Question

# A mass of 4 kg is moving at 11 m/s in the +x direction and it...

A mass of 4 kg is moving at 11 m/s in the +x direction and it collides inelastically with a mass of 6 kg moving in the -x direction. The collision takes places in 0.40 seconds and the average force on the mass moving in the +x direction is 217 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.

here,

mass , m1 = 4 kg has initial speed , u1 = 11 m/s

mass , m2 = 6 kg

force , F = 217 N

let teh final speed of m1 be v1

impulse delivered to 1 , I1 = - F * t = m * ( v1 - u1)

- 217 * 0.4 = 4 * ( v1 - 11)

v1 = - 10.7 m/s

let the inital speed of m2 = 6 kg mass be u2

using comservation of momentum

m1 * u1 + m2 * u2 = ( m1+ m2) * v1

4 * 11 + 6 * u2 = ( 4 + 6) * (-10.7)

u2 = - 10.5 m/s

the total kinetic energy is lost in the collision , KE = initial kinetic energy - final kinetic energy

KE = 0.5 * (m1 * u1^2 + m2*u2^2) - 0.5 * ( m1 + m2) * v1^2

KE = 0.5 * ( 4 * 11^2 + 6 * 10.5^2 - (4 + 6) * 10.7^2)

KE = 0.3 J

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