Question

Activity 4c: Analyzing Equations for Elastic Collisions Our textbook claims (without deriving, due to some "straightforward but messy algebra”) that we can predict the velocities of the two carts after an elastic collision with a relatively simple formula: V1.5 = (mi - m2 V11 \m₂ + m₂ (Equation 1) V2.5 = 2mi V1, \mi + m2 (Equation 2) where subscripts 1 and 2 refer to the first cart and the second cart, respectively, i and frefer to the time before the collision and after the collision, respectively, and the second cart's initial velocity is 0. (Note: an interesting fact from the theory of relativity is that we may add a fixed velocity to all objects in a system without changing any consequences of a collision, meaning that we can always find an analogous system where the second cart's initial velocity is 0 by adding or subtracting a particular amount) Question 4.3 Suppose the two carts have equal mass, m = m2. Algebraically, what does the equation for V1,8 reduce to? V2,5? Question 4.4 Look back at your equations in Case 1 for elastic collisions. Do your observations of the carts match with your algebraic expressions you derived in Question 4.3 above? Question 4.5 Look back at Equation 1. Suppose the mass of cart 1 is greater than the mass of cart 2. Can ma-ma ever be equal to 0 or less than 0? (Hint: you may choose arbitrary values for m+m2 m1 and m2 to test your answer; if you can find a set values that contradict your answer, you know that your assertion is incorrect)

Answer 1

I have solved your problem which is shown below:

In this question there are some parts which are related to observations and as I dont know the observation that has been taken in this experiment so i answered the question on the basis that it is purely elastic collison in which there is no loss of energy.

Own Vis? mm2 Vui - m, tm. Ured شارا V m, + m2 Ou +4.3 miam then Vigo Vaig [ 2m.] Vije Vas Visi Ow-414 If the collision is beyochly eleashe then the equation must sahisfy. But un ochial there is Somo loss of velocity because of friction and ani resistanu and these faches. results Comes close but not exachly matches with the theoretical because berfectly elash collision is not bossible,

Ouer 4.5 Suplese mi> m2 No mi-me cen never be equal as less than o mit m₂ y m,m. Suppose m, a 519, Зl8 mi>m₂ miam 5-3 5+3 مه 2 mit me - 0:25 -J which is greater than So this statement wro incorrecto 0 +4.6 mia sig M2 2314 Viisa mm2 را با 5-3 vii ☺ Vii = 0.25 Uli mitom 5+3 U2iS 2m, Vui 5 2x 5 :نا رنا V to videa 1.25 VI, i mitm. (5+3) su therehe results. This is the experimentally น collisions an eleshe then it should Support this theorend obsenchon.

0+4.7 mi Lm₂ mi-m2 m, tm₂ Subbowe mia 3kg , m2a519 - 3-5 doo -0.25 3+5 No this con not be greata a equal to you. it is always less then o y micms. 04.8 m = 319. M22 sig Visg? mim Vtis - 3-5 Visi 2 -0.25 Visi m,+ m2 3+5 Vaig 3m. Visi دارا دا 2 1.25 Visi + m2 8 If collisions are elesh then it most will Subolont theoretical and experiment al results. هوا Sign in vig indicates after collision the mi will move backw and in eleshi Collision.

024.9 2 mi Suppose mi? 3 is a m₂2 Sly 2 m. 2+ 3 6 8 0.75 m, tm, 8 AS masses مبله ays be the and greater then So this resuot con never be less than as equal yew. 074.10 Valis 2 m, vii mitmz 27 3 : نارا 0 0.75 Vasi 3 + S Yes this supports бол obserwations is Collision is purely elastic

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