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# Elastic/inelastic problems: A 15.0 kg penguin waddling east at a velocity of 7.0 m/s collides with a ...

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A month ago
 Elastic/inelastic problems: A 15.0 kg penguin waddling east at a velocity of 7.0 m/s collides with a ... Hi there, I was wondering if I could get help with this question. Thanks a lot A 15.0 kg penguin waddling east at a velocity of 7.0 m/s collides with a stationary 10.0 kg penguin. After the collision the 15.0 kg penguin is traveling at a velocity Of 4.2 m/s 20.00 S of E. a. What is the velocity of the 10.0 kg penguin after collision? b. is this collision elastic or inelastic? Read 101 times 6 Replies

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Staff Member
A month ago
 Part A:Using momentum conservation we have:Direction $$x$$:(15) (7.0) + 0 = (15) (4.2) cos (-20 °) + (10) v₂ (f) cosθ(10) v₂ (f) cosθ = (15) (7.0) - (15) (4.2) cos (-20 °) ... (Eq 1)Direction $$y$$:0 + 0 = (15) (4.2) sin (-20 °) + (10) v₂ (f) sinθ(10) v₂ (f) sinθ = - (15) (4.2) sin (-20 °) ... (Eq 2)We divide both equations (1) and (2):Left side:(10) v₂ (f) sinθ / (10) v₂ (f) cosθ = tanθRight side:- (15) (4.2) sin (-20 °) / (15) (7.0) - (15) (4.2) cos (-20 °)Clearing the angle we have:θ = tan⁻¹ [ - (15) (4.2) sin (-20 °) / (15) (7.0) - (15) (4.2) cos (-20 °) ]θ = 25 °We use any of the equations to find the speed.From (2) we have:(10) v₂ (f) sinθ = - (15) (4.2) sin (-20 °)v₂ = - (15) (4.2) sin (-20 °) / (10) sin25 °Answer:v₂ = 5.1m / sNote: θ = 25 ° (direction is in the first quadrant, north of east)Part B:Initial kinetic energy: K (i) = 0.5 (15) (7.0) ² = 370J (rounded)Final kinetic energy: KE (f) = 0.5 (15kg) (4.2m / s) ² + 0.5 (10kg) (5.1m / s) ² = 260J (rounded)Answer:A difference of 110J, so it was an inelastic collision.
 - Master of Science in Biology- Bachelor of Science (Biology)- Bachelor of Education
wrote...
A month ago
 Hey duddy it makes sense but could you write the initial equations to what we are plugging the numbers in? Thankss
wrote...
Staff Member
A month ago
 The conservation of momentum formula goes like this:total momentum before = total momentum afterlinear momentum = mass * velocityIn other words: $$\rho =m\cdot v$$I'll break down the first one for you, and hopefully you can apply it to the rest.Recall:Direction $$x$$:m*v + m*v = m*v + m*v1..........2.........3....... ...4in term 1: (15) (7.0) in term 2: (10) (0) = 0in term 3: (15) (4.2) cos (-20°)in term 4: (10) v₂ (f) cosθhow's that?
 - Master of Science in Biology- Bachelor of Science (Biology)- Bachelor of Education
wrote...
A month ago
 Yeah for sure thanks a lot!
wrote...
A month ago
 you just need number 5?
wrote...
A month ago
 Yeah, as it’s the only number circled.