A student holds a 2.0 kg air rifle, un-braced with a very loose grip. The muzzle velocity of a 2.0 g bullet fired from the rifle is about 140 m/s. What is the recoil speed of the gun? What could the student do to reduce the recoil speed of the air rifle? Explain.
To determine the recoil speed of the air rifle, 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. In this case, we need to consider the momentum of the bullet and the rifle.
The momentum of an object is given by the product of its mass and velocity:
momentum = mass * velocity
Let's find the momentum of the bullet first. Given the mass of the bullet is 2.0 grams (0.002 kg) and the velocity is 140 m/s:
momentum of bullet = 0.002 kg * 140 m/s
Next, let's calculate the momentum of the air rifle. Given the mass of the air rifle is 2.0 kg and assuming the initial velocity of the air rifle is 0 m/s:
momentum of air rifle = 2.0 kg * 0 m/s
Since the air rifle is initially at rest, the total initial momentum is zero. According to the principle of conservation of momentum, the total final momentum (bullet + air rifle) must also be zero:
Total final momentum = momentum of bullet + momentum of air rifle
0 = (0.002 kg * 140 m/s) + (2.0 kg * recoil speed)
Solving for the recoil speed, we get:
recoil speed = -((0.002 kg * 140 m/s) / 2.0 kg)
recoil speed = -0.14 m/s
The negative sign indicates the opposite direction of the bullet's velocity. Therefore, the recoil speed of the air rifle is 0.14 m/s in the opposite direction of the bullet.
To reduce the recoil speed of the air rifle, the student can try a few things:
1. Bracing the rifle: By holding the air rifle tightly against a solid object (e.g., shoulder), the student can effectively transfer some of the recoil energy to the object. This reduces the recoil speed experienced by the student.
2. Increasing the mass: Adding mass to the air rifle can help reduce the recoil velocity. This can be achieved by attaching a heavier stock or additional weights to the rifle. The increase in mass will distribute the recoil energy over a larger mass, resulting in a lower recoil velocity.
3. Using a recoil-absorbing mechanism: Some air rifles come with built-in recoil-absorbing mechanisms, such as recoil pads or springs. These mechanisms help absorb and dissipate the recoil energy, reducing the recoil speed felt by the student.
By implementing these measures, the student can effectively reduce the recoil speed and make the shooting experience more comfortable and controllable.