PY CH6 HW6:-

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You throw a ball of mass 0.8 kg straight up. You observe that it takes 2.6 s to go up and down, returning to your hand. Assuming we can neglect air resistance, the time it takes to go up to the top is half the total time, 1.3 5, Note that at the top the momentum is momentarily zero, as it changes from heading upward to heading downward. (a) Use the momentum principle to determine the speed that the ball had just AFFER it left your hand, Vinitial = m/s (b) Use the Energy Principle to determine the maximum height above your hand reached by the ball. h = m Two protons are a distance 8 x 10.9 m apart. What is the electric potential energy of the system consisting of the two protons? Uel = joules Ifthe two protons move closer together, will the electric potential energy of the system increase, decrease, or remain the same? remain the same increase decrease A proton and an electron are a distance 8 x 10'9 m apart. What is the electric potential energy of the system consisting of the proton and the electron? Uel = joules Ifthe proton and the electron move closer together, will the electric potential energy of the system increase, decrease, or remain the same? increase decrease remain the same Which of the following statements are true? If released from rest two protons would move closer together, increasing the potential energy of the system. If any two charged particles are released from rest, they will spontaneously move in the direction in which the potential energy of the system will be decreased. In some situations charged particles released from rest would move in a direction that increases electric potential energy, but not in other situations. K K+U D E K K+U K K u K+U U U K+ K U U Which of the diagrams above corresponds to a system of two electrons which start out far apart, moving toward each other (that is, their initial velocities are nonzero and they are heading straight at each other)? which of the diagrams above corresponds to a system of a proton and an electron which start out far apart, moving toward each other (that is, their initial velocities are nonzero and they are heading straight at each other)? \fTwo protons that are very far apart are hurled straight at each other, each with an initial kinetic energy of 0.16 MeV, where 1 mega electron volt is equal to 1x106 X (1.6X10'19) joules. What is the separation of the protons from each other when they momentarily come to a stop? separation = m In a fusion reaction, the nuclei of two atoms join to form a single atom of a different element. In such a reaction, a fraction of the rest energy of the original atoms is converted to kinetic energy of the reaction products. A fusion reaction that occurs in the Sun converts hydrogen to helium. Since electrons are not involved in the reaction, we focus on the nuclei. Hydrogen and deuterium (heavy hydrogen) can react to form helium plus a high-energy photon called a gamma ray: 1H +2 H -3 Hety Objects involved in the reaction: Particle # of # of neutrons Charge Rest Mass (atomic mass protons units) 1H (proton) 1 O 1.0073 2 H 2.0136 (deuterium) 3 He +26 3.0155 (helium) gamma ray 0 0 Although in most problems you solve in this course you should use values of constants rounded to 2 or 3 significant figures, in this problem you must keep at least 5 significant figures throughout your calculation. Problems involving mass changes require many significant figures because the changes in mass are small compared to the total mass. In this problem you must use the following values of constants, accurate to 5 significant figures: Constant Value to 5 significant figures c (speed of light) 2.9979e8 m/s e (charge of a 1.6022e-19 coulomb proton) atomic mass unit 1.6605e-27 kg 8.9875e9 N.m2 /C2 The diagrams below represent different states in the fusion process: (a) (b) C) A proton ( H nucleus) and a deuteron ("H nucleus) start out far apart. An experimental apparatus shoots them toward each other (with equal and opposite momenta). If they get close enough to make actual contact with each other, they can react to form a helium-3 nucleus and a gamma ray (a high energy photon, which has kinetic energy but zero rest energy). Consider the system containing all particles. Work out the answers to the following questions on paper, using symbols (algebra), before plugging numbers into your calculator. A: Bringing the particles together Which diagram depicts the initial state in the process of bringing the particles together? C a Which diagram depicts the final state in the process of bringing the particles together? a C Compare the initial state and final states of the system. Which quantities have changed? potential energy kinetic energy rest energy The deuterium nucleus starts out with a kinetic energy of 8.4e-14 joules, and the proton starts out with a kinetic energy of 1.67e-13 joules. The radius of a proton is 0.9e-15 m; assume that if the particles touch, the distance between their centers will be twice that. What will be the total kinetic energy of both particles an instant before they touch? Kin + K2# = joules B: Reaction to make helium Now that the proton and the deuterium nucleus are touching, the reaction can occur. Take the final state from the previous process to be the initial state of the system for this new process. Which diagram depicts the final state?Compare the initial state and nal states of the system. Which quantities have changed? kinetic energy rest energy potential energy What is the kinetic energy of the reaction products (helium nucleus plus photon)? Km + R3 = joules C: Gain of kinetic energy: What was the gain of kinetic energy in this reaction? (The products have more kinetic energy than the original particles did when they were far apart. How much more?) AK : joules D: Fusion as energy source Kinetic energy can be used to drive motors and do other useful things. If a mole of hydrogen and a mole of deuterium underwent this fusion reaction, how much kinetic energy would be generated? joules (For comparison, around le joules are obtained from burning a mole of gasoline.) A spring whose stiffness is 1060 N/m has a relaxed length of 0.55 m. If the length of the spring changes from 0.30 m to 0.85 m, what is the change in the potential energy of the spring? AU= J A spring has a relaxed length of 8 cm and a stiffness of 50 N/m. How much work must you do to change its length from 11 cm to 15 cm? N.mA horizontal spring with stiffness 0.2 N/m has a relaxed length of 16 cm (0.16 m). A mass of 19 grams (M19 kg) is attached and you stretch the spring to a total length of 29 cm (0.23 m). The mass is then released from rest. What is the speed of the mass at the moment when the spring returns tg its relaxed length of 16 cm (0.16 m)7 v = m/s The figure shows a potential energy curve for the interaction of two neutral atoms. The two-atom system is in a vibrational state indicated by the heavy solid horizontal line. DEV 43.2 av: 0.4 avg 43.5 av: 413 av: 1.0 6V7 4.? av: 1.4 av: l.6 av: (a) At r : r1, what are the approximate values of the kinetic energy K, the potential energy U, and the quantity K+U? K= eV U = eV K+U = eV (b) What minimum (positive) amount of energy must be supplied to cause these two atoms to separate? eV