A rifle of mass 3.0 kg fires a 15 gram bullet with a muzzle speed of 1.5 km/s. The
initial speed of the rifle’s recoil would be ?
3000 * v = 15 * 1.5
To find the initial speed of the rifle's recoil, we can use the principle of conservation of momentum. According to this principle, the total momentum before firing is equal to the total momentum after firing.
The momentum of an object is calculated by multiplying its mass by its velocity.
Given:
Mass of the rifle (m1) = 3.0 kg
Mass of the bullet (m2) = 15 g = 0.015 kg (converted from grams to kilograms)
Muzzle speed of the bullet (v2) = 1.5 km/s
Let's assume the initial speed of the rifle's recoil is v1.
Using the conservation of momentum equation:
(m1 * v1) + (m2 * v2) = 0
Plugging in the given values:
(3.0 kg * v1) + (0.015 kg * 1.5 km/s) = 0
Now, we need to convert the muzzle speed of the bullet from km/s to m/s, as the unit of velocity should be in meters per second for consistent calculations.
1 km/s = 1000 m/s
(0.015 kg * 1.5 * 1000 m/s) = 22.5 kg m/s
Substituting this value back into the equation:
(3.0 kg * v1) + 22.5 kg m/s = 0
To solve for v1, we isolate it on one side of the equation:
3.0 kg * v1 = -22.5 kg m/s
v1 = (-22.5 kg m/s) / 3.0 kg
v1 = -7.5 m/s
Therefore, the initial speed of the rifle's recoil is -7.5 m/s. The negative sign indicates that the rifle moves in the opposite direction of the bullet's motion.