now tasked with proving the relations with the simulation and showing you can shift between frames. Procedure: Table 1: Ground Frame Speed of Light (c) Measured Time (ns) Path Length (m) 0.1 3.3524 1.0050 0.2 3.4044 1.0206 0.3 3.4967 1.0483 0.4 3.6394 1.0911 0.5 3.8516 1.1547 0.6 4.1695 1.2500 0.7 4.6708 1.4003 0.8 5.5593 1.6666 0.9 7.6524 2.2941 Table 2: Rocket Frame Speed of Light (c) Measured Time (ns) Path Length (m) 0.1 3.3356 1.0000 0.2 3.3356 1.0000 0.3 3.3356 1.0000 0.4 3.3356 1.0000 0.5 3.3356 1.0000 0.6 3.3356 1.0000 0.7 3.3356 1.0000 0.8 0.9 3.3356 3.3356 1.0000 1.0000 1. Using equation 36-2 find gamma (X) for each of the Speed of Light values and record it in Table 3. Table 3: Gamma Values Speed of Light (c) Gamma (X) 0.1 1.0050 0.2 1.0206 0.3 1.0483 0.4 1.0911 0.5 1.1547 0.6 1.2500 0.7 1.4003 0.8 1.6666 0.9 2.2941 2. Using Equations 36-1a and 36-1b, please transfer the times and distance from the Ground frame to the Rocks frame and then transfer the times and distance from the Rocket frame to the Ground frame. Record your values in Table 4 3. Find the percentage error for the Ground Frame and the values you got by shifting the Rocket values to the Ground frame. Record your values in Table 4 4. Find the percentage error for the Rocket Frame and the values you got by shifting the Ground values to the Rocket frame. Record your values in Table 4 Ground Frame Shifted to Rocket Frame Measured Path length Time (ns) |(m) Time Percent Error Distance Percent Error Measured Time (ns) (m) Error Rocket Frame Shifted to Ground Frame Path length Distance Percent Error Time Percent 3.3524 1.0050 3.3356 1.0000 3.4044 1.0206 3.3356 1.0000 3.4967 1.0483 3.3356 1.0000 3.6394 1.0911 3.3356 1.0000 3.8516 1.1547 3.3356 1.0000 4.1695 1.2500 3.3356 1.0000 4.6708 1.4003 3.3356 1.0000 5.5593 1.6666 3.3356 1.0000 7.6524 2.2941 3.3356 1.0000