Question

+ Conservation of Momentum Ph X Phy 1010-F19-Chapter 6-PH X webassignunet/web/Student/Assignment-Responses/submthdep 219474888tagssautosave C dimension. The system consists of the two objects and the only forces affecting the motion are the internal forces betwoen them during collision. ANALYZE (A) Determine the velocity after collision Because no external force acts, the colligion does not change the total momentum of the system of two particles. We set the total momentum before collision to the total momentum afterward: myVsm (m + m)v The final velocity of the two objects jolned together is given by the previous momentum conservation equation: (1) v V1 mv Using the valaes of this exercise, we get w4 kg-11 ms)-(13 kg)(4 m) m/s. (c1) (E) (8) Determine the change in total mechanical energy while the forces that the two objects exert on each other cannot change their total momentum, they can change the total kinetic energy in an inelastic collision such as the one being considered. All of the mechanical energy in the problem is kinetic energy. The change in kinetic energy is then KWmm?-m m At this point, we can either substitute the numerical values to evaluate AK, or we could substitute in Equation (1) for vy into the axpression for AK and simplity the apression before doing the calculation The first procedure is easler if only a numerical anmer is needed, while the second is more useful in exgloring how the less in kinetic energy depends on the velocities and masses of the colliding objects. Directly substituting in numerical values gives AK-4 kg13 kg(ym/s-4 kg-1 m/s 13 kg)34 m/) Following the second procedure instead leads to AK This could be used to calculate the same numerical aner, but it also show various features that you might examine in the simulation For example, notice that the change in kimetic energy depends on velocity only through the relative Intial velocty, or dfference in leal velocty f the two partides FINALIZE For a given inisal velocty wth the second object iniay at rest, does the sokution to this problem suggest that a large ratio of m to m or a smal ratio produces the largest pesble final velocity? when the two objects intialy have equal and oppositely-directed velodties what does the momentm conservation equation indicate wil happen? f the teo partides are of eual mass and the secn paricle s intaly staonaryhat simple relation applies between the initial valocty and the fnal velootand hy O Tyoe here to search y -9-Chp Sign n or Sign Che acer

Answer 1

It is an inelastie collision since the particles stick together, and velocity of separation is zero! When perfectly inelastic objects moving along the same line collide, they stick to each. other. 1. Let me and my be the masses re, and er be their velocities bebore collisions and Vb be their common velocity of a bodies after collision The brem conservation od momentum miv,+ ma una m, vt mor or v= m, o,tmavo Tm+mat - here we have assumed

both in the the objects are moving same direction such as en V muz Ilelase collision O -v Jatter ellision m, tm. But in more o ise, our problem objects in opposite direction ton here U is positive (ie and w, is negative simee it moves along negative a axis

17 So brom © we get V= m. (to) + mau I mitma = 4 xgx (-11) mis + 15 yg x rýmis - (4+13) ug = (-44 + 182) sq.m 17 kg = 158 kgon ing : : 8.117 mi = 8.117 mis so we see that final velocity Vf is positive, it means that after collision both particles move along positive a direction with speed 8.117 m/s

bo in total mechanical Change energy The kinetic energy before collision is I m, 1,2 + 1 mave? and kinetic energy after collision is ² (mitm) ut So change in kinetic energy =(Final ke - Initial KE) = +ma) ve 2 minutes amate? 3 [ormal) ter 1. ovog fimv,2 I marma)? - Movie) we have but the value of mitmet

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So change in mechanical energy i amima (20,-22)? 2 (m, + m2) bet V,= -11 mis V.2=14 m/s m, qug m2 = 13 kg =-4813(-11-14)? 2X 17 . - 950 Joule Total mechanical energy decreases ley 950 Joule Since change is negative.