Question 4 1 point Two protons collide in the large hadron c

Question 4 (1 point)

Two protons collide in the large hadron collider (LHC). The world record collisions are at 13 TeV, with both protons having 6.5 TeV of energy, but many millions of collisions happen. When a proton is moving along the beam with a speed of 0.320c, what is its Newtonian momentum in the frame of reference of the LHC (to 2 significant figures)? [You will have to look up some quantities to 3 significant figures]

Note: Your answer is assumed to be reduced to the highest power possible.

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Question 5 (1 point)

When a proton is moving along the LHC beam with a speed of 0.320c, what is its relativistic momentum in the frame of reference of the LHC (to 2 significant figures)?

Note: Your answer is assumed to be reduced to the highest power possible.

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Question 6 (2 points)

How slowly would a proton have to be moving along the LHC beam for its relativistic momentum to be 1% different from the Newtonian momentum in the frame of reference of the LHC (to 2 significant figures)? Enter your answer as some number (in scientific notation) with the units as c (e.g. 0.320c would be entered as 3.2 x 10^-1 c).

Note: Your answer is assumed to be reduced to the highest power possible.

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Solution

Question 4. Newtonian mometum   p = m_o v

              m_o rest mass of proton , v = velocity of proton = 0.32 c

                                                 p = 1.6726219 * 10^ -27 * 032 * 3 * 10^8 m /sec

                                                    p = 1.605 * 10^-19 kg m/sec

question 5

                            Relativistic mometum , p = m_o v / sqrt (1- v^2 /c^2)             using v = 0.32 c

                                                                          = 1.605 * 10^-19 / 0.947

                                                                          = 1.694 * 10^-19 kg .m/sec