DATA As a research scientist at a linear accelerator, you are studying an unstable particle. You measure its mean lifetime Δ t as a function of the particle’s speed relative to your laboratory equipment. You record the speed of the particle u as a fraction of the speed of light in vacuum c . The table gives the results of your measurements. (a) Your team leader suggests that if you plot your data as (Δ t ) 2 versus (1− u 2 / c 2 ) −1 data points will be fit well by a straight line. Construct this graph and verify the team leader’s prediction. Use the best-fit straight line to your data to calculate the mean lifetime of the particle in its rest frame. (b) What is the speed of the particle relative to your lab equipment (expressed as ( U /C) if the lifetime that you measure is four times its rest-frame lifetime?
DATA As a research scientist at a linear accelerator, you are studying an unstable particle. You measure its mean lifetime Δ t as a function of the particle’s speed relative to your laboratory equipment. You record the speed of the particle u as a fraction of the speed of light in vacuum c . The table gives the results of your measurements. (a) Your team leader suggests that if you plot your data as (Δ t ) 2 versus (1− u 2 / c 2 ) −1 data points will be fit well by a straight line. Construct this graph and verify the team leader’s prediction. Use the best-fit straight line to your data to calculate the mean lifetime of the particle in its rest frame. (b) What is the speed of the particle relative to your lab equipment (expressed as ( U /C) if the lifetime that you measure is four times its rest-frame lifetime?
DATA As a research scientist at a linear accelerator, you are studying an unstable particle. You measure its mean lifetime Δt as a function of the particle’s speed relative to your laboratory equipment. You record the speed of the particle u as a fraction of the speed of light in vacuum c. The table gives the results of your measurements.
(a) Your team leader suggests that if you plot your data as (Δt)2 versus (1−u2/c2)−1 data points will be fit well by a straight line. Construct this graph and verify the team leader’s prediction. Use the best-fit straight line to your data to calculate the mean lifetime of the particle in its rest frame. (b) What is the speed of the particle relative to your lab equipment (expressed as (U/C) if the lifetime that you measure is four times its rest-frame lifetime?
Definition Definition Rate at which light travels, measured in a vacuum. The speed of light is a universal physical constant used in many areas of physics, most commonly denoted by the letter c . The value of the speed of light c = 299,792,458 m/s, but for most of the calculations, the value of the speed of light is approximated as c = 3 x 10 8 m/s.
The force of the quadriceps (Fq) and force of the patellar tendon (Fp) is identical (i.e., 1000 N each). In the figure below angle in blue is Θ and the in green is half Θ (i.e., Θ/2). A) Calculate the patellar reaction force (i.e., R resultant vector is the sum of the horizontal component of the quadriceps and patellar tendon force) at the following joint angles: you need to provide a diagram showing the vector and its components for each part. a1) Θ = 160 degrees, a2) Θ = 90 degrees. NOTE: USE ONLY TRIGNOMETRIC FUNCTIONS (SIN/TAN/COS, NO LAW OF COSINES, NO COMPLICATED ALGEBRAIC EQUATIONS OR ANYTHING ELSE, ETC. Question A has 2 parts!
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