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Homework Statement
A rifle with a mass of 3.22 kg fires an 11.9 g bullet at a velocity of 590 m/s. What is the recoil velocity of the rifle? Compare the change in momentum of the bullet and the rifle. Compare the change in kinetic energy of the bullet and the rifle. Which is bigger, by what factor?
Homework Equations
m_1v_1 + m_2v_2 = m_1v_1 + m_2v_2
(initial) (final)
K = 1/2mv²
The Attempt at a Solution
(a)What is the recoil velocity of the rifle?
We know
mass of rifle = 3.22 kg
mass of bullet = .0119 kg
initial velocity of rifle = 0
initial velocity of bullet = 0 (this one I thought would be the 590m/s but my prof said they both start from rest)
final velocity of bullet = 590 m/s
final velocity of rifle = V_1 (what we want)
m_1v_1(initial) + m_2v_2(initial) = m_1v_1(final) + m_2v_2(final)
So this would be solving for v_1 final so rearrange for that
V_1 = [m_1v_1(initial) + m_2v_2(initial) - m_2v_2(final)]/ m_1
V_1 = [3.22 kg(0) + .0119 kg(0) - .0119 kg(590m/s)] / 3.22 kg
(the answer would be a negative number which makes sense because the direction is opposite)
so V_1 = -2.18m/s
(b) Compare the change in momentum of the bullet and the rifle.
I'm not sure about this one
(c) Compare the change in kinetic energy of the bullet and the rifle
I was thinking
1/2mV_f² - 1/2mV_i² for the bullet and for the rifle
so
mass of rifle = 3.22 kg
mass of bullet = .0119 kg
initial velocity of rifle = 0
initial velocity of bullet = 0 (this one I thought would be the 590m/s but my prof said they both start from rest)
final velocity of bullet = 590 m/s
final velocity of rifle = V_1 (what we want)
Rifle
ΔK_r = 1/2mV_f² - 1/2mV_i²
= 1/2(3.22kg)(-2.18m/s)² - 1/2(3.22kg)(0)²
K_r = 7.65J
Bullet
ΔK_b = 1/2mV_f² - 1/2mV_i²
= 1/2(.0119 kg)(590 m/s)² - 1/2(.0119 kg)(0)²
K_b = 2071.2J
Are these correct? and how would I go about (b)? I'm just not too sure what it is asking