Question

A mass of 5 kg is moving at 12 m/s in the +x direction and it collides inelastically with a mass of 10 kg moving in the -x direction. The collision takes places in 0.27 seconds and the average force on the mass moving in the +x direction is 170 Newtons in the -x direction. How much total kinetic energy is lost in the collision in Joules? Answer is a positive number since I'm asking how much is lost.

please read question carefully. i posted this question before and i got the wrong answer. thank you.

Answer 1

m1 = 5 kg

v1x = 12 m/s

m2 = 10 kg

v2x = -v2

after collsion

v1'x = ?

v2'x = ?

Force applied on m1

F1 = m1*(v1'x-v1x)/t

-170 = 5*(v1'x - 12)/0.27

Force applied on m2

F2 = m2*(v2'x-v2x)/t

170 = 10*(v2'x - v2x)/0.27

v2'x - v2x = 4.59

v2'x = 4.59 + v2x

final velocity of m1 , v1'x = 2.82 m/s

final velocity of m2 , v2'x = 2.82 m/s

v1'x = v2'x = v = 2.82 m/s

from momentum conservation

mometum before collision = momentum after collision

m1*v1x + m2*v2x = (m1 + m2)*v2'x

(5*12) + (10*v2x) = (15)*2.82

v2x = -1.77 m/s

initial energy Ki = (1/2)*m1*v1x^2 + (1/2)*m2*v2x^2

Ki = (1/2)*5*12^2 + (1/2)*10*1.77^2 = 375.7 J

final energy Kf = (1/2)*(m1+m2)*v^2

Kf = (1/2)*15*2.82^2 = 59.643 J

energy lost = 316.057 J