Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

(10%) Problem 8: A cue ball of mass m1-0.365 kg is shot at another billiard ball

ID: 2039376 • Letter: #

Question

(10%) Problem 8: A cue ball of mass m1-0.365 kg is shot at another billiard ball, with mass m2 OS6 kg, which is at rest. The cue ball has an initial speed of v 6.5 m/s in the positive direction. Assume that the collision is elastic and exactly head-on. 50% Part (a) what is the horizontal component of the cue ball's velocity, vr after the collision, in meters per second? Grade Summary Potential1 Submissions (2% per attempt) sinO cos0 tan7 89 cotan0 asinO acoso detailed view atan0 acotan0 sinh 0 tanhO cotanh Radians I give up Hint Hints: 2 deduction per hint. Hints remaining: - -& 50% Part(b) what is the horizontal component of the cue ball's final velocity,vir in meters per second?

Explanation / Answer

m1 = 0.365 kg                           m2 = 0.56 kg


speeds before collision


v1i = 6.5 m/s                       v2i = 0 m/s

speeds after collision


v1f = ?                         v2f = ?


initial momentum before collision


Pi = m1*v1i + m2*v2i

after collision final momentum

Pf = m1*v1f + m2*v2f

from momentum conservation


total momentum is conserved

Pf = Pi


m1*v1i + m2*v2i = m1*v1f + m2*v2f .....(1)


from energy conservation


total kinetic energy before collision = total kinetic energy after collision


KEi = 0.5*m1*v1i^2 + 0.5*m2*v2i^2

KEf =   0.5*m1*v1f^2 + 0.5*m2*v2f^2


KEi = KEf


0.5*m1*v1i^2 + 0.5*m2*v2i^2 = 0.5*m1*v1f^2 + 0.5*m2*v2f^2 .....(2)

solving 1&2


we get


v1f = ((m1-m2)*v1i + (2*m2*v2i))/(m1+m2)

v2f = ((m2-m1)*v2i + (2*m1*v1i))/(m1+m2)

==============================


part(a)

final speed of goalie


v1f = ((m1-m2)*v1i + (2*m2*v2i))/(m1+m2)

v1f = ((0.365-0.56)*6.5 + (2*0.56*0))/(0.356 + 0.56)


v1f = -1.4 m/s


=====================


part(b)

v2f = ((m2-m1)*v2i + (2*m1*v1i))/(m1+m2)


v2f = ((0.56-0.365)*0 + (2*0.56*0.365))/(0.365 + 0.56)

v2f = 0.44 m/s