A 27 kg gun is standing on a frictionless sur-
face. The gun fires a 56 g bullet with a muzzle
velocity of 314 m/s.
The positive direction is that of the bullet.
Calculate the momentum of the bullet im-
mediately after the gun was fired.
Answer in units of kg · m/s
Calculate the momentum of the gun immedi-
ately after the gun was fired.
Answer in units of kg · m/s
Calculate the kinetic energy of the bullet im-
mediately after the gun was fired.
Answer in units of J
Calculate the kinetic energy of the gun imme-
diately after the gun was fired.
Answer in units of J
To solve these problems, we will use the principles of conservation of momentum and conservation of kinetic energy.
First, let's calculate the momentum of the bullet immediately after the gun was fired. The momentum of an object is given by the product of its mass and velocity.
Given:
Mass of the bullet, m_bullet = 56 g = 0.056 kg
Muzzle velocity of the bullet, v_bullet = 314 m/s
Momentum of the bullet, p_bullet = m_bullet * v_bullet
Substituting the values, we have:
p_bullet = 0.056 kg * 314 m/s = 17.584 kg · m/s
So, the momentum of the bullet immediately after the gun was fired is 17.584 kg · m/s.
Next, let's calculate the momentum of the gun immediately after it was fired. Since the gun and bullet are initially at rest, the momentum of the gun before firing is zero. According to the conservation of momentum, the total momentum before firing must be equal to the total momentum after firing.
Total momentum before firing = Total momentum after firing
Since the bullet is the only object moving after the gun was fired, the momentum of the gun must be equal in magnitude and opposite in direction to the momentum of the bullet.
Therefore, the momentum of the gun immediately after it was fired is also 17.584 kg · m/s but in the negative direction.
Next, let's calculate the kinetic energy of the bullet immediately after it was fired. The kinetic energy of an object is given by the formula KE = (1/2) * m * v^2.
Given:
Mass of the bullet, m_bullet = 56 g = 0.056 kg
Muzzle velocity of the bullet, v_bullet = 314 m/s
Kinetic energy of the bullet, KE_bullet = (1/2) * m_bullet * v_bullet^2
Substituting the values, we have:
KE_bullet = (1/2) * 0.056 kg * (314 m/s)^2 = 2782.408 J (rounded to three decimal places)
So, the kinetic energy of the bullet immediately after the gun was fired is approximately 2782.408 J.
Finally, let's calculate the kinetic energy of the gun immediately after it was fired. Since the gun is initially at rest, its kinetic energy before firing is zero. According to the conservation of kinetic energy, the total kinetic energy before firing must be equal to the total kinetic energy after firing.
Total kinetic energy before firing = Total kinetic energy after firing
Since the bullet is the only object moving after the gun was fired, the kinetic energy of the gun must be zero.
Therefore, the kinetic energy of the gun immediately after it was fired is zero Joules.