Name: Grade 8- Section: Score: School: Teacher: Sublect: General Physics 2 LAS Writer: JAN JEFFREY R. CAMINA Content Editor: Learning Topic: Relativistic Momentum and Energy; Quarter 4-Week 7 LAS 1 Learning Targets: Calculate kinetic energy, rest energy, momentum, and speed of objects moving with speeds comparable to the speed of light. STEM_GP12MP-lVg-42 Reference(s): Walker, Jearl, David Halliday, and Robert Resnick. 2004. Fundamentals 0f Physics. 7th ed. New Jearsey: John Wiley and Sons Inc., pp.1270-1274. Relativistic Momentum and Energy Relativistic Momentum (p) a 4.0 It is iust classical momentum multiplied by the relativistic factor (y). E, 30 e. . P = ymu cf where m is the rest mass of the object, it is its velocity relative to an observer, 5 1 and the relativistic factor. 5 1.0 _ 1 E Y _ 2 1_u_ 0 r2 0 0.2:; 0.4:.- ucc use 1.0: speed H (We) Figure 1. Relativistic momentum approaches infinity as the velocity of Relativistic momentum has the same intuitive feel as classical momentum. It is greatest for large masses moving at high velocities, but, because of the lactor (y), relativistic momentum approaches infinity as velocity (u) approaches speed of light to). (See Figure 1)This is another indication that an object with mass cannot reach the speed of light. If it did, its momentum would become infinite, an unreasonable value. an object approaches the speed of light. Example: An electron, which has a mass of 9.11 x 10*11 kg, moves with a speed of 0.750c. Find its relativistic momentum. Given: Solution: m.=9.11 x10'3' kg 9.11 111: [1.7 3.0 1"m u:0.750c P= m[_eu g x u 3 5\" 5W2" x " /}=3.1ox1o-22kgm/s 13: 1_(0.7:r:) C Relativistic Energy The first postulate of relativity states that the laws of physics are the same in all inertial frames. Einstein showed that the law of conservation of energy is valid relativistically, if we define energy to include a relativistic factor. It can be summarized by the equation below: Kinetic Energy (K) is dened as: K : ymcz- rm-2 'I' Total Energy (E) is dened as: Rest Energy Energy (Ea) is dened as: E : rm:2 E:ymc' The Relationship of relativistic momentum and energy can be defined by: E1 : (pa)2 + (new?)2 Example: An electron in a television picture tube typically moves with a speed a = 0.250. Find its total energy and kinetic energy in electron volts (E9 = 0.511 MeV). Given: Solution: E0=CL511 MeV 62 E 0 511 M V n = 0.25:: L = " = T; = 0.523 MeV K: E E): 0.523 MeV 0.511 MeV 1.12 u1 1 1:2 i172 \"2 = o. 7 MeV Activity: Solve the following problems. Use the rubrics as your guide in presenting your solution (refer to attachment A.1 at the next page). 1. An electron, which has a mass of 8.45 x 10-31 kg, moves with a speed of 0.45c. Find its relativistic momentum and lind the percentage increase of its relativistic momentum lrom its classical momentum. 2. An electron in a television picture tube typically moves with a speed it = 0.25c. Find its total energy and kinetic energy in electron volts (Ea = 0.385 MeV} A.1 Rubrlce for the Activity Fully meet the and labels it correctly. (2 points) Mlnlmelly meet the error or did not label it correctly. (1 point) Did not meet the expectations expectations expectations Solution Correct and complete Incomplete solution with Wrong solution solution with no minimal mathematical errors _ mathematical errors (1 WW} (2 points) (3 points) Flnal Answer Final answer is correct Makes a small computation Answer is incorrect, or student does not have a final answer. (0)