A beam of protons is directed from the left onto a small target. The interactions produce...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A beam of protons is directed from the left onto a small target. The interactions produce secondary particles, which travel to the right after emitting from the target. The y coordinates of the secondary particles are measured by a series of detector planes that are accurately situated at x = 10, 14, 18, 22, 26, 30 cm downstream from the target (assume that the target is at x = 0 cm). The detectors at the first and the last planes have an accuracy of ±0.10 cm for the y measurements, while that for the other four planes is ±0.30 cm. The following y coordinates are obtained for the six planes after one specific interaction: 2.02, 2.26, 3.24, 3.33, 3.93, 4.03 cm. We want to determine whether these measurements are consistent with the hypothesis that the particle traces a straight track given by y = a + bx. a) Perform a least squares straight line fit to the data: find the weighted mean x position(x), the intercept a, the slope b, and the height a' at x =(x). Determine Smin and the number of degrees of freedom v. b) Decide whether this track is consistent with coming from the target (situated at x = 0 cm) and extends from y = -1 cm to y = +1 cm, as follows: Determine the accuracies with which a' and b are determined, and then use the relation y = a + bx' (where x¹ = x -(x)) to calculate the error & on the extrapolated position yo of the track at the x' value corresponding to x = 0. Then decide whether, given yo and E, the track is consistent with being produced in the target. c) How would your answers to part (b) have changed if the accuracies of determining the y positions were ten times smaller, i.e., 10.01 cm and ±0.03 cm? A beam of protons is directed from the left onto a small target. The interactions produce secondary particles, which travel to the right after emitting from the target. The y coordinates of the secondary particles are measured by a series of detector planes that are accurately situated at x = 10, 14, 18, 22, 26, 30 cm downstream from the target (assume that the target is at x = 0 cm). The detectors at the first and the last planes have an accuracy of ±0.10 cm for the y measurements, while that for the other four planes is ±0.30 cm. The following y coordinates are obtained for the six planes after one specific interaction: 2.02, 2.26, 3.24, 3.33, 3.93, 4.03 cm. We want to determine whether these measurements are consistent with the hypothesis that the particle traces a straight track given by y = a + bx. a) Perform a least squares straight line fit to the data: find the weighted mean x position(x), the intercept a, the slope b, and the height a' at x =(x). Determine Smin and the number of degrees of freedom v. b) Decide whether this track is consistent with coming from the target (situated at x = 0 cm) and extends from y = -1 cm to y = +1 cm, as follows: Determine the accuracies with which a' and b are determined, and then use the relation y = a + bx' (where x¹ = x -(x)) to calculate the error & on the extrapolated position yo of the track at the x' value corresponding to x = 0. Then decide whether, given yo and E, the track is consistent with being produced in the target. c) How would your answers to part (b) have changed if the accuracies of determining the y positions were ten times smaller, i.e., 10.01 cm and ±0.03 cm?
Expert Answer:
Answer rating: 100% (QA)
a Perform a least squares straight line fit to the data find the weighted mean x positionx the intercept a the slope b and the height a at x x Determine Smin and the number of degrees of freedom v The ... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
A beam of protons is accelerated easterly from rest through a potential difference of 3.0 kV. It enters a region where there exists an upward pointing uniform electric field. This field is created by...
-
A beam of protons and a beam of alpha particles (of mass 6.64 x 10-27 kg and charge +2e) are accelerated from rest through the same potential difference and pass through identical circular holes in a...
-
A beam of protons exits from a particle accelerator due east at a speed of 3.0 x 105 m/s. The protons then enter a uniform magnetic field of magnitude 0.50 T that is oriented at above 37o the...
-
You have recently been hired as a consultant for a personal financial planning firm. One of your first projects is creating a retirement plan for a couple, Tom and Helena Keeley. They have just...
-
Refer to PE 7-60. Compute the correct amount of net income in year 2. Data from PE 7-60 At the beginning of year 1, the companys inventory level was stated correctly. At the end of year 1, inventory...
-
Construct a normal probability plot for the PM data in Table 1.2 (page 21). Do the PM data appear to come from a normal population? In Table 1.2 TABLE 1.2 Particulate matter (PM) emissions (in g/gal)...
-
10. YOU BE THE JUDGE WRITING PROBLEM Sara Kearns went to an auction at Christie's to bid on a tapestry for her employer, Nardin Fine Arts Gallery. The good news is that she purchased a Dufy tapestry...
-
Navajo Companys financial statements show the following. The company recently discovered that in making physical counts of inventory, it had made the following errors: Inventory on December 31, 2012,...
-
Cash Budget long dash?? Basic Grenoble Enterprises had sales of $50,000 in March and $60,000 in April. Forecast sales for? May, June, and July are $70,000?, $80,000?, and $100,000?, respecti...
-
Let f(x) be a pdf and let a be a number such that, for all > 0, f(a + ) = f(a - ). Such a pdf is said to be symmetric about the point a. (a) Give three examples of symmetric pdfs. (b) Show that if X...
-
A conducting loop is made in the form of two squares of sides s = 3.9cm and s = 5.2 cm as shown. At time t = 0, the loop enters a region of length L = 18 cm that contains a uniform magnetic field B =...
-
Bond valuation Lahey Industries has outstanding a $1,000 par-value bond with an 8% coupon interest rate. The bond has 12 years remaining to its maturity date. a. If interest is paid annually, find...
-
Q3: My Wordle performance to date is shown here: 10 20 3 GUESS DISTRIBUTION 2 4 3 5 6 6 2 NEXT WORDLE So, for instance, my score was 5 in six games (attempts). Use these statistics to estimate the...
-
1:List 4 warning signs of risk when managing risk. 2:Insurance can mitigate political risks. what are exemplary hazards ? name the 5.
-
Many factors and influences combine to create the regulatory environment. Major events be these legislative, economic, industry driven, political, environmental or indeed scandals relating to some or...
-
Professor Baker discusses the fact that some groups in society are perceived of as not being capable of learning well and aggressive toward other people. The data illustrates that these groups are...
-
I have the following diagrams histograms of plots, scatter plots and heat map, i created this in jupyter notebook and python using pandas 1. Explain the histograms in regards to the distribution and...
-
(a) Prove that form an orthonormal basis for R3 for the usual dot product. (b) Find the coordinates of v = (1, 1, 1)T relative to this basis. (c) Verify formula (5.5) in this particular case. 48-65...
-
During a plane flight, a passenger experiences ear pain due to a head cold that has clogged his Eustachian tubes. Assuming the pressure in his tubes remained at 1.00 atm (from sea level) and the...
-
In a proton linear accelerator, a 9.5-mA proton current hits a target. (a) How many protons hit the target each second? (b) How much energy is delivered to the target each second if each proton has a...
-
A flint glass plate 3.5 cm thick is placed over a news-paper. How far beneath the top surface of the plate would the print appear to be if you were looking almost vertically downward through the...
-
Rewrite the approximate factorization method of Section 9.3 .3 for the case of three-dimensional heat conduction equation.
-
The two-dimensional heat equation is solved in a rectangular domain \(0
-
Show that the ADI scheme for two-dimensional heat equation can be obtained from the Crank-Nicolson scheme ( 9.35 ) by approximate factorization and that the factorization error is \(O\left((\Delta...
Study smarter with the SolutionInn App