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iPad? 7:52 PM * 53% a usi38ok.theexpertta.com The Expert TA I Human-like Grading, Automated! Chegg Study Guided Solutions and Study Help | Chegg.com (8%) Problem 1: A cue ball of mass m,-0.39 kg is shot at another billiard ball, with mass m2-0.575 kg, which is at rest. The cue ball has an initial speed of v= 9.5 m/s in the positive direction. Assume that the collision is elastic and exactly head-on X 25% Part (a) Write an expression for the horizontal component of the billiard ball's velocity, v26 after the collision, in terms of the other variables of the problenm 2(2 ml/(mi+m2))/v Grade Summary Deductions Potential 2% 98% Submissions (789HOME Attempts remaining: 3 45 6- %per attempt) detailed view 0% 0% 0% 0% 0 END V(| | BACKSPACE | | DEL?? CLEAR Submit I give up! Hints: 1 for a 2% deduction. Hints remaining: 0 Feedback: 2% deduction per feedback. Think about what is conserved in an elastic collision. In an elastic collision, both momentum and kinetic energy are conserved. Apply both of these equations and then carefully do the required algebra to solve for V2f 25% Part (b) What is this velocity, in meters per second? 25% Part (c) Write an expression for the horizontal component of the cue ball's velocity, vif, after the collision. 25% Part (d) What is the horizontal component of the cue ball's final velocity. In meters per second?Explanation / Answer
Two balls m1= 0.39 and m2= 0.575.
Before: v1 = v = 6.5 and v2 = 0
After v1f and v2f
Elastic collision means 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 = 0.575/0.39 =1.474
v2f = 2*9.5 / (1.474+1) = 7.679m/s
From above we have v1f = v - k* v2f
= 9.5 - 1.474* 7.679 = - 1.82m/s
a) v2f = 2v / ((m2/m1) + 1)
b) v2f = 7.679 m/s
c) v1f = v - (m2/m1)*v2f
d) v1f = - 1.82 m/s ( negative x) opposite direction
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