a 10 kg gun recoils with a speed of 0.1 meter per second as it fires a 0.001kg bullet. what is the speed of the bullet as it leaves the gun
Conservation of momentum:
initial momentum=final momentum
0=10kg*(-0.1m/s)+.001kg*deltaV
solve for delta V
10.20
To find the speed of the bullet as it leaves the gun, we can use the principle of conservation of momentum. The total momentum before firing is equal to the total momentum after firing.
Before firing, the gun and bullet are at rest, so the total momentum is zero.
Let's denote the speed of the bullet as v (we are looking for this value).
The momentum of the bullet is given by:
Momentum_bullet = mass_bullet * velocity_bullet
After firing, the gun and bullet have opposite velocities. The momentum of the gun is given by:
Momentum_gun = -mass_gun * velocity_gun
The negative sign indicates that the gun's momentum is in the opposite direction to the bullet's momentum.
The total momentum after firing is:
Total_momentum_after = Momentum_bullet + Momentum_gun
Since the bullet leaves the gun, the total momentum after firing is only due to the bullet:
Total_momentum_after = Momentum_bullet
Therefore, we have:
Total_momentum_after = Momentum_bullet = mass_bullet * velocity_bullet
Total_momentum_after = - mass_gun * velocity_gun
Since the total momentum before firing is zero, we can set the two equations equal to each other:
mass_bullet * velocity_bullet = - mass_gun * velocity_gun
Now we can solve for the velocity of the bullet:
velocity_bullet = (- mass_gun * velocity_gun) / mass_bullet
Substituting the given values:
mass_gun = 10 kg
velocity_gun = -0.1 m/s
mass_bullet = 0.001 kg
velocity_bullet = (- 10 kg * -0.1 m/s) / 0.001 kg
Simplifying:
velocity_bullet = (1 kg m/s) / 0.001 kg
velocity_bullet = 1000 m/s
Therefore, the speed of the bullet as it leaves the gun is 1000 m/s.
To find the speed of the bullet as it leaves the gun, we can make use of the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired should be equal to the total momentum after the bullet is fired.
The momentum of an object is calculated by multiplying its mass with its velocity. In this case, the total momentum before the bullet is fired is the sum of the momentum of the gun and the momentum of the bullet, and the total momentum after the bullet is fired is just the momentum of the bullet.
Given:
Mass of the gun (m1) = 10 kg
Speed of the gun (v1) = 0.1 m/s
Mass of the bullet (m2) = 0.001 kg
Speed of the bullet (v2) = ?
Using the conservation of momentum, we can write the equation:
(m1 * v1) + (m2 * v2) = m2 * v2
Plugging in the values:
(10 kg * 0.1 m/s) + (0.001 kg * v2) = 0.001 kg * v2
Simplifying the equation:
1 kg*m/s + 0.001 kg*m/s = v2 * (0.001 kg)
Combining like terms:
1.001 kg*m/s = 0.001 kg * v2
Dividing both sides by 0.001 kg:
v2 = 1.001 kg*m/s / 0.001 kg
Simplifying:
v2 = 1001 m/s
Therefore, the speed of the bullet as it leaves the gun is 1001 meters per second.