A rifle with a mass of 2.0kg is used to fire a bullet with a mass of 50.g. The bullet leaves the gun with a speed of 200. m/s. What is the recoil velocity of the gun?
Use the law of conservation of momentum. The bullet and the gun will have equal and opposite momenta right after the bullet leaves the rifle.
2.0 * Vrecoil = 0.05 kg * 200 m/s
Solve for Vrecoil
commanly the formula is: *m1u1+m2u2+m1v1+m2v2*
substitute the values according to this formulae.
This data can be likely:
mass of rifle=m1=2.0kg
mass of bullet=m2=50g=kg= 50/1000=0.05kg
velocity of gun=v1=0m/s
velocity of recoil of gun=v2=?
To find the recoil velocity of the gun, we can use the principle of conservation of momentum. According to this principle, the momentum before firing should be equal to the momentum after firing.
Step 1: Calculate the momentum of the bullet
Momentum (p) is defined as the product of the mass (m) and velocity (v).
Given:
Mass of the bullet (m₁) = 50 g = 0.050 kg
Velocity of the bullet (v₁) = 200 m/s
Momentum of the bullet (p₁) = m₁ * v₁
p₁ = 0.050 kg * 200 m/s
Step 2: Calculate the momentum of the gun
Given:
Mass of the gun (m₂) = 2.0 kg
Recoil velocity of the gun (v₂) = ?
Momentum of the gun (p₂) = m₂ * v₂
Step 3: Apply the conservation of momentum
According to the principle of conservation of momentum, the total momentum before firing is equal to the total momentum after firing.
Initial momentum = Final momentum
m₁ * v₁ + m₂ * 0 = 0 + m₂ * v₂
0.050 kg * 200 m/s + 2.0 kg * 0 = 0 + 2.0 kg * v₂
0.050 * 200 = 2.0 * v₂
10 = 2.0 * v₂
Divide by 2.0 on both sides:
v₂ = 10 / 2.0
v₂ = 5.0 m/s
Therefore, the recoil velocity of the gun is 5.0 m/s.
To find the recoil velocity of the gun, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
In this case, let's assume that the rifle and the bullet form a closed system. Initially, the rifle and bullet are at rest, so the total momentum before the event is zero. After firing the bullet, the rifle gains a recoil velocity while the bullet acquires its own velocity.
We can calculate the recoil velocity of the gun using the conservation of momentum equation:
(mass of rifle * velocity of rifle) + (mass of bullet * velocity of bullet) = 0
Given:
Mass of rifle (m1) = 2.0 kg
Mass of bullet (m2) = 50 g = 0.050 kg
Velocity of bullet (v2) = 200 m/s
Rearranging the equation, we have:
(m1 * v1) + (m2 * v2) = 0
To find the recoil velocity of the gun (v1), we can substitute the known values into the equation and solve for v1:
(2.0 kg * v1) + (0.050 kg * 200 m/s) = 0
Simplifying the equation further:
2.0 kg * v1 = -0.050 kg * 200 m/s
2.0 kg * v1 = -10 kg·m/s
Dividing both sides by 2.0 kg:
v1 = -10 kg·m/s / 2.0 kg
v1 = -5 m/s
Therefore, the recoil velocity of the gun is -5 m/s. The negative sign indicates that the gun moves in the opposite direction of the bullet.