Question

i) A mass of 5 kg is moving at 9 m/s in the +x direction which collides inelastically with a mass (mass 2) of 4 kg. After the collision, the masses are moving at 5 m/s in the +x direction. What is change in total KE in the collision, in Joules? If negative, include a negative sign.

ii) Mass 1 is initially moving at 5 m/s in the +x direction and it collides perfectly elastically with mass 2 moving at 8 m/s in the -x direction. After the collision, mass 1 is moving at 5 m/s in the +x direction. What is the final velocity of mass 2 in m/s? If in the negative x direction, include a negative sign. (Note: the masses are not needed to answer this question.)

Answer 1

Solution)(i) m1 = 5 kg

u1 = 9 m/s in +X direction

u1 = 9(i) m/s

m2 = 4 kg

u2 = 0

V = 5 m/s in + X direction

V = 5(i) m/s

Total change in KE = ?

KE = KEf - KEi

KE = (1/2)(m1+m2)(V^2) - [(1/2)(m1)(u1^2) + (1/2)(m2)(u2^2)]

KE = (1/2)(9)(5^2) - [(1/2)(5)(9^2) + (1/2)(4)(0^2)]

KE = - 90 J

(ii) m1

m2

u1 = 5 m/s in +X direction

u1 = 5(i) m/s

u2 = 8 m/s in - X direction

u2 = 8(-i) = - 8(i) m/s

V1 = 5 m/s in + X direction

V1 = 5(i) m/s

V2 = ?

Applying conservation of momentum

(m1)(u1) + (m2)(u2) = (m1)(V1) + (m2)(V2)

(m1)(5(i)) + (m2)(-8(i)) = (m1)(5(i)) + (m2)(V2)

- 8(i) = V2

V2 = - 8(i) m/s

So m2 moves in - X direction with speed V2 = 8 m/s