a bullet of mass 30 g. is fired from a pistol of 2.1kg at a velocity of 300 m/s calculate the recoil velocity of the pistol
Total momentum remains zero.
The recoil momentum of the gun therefore equals the forward momentum of the bullet.
Vbullet*0.030 kg = Vrecoil*2.1kg
Vrecoil = (0.030/2.1)*300 m/s = 4.3 m/s
To calculate the recoil velocity of the pistol, we can use the principle of conservation of momentum.
The momentum before the firing is equal to the momentum after the firing. The momentum of an object is calculated by multiplying its mass by its velocity.
Given:
Mass of the bullet (mb) = 30 g = 0.03 kg
Mass of the pistol (mp) = 2.1 kg
Velocity of the bullet (vb) = 300 m/s
Let's denote the recoil velocity of the pistol as vp.
The momentum before firing is the initial momentum of the system, which is 0 since both the bullet and the pistol are initially at rest.
The momentum after the firing is the sum of the momenta of the bullet and the pistol.
Momentum of the bullet (pb) = mb * vb
Momentum of the pistol (pp) = mp * vp
Conservation of momentum equation:
0 = pb + pp
Substituting the given values:
0 = (0.03 kg) * (300 m/s) + (2.1 kg) * vp
Solving for vp:
(0.03 kg) * (300 m/s) = (2.1 kg) * vp
9 kg * m/s = (2.1 kg) * vp
vp = (9 kg * m/s) / (2.1 kg)
vp ≈ 4.286 m/s
Therefore, the recoil velocity of the pistol is approximately 4.286 m/s.
To calculate the recoil velocity of the pistol, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired is equal to the total momentum after the bullet is fired.
The momentum (p) of an object is defined as the product of its mass (m) and velocity (v). Mathematically, it can be written as:
p = m * v
The momentum of the bullet can be calculated as:
momentum of the bullet = mass of the bullet * velocity of the bullet
m_bullet = 30 g = 0.03 kg (since 1 kg = 1000 g)
v_bullet = 300 m/s
momentum of the bullet = 0.03 kg * 300 m/s = 9 kg·m/s
Now, let's assume the recoil velocity of the pistol as v_recoil. According to conservation of momentum:
Total momentum before = Total momentum after
momentum of the pistol + momentum of the bullet = 0 (since there is no initial velocity)
momentum of the pistol = (-1) * momentum of the bullet (since they are in opposite directions)
momentum of the pistol = -9 kg·m/s
Now, we can calculate the recoil velocity of the pistol using the initial momentum (0) and the mass of the pistol.
momentum of the pistol = mass of the pistol * velocity of the pistol
m_pistol = 2.1 kg
momentum of the pistol = 2.1 kg * v_recoil
2.1 kg * v_recoil = -9 kg·m/s
Dividing both sides by 2.1 kg:
v_recoil = (-9 kg·m/s) / 2.1 kg
v_recoil ≈ -4.3 m/s
Therefore, the recoil velocity of the pistol is approximately -4.3 m/s. The negative sign indicates that the pistol moves in the opposite direction of the bullet's motion.