A 10 gram bullet is shot from a 500 gram gun at a speed of 230 m/s. Find the speed and kinetic energy of the bullet and the gun. Assume that the momentum and energy of the escaping gasses are negligible.
To find the speed and kinetic energy of the bullet, we can use the equation:
Kinetic energy = (1/2) * mass * velocity^2
The mass of the bullet is given as 10 grams, which is equivalent to 0.01 kg. The velocity of the bullet is given as 230 m/s.
Kinetic energy of the bullet = (1/2) * 0.01 kg * (230 m/s)^2
= 0.01 kg * 132,250 m^2/s^2
= 1,322.5 Joules
So, the kinetic energy of the bullet is 1,322.5 Joules.
To find the speed and kinetic energy of the gun, we can use the concept of conservation of momentum.
According to the principle of conservation of momentum, the momentum before the bullet is fired is equal to the momentum after the bullet is fired. The momentum of an object is given by the equation:
Momentum = mass * velocity
The initial momentum of the system (bullet + gun) is 0, since both the bullet and the gun are at rest initially.
After the bullet is fired, the momentum of the bullet is given by:
Momentum of the bullet = mass of the bullet * velocity of the bullet
= 0.01 kg * 230 m/s
= 2.3 kg m/s
According to the principle of conservation of momentum, the momentum of the gun after the bullet is fired should be equal in magnitude and opposite in direction to the momentum of the bullet.
Therefore, the momentum of the gun after the bullet is fired is -2.3 kg m/s.
Now, we can find the speed and kinetic energy of the gun.
Momentum of the gun = mass of the gun * velocity of the gun
Since the mass of the gun is given as 500 grams, which is equivalent to 0.5 kg, we can rearrange the equation to solve for the velocity of the gun:
Velocity of the gun = Momentum of the gun / Mass of the gun
= (-2.3 kg m/s) / (0.5 kg)
= -4.6 m/s
Therefore, the speed of the gun after the bullet is fired is 4.6 m/s.
The kinetic energy of the gun can be calculated using the equation:
Kinetic energy of the gun = (1/2) * mass of the gun * (velocity of the gun)^2
= (1/2) * 0.5 kg * (4.6 m/s)^2
= 5.29 Joules
So, the kinetic energy of the gun is 5.29 Joules.