How to calculate kinetic energy of a system? (Momentum and impulse)

Question

I posted this question yesterday, but there is another part of the problem I don't understand

 

A 0.76 kg fireworks rocket moving at a speed of 32 m/s breaks into two pieces as the result of an explosion. After the explosion a 0.28 kg piece moves with a speed of 42 m/s in the original direction. What is the velocity of the other piece?

 

The velocity is 26 m/s

 

b) Find the changes in momentum and the kinetic energy of the system

 

I= p_f-p_i

 

I=[0.28(42)+0.48(26)]-[0.76(32)]

I=24.24-24.32

I= -0.1   ?

 

Not sure if this is correct

 

 

How do I find the change in kinetic energy of the system?

Answer 1

(A)

 

Use conservation of momentum.

 

M = mass of rocket = 0.76 kg

m = 0.28 kg

v = initial velocity of rocket = 32 m/s

u = final velocity of the 0.28 kg piece = 42 m/s

u' = final velocity of the other piece = ?

 

Mv = mu + (M - m)u' ⇒

 

u' = (Mv - mu) / (M - m) = [0.76(32) - 0.28(42)] / (0.76 - 0.28) m/s ≅ 26.167 m/s

 

(B)

 

Δp = 0,

 

since total momentum of the SYSTEM is conserved.

 

K = kinetic energy

 

ΔK = K_f - K_i = [mu²/2 + (M - m)u'²/2] - Mv²/2

 

ΔK =  [0.28(42)²/2 + (0.76 - 0.28)(26.167)²/2] - 0.76(32)²/2 (joules)

 

ΔK = [246.96 + 164.331] - 389.12 = 22.171 J

 

The increase in kinetic energy may be attributed to the energy provided by the explosion.  However, momentum is conserved, since the explosion is an internal interaction between the parts of the system.