The lead female character in the movie Diamonds Are Forever is standing at the edge of an offshore oil rig. As she fires a gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is 0.011 kg, and its velocity is +731 m/s. Her mass (including the gun) is 56 kg.
a) What recoil velocity does she acquire in response to a single shot from a stationary position, assuming that no external force keeps her in place?
b) Under the same assumption, what would be her recoil velocity if, instead, she shoots a blank cartridge that ejects a mass of 5.0 10-4 kg at a velocity of +731 m/s?
m1v1 = m2v2
Cons of momentum
To find the recoil velocity of the lead female character in the movie Diamonds Are Forever, we will use the principle of conservation of momentum. The equation for conservation of momentum is:
Total momentum before = Total momentum after
a) In this case, the total momentum before the shot is fired is zero since the character is initially stationary. So, the total momentum before is 0 kg*m/s.
The momentum after the shot is fired consists of the momentum of the bullet and the momentum of the character (including the gun). The momentum of the bullet can be calculated by multiplying the mass of the bullet (0.011 kg) by its velocity (+731 m/s). The momentum of the character can be calculated by multiplying the mass of the character (56 kg) by her recoil velocity (which is what we want to find).
So, the equation for conservation of momentum becomes:
0 kg*m/s = (0.011 kg * 731 m/s) + (56 kg * recoil velocity)
Now we can solve for the recoil velocity:
0 kg*m/s = 8.041 kg*m/s + (56 kg * recoil velocity)
Rearranging the equation:
(56 kg * recoil velocity) = -8.041 kg*m/s
Dividing both sides by 56 kg:
recoil velocity = (-8.041 kg*m/s) / 56 kg
Calculating the recoil velocity:
recoil velocity = -0.1436 m/s
Therefore, the lead female character would acquire a recoil velocity of approximately -0.1436 m/s (negative because she would be pushed back).
b) In this scenario, the bullet is replaced with a blank cartridge that ejects a mass of 5.0 * 10^-4 kg at a velocity of +731 m/s. Again, using the principle of conservation of momentum:
Total momentum before = Total momentum after
The total momentum before the shot is fired is still zero.
The momentum after the shot is fired consists of the momentum of the ejected mass and the momentum of the character.
The momentum of the ejected mass can be calculated by multiplying its mass (5.0 * 10^-4 kg) by its velocity (+731 m/s).
The equation for conservation of momentum becomes:
0 kg*m/s = (5.0 * 10^-4 kg * 731 m/s) + (56 kg * recoil velocity)
Now we can solve for the recoil velocity:
0 kg*m/s = 0.3655 kg*m/s + (56 kg * recoil velocity)
Rearranging the equation:
(56 kg * recoil velocity) = -0.3655 kg*m/s
Dividing both sides by 56 kg:
recoil velocity = (-0.3655 kg*m/s) / 56 kg
Calculating the recoil velocity:
recoil velocity = -0.0065 m/s
Therefore, if the lead female character shoots a blank cartridge, she would acquire a recoil velocity of approximately -0.0065 m/s.