Help W13( Linear momentum) Begin Date: 10/20/2017 12:00:00 AM- Due Date: 10/30/2
ID: 1791231 • Letter: H
Question
Help W13( Linear momentum) Begin Date: 10/20/2017 12:00:00 AM- Due Date: 10/30/2017 11:59:00 PM End Date: 12/14/2017 12:00:00 AM (1096) Problem 8: A cue ball ornass m1-0.395 kg is shot at another billiard ball, with mass m2 0.56 kg, which is at rest. The cue ball has an initial speed of 9.5 m s in the positive direction. Assume that the collision is elastic and exactly head-on. Randomized Variables m-0.395 kg m2 = 0.56 kg v=9.5 m/s 2596 Part (a) write an expression for the horizontal component of the billiard ball's velocity variables of the problem after the collision in terms of the other Grade Summary 0% 100% Potential Submissions Attempts remaining: 10 (2% per attempt) etailed view mi m2 Submit Hint I give up deduction per feedback Hints:--deduction per hnt Hints remaining:- Feedback: 0 25% Part (bewhat is this velocity, in maeters per second? 25% Part (c) write an expression for the horizontal component of the cue ball's velocity, ve, after the collision. 25% Part (d) what is the horizontal component of the cue ball's final velocity, in meters per second? All coatm' © 2017 Expert TA, LLCExplanation / Answer
Draw figures before and after collision
Two balls m1= 0.395 and m2= 0.56.
Before: v1 = v = 9.5 and v2 = 0
After v1f and v2f
Elastic collision => Total momentum is constant (1) and
.............................Total kinetic energy is constant (2)
m1* v + m2* 0 = m1* v1f + m2* v2f ........... (1)
m1* v²/2 + 0 = m1* (v1f)²/2 + m2* (v2f)²/2 ... (2) Let m2=k*m1 and simplify =>
v = v1f + k* v2f ...........(1) => v1f = v - k* v2f plug in (2)
v² = (v1f)² + k* (v2f)² ....(2)
v² = (v - k* v2f)² + k* (v2f)²
v² = v² - 2k* v*v2f + (k*v2f)² + k* (v2f)² , but v2f 0 divide by v2f =>
0 = -2k* v + k² * v2f + k* v2f
2k*v = v2f* (k² + k) , divide by k
v2f = 2v / (k+1) , now we plug in v = 9.5 and k = m2/m1 = 0.56/0.395 1.42
v2f = 2*9.5 / (1.42+1) = 7.85
From above we have v1f = v - k* v2f = 9.5 - 1.42* 7.85 = - 1.647
a) v2f = 2v / ((m2/m1) + 1)
b) v2f = 7.85 m/s
c) v1f = v - (m2/m1)*v2f
d) v1f = - 1.647 m/s ( negative x) opposite direction
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