In Class Quiz On a piece of paper, write down your ****NAME**** and ****Your Student ID Number**** and ****Class (PHYS 215-01)**** and ****Date: Tuesday, 01-23-2018**** Q1: The magnetic moment of the proton was recently measured to be 2.79284734462 ± 0.00000000082 𝜇𝑁 𝜇𝑁 = 𝑁𝑢𝑐𝑙𝑒𝑎𝑟 𝑀𝑎𝑔𝑛𝑒𝑡𝑜𝑛 (a) How many significant figures does this measurement have? (b) Looking at the last few decimal places in the measurement, ….462, should the experimentalists be highly confident in the 4? (c) How about their confidence in the 6? (d) Should they have high confidence in the 2? Please explain your answers to all four parts. Read more at: https://phys.org/news/2017-11-physicists-precise-proton-magnetic-moment.html#jCp Q2: Find the ****positive**** angles between the vectors and the x-axis Express angles in degree units. Copy this table onto your answer sheet and then fill in the blank cells. Show all steps. y 45.0° 𝐴Ԧ x 𝐵 𝑽𝒆𝒄𝒕𝒐𝒓 𝑴𝒂𝒈𝒏𝒊𝒕𝒖𝒅𝒆 𝐴Ԧ 1.00 cm 𝐵 2.00 cm 𝑨𝒏𝒈𝒍𝒆 −165° 𝒙 − 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 𝒚 − 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 𝒛 − 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 Q3: Using 𝐴Ԧ and 𝐵 from question 2 as the input vectors, compute the vector product, 𝐴Ԧ × 𝐵, of the two vectors by filling in the table below. Copy this table onto your answer sheet and then fill in the blank cells. Show all steps. 𝑽𝒆𝒄𝒕𝒐𝒓 𝐴Ԧ × 𝐵 𝑴𝒂𝒈𝒏𝒊𝒕𝒖𝒅𝒆 𝒙 − 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 𝒚 − 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 𝒛 − 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 Q4: Once again, using 𝐴Ԧ and 𝐵 from question 2 as the input vectors, compute the vector product 𝐵 × 𝐴Ԧ by filling in the table below. Copy this table onto your answer sheet and then fill in the blank cells. Note that as discussed in class 𝐵 × 𝐴Ԧ = −𝐴Ԧ × 𝐵, so you can simply put a negative sign before all the components for 𝐴Ԧ × 𝐵; however, I want you to explicitly compute the components and verify that indeed 𝐵 × 𝐴Ԧ = −𝐴Ԧ × 𝐵. As usual, you should show all steps of you computation. 𝑽𝒆𝒄𝒕𝒐𝒓 𝐵 × 𝐴Ԧ 𝑴𝒂𝒈𝒏𝒊𝒕𝒖𝒅𝒆 𝒙 − 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 𝒚 − 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 𝒛 − 𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 Q5: Refer to question 3 – using the right hand rule, determine if 𝐴Ԧ × 𝐵 points into or out of the plane of the screen (or page). Q6: Refer to question 4 – using the right hand rule, determine if 𝐵 × 𝐴Ԧ points into or out of the plane of the screen (or page). (Hint: how are the orientations of 𝐵 × 𝐴Ԧ and 𝐴Ԧ × 𝐵 related?) Q7: Explain the difference between accuracy and precision of a measurement. In your opinion, which one, accuracy or precision, is harder to establish? Please explain. Q8: Copy this table onto your answer sheets. The two vectors 𝑣Ԧ and 𝑎Ԧ are the velocity and acceleration vectors of a particle travelling with constant speed around a circle of radius R. The components are expressed in symbolic form with 𝝎 a constant called the angular velocity and t standing for time . You do not have to use any knowledge about particle kinematics here; this question is about vectors. Using the Pythagorean theorem formula, compute , in symbolic form, the magnitudes of the two vectors. You will have to use a trig identity to simplify your answers: 𝑠𝑖𝑛2 𝜃 + 𝑐𝑜𝑠 2 𝜃 = 1 𝑉𝑒𝑐𝑡𝑜𝑟 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑥 − 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑦 − 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑧 − 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑣Ԧ −𝝎𝑹𝒔𝒊𝒏(𝝎𝒕) 𝝎𝑹𝒄𝒐𝒔(𝝎t) 0 𝑎 −𝝎2𝑹𝒄𝒐𝒔(𝝎𝒕) −𝝎2𝑹𝒔𝒊𝒏(𝝎t) 0 Q9: Show that 𝑣Ԧ and 𝑎Ԧ are mutually orthogonal, i.e. the angle between them is 90°. You can do this by symbolically computing the scalar product of the two vectors and verifying that 𝑣Ԧ ∙ 𝑎Ԧ = 0 Note that if the scalar product of any two vectors is zero, those vectors are guaranteed to be mutually orthogonal. Show all steps in your computation. (Hint: use the scalar product formula in terms of the components of the input vectors)
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