A bullet of mass 50g is fired from a gun of mass 6kg with a velocity of 400m/s. calculate the recoil velocity of the gun?
yup mb=50g=50/1000g
mg=6kg
vb=400m/s
vg=?
To determine the recoil velocity of the gun, we can make use of the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. According to the conservation of momentum principle, the total momentum of a system remains constant before and after any interaction takes place.
Before the bullet is fired, the total momentum of the system (bullet + gun) is zero since both objects are at rest.
After the bullet is fired, the momentum of the bullet is given by:
Momentum of bullet = mass of bullet × velocity of bullet
= 0.05 kg × 400 m/s
= 20 kg·m/s
To calculate the recoil velocity of the gun, we can set up an equation using the conservation of momentum principle:
Total momentum before = Total momentum after
0 = momentum of bullet + momentum of gun
0 = 20 kg·m/s + mass of gun × velocity of gun
Since the mass of the gun is 6 kg, we can substitute this value into the equation:
0 = 20 kg·m/s + 6 kg × velocity of gun
Simplifying the equation:
-20 kg·m/s = 6 kg × velocity of gun
Dividing both sides by 6 kg:
-20 kg·m/s / 6 kg = velocity of gun
This gives us:
-3.33 m/s = velocity of gun
Therefore, the recoil velocity of the gun is approximately -3.33 m/s. The negative sign implies that the gun moves in the opposite direction to the bullet.
To calculate the recoil velocity of the gun, we can use the principle of conservation of momentum. In an isolated system, the total momentum before an event is equal to the total momentum after the event.
The momentum of an object is calculated by multiplying its mass by its velocity. Let's denote the mass of the bullet as "m1" and the mass of the gun as "m2". The initial velocity of the bullet is "v1" and the initial velocity of the gun is "v2". The final velocity of the bullet is "v1'" and the final velocity of the gun is "v2'".
According to the conservation of momentum, the total momentum before the bullet is fired is equal to the total momentum after firing:
(m1 * v1 + m2 * v2) = (m1 * v1' + m2 * v2')
In this case, the bullet is fired in one direction, while the gun recoils in the opposite direction. Therefore, the final velocity of the bullet ("v1'") is in the opposite direction and the final velocity of the gun ("v2'") is what we need to calculate.
Given:
m1 = 50 g = 0.05 kg (mass of the bullet)
m2 = 6 kg (mass of the gun)
v1 = 400 m/s (initial velocity of the bullet)
Substituting these values into the momentum conservation equation:
(0.05 kg * 400 m/s + 6 kg * v2) = (0.05 kg * v1' + 6 kg * v2')
Since the bullet is fired, its final velocity can be assumed to be zero (v1' = 0). Rearranging the equation:
(0.05 kg * 400 m/s + 6 kg * v2) = (0.05 kg * 0 + 6 kg * v2')
Now we can solve for v2', the recoil velocity of the gun:
6 kg * v2 = 6 kg * v2'
v2' = v2
The recoil velocity of the gun is equal in magnitude but opposite in direction to the initial velocity of the bullet. Therefore, the recoil velocity of the gun is 400 m/s in the opposite direction to that in which the bullet was fired.