A bullet with mass 0.40 kg is fired with an initial velocity of 400 m/s from a gun with mass 5.0 kg. The speed of the recoil of the gun is?
See what you get by using the law of conservation of momentum. Total momentum remains zero. Bullet and rifle movie in opposite directions, and their momenta must cancel each other.
To find the speed of the recoil of the gun, we can use the principle of conservation of momentum. According to this principle, the total momentum before the firing should be equal to the total momentum after the firing.
The momentum of an object is given by the product of its mass and velocity.
Let's denote the mass of the bullet as m1 (0.40 kg) and the mass of the gun as m2 (5.0 kg).
The initial velocity of the bullet is v1 (400 m/s), and we want to find the speed of the recoil of the gun, which we'll call v2.
Before the firing, the momentum of the system is given by:
Total momentum before = (mass of bullet x initial velocity of bullet) + (mass of gun x initial velocity of gun)
Total momentum before = (m1 x v1) + (m2 x 0) (since the initial velocity of the gun is zero)
Total momentum before = m1 x v1
After the firing, the momentum of the system is given by:
Total momentum after = (mass of bullet x final velocity of bullet) + (mass of gun x final velocity of gun)
Total momentum after = (m1 x 0) + (m2 x v2) (since the final velocity of the bullet is zero after being fired)
Total momentum after = m2 x v2
According to the principle of conservation of momentum, the total momentum before the firing should be equal to the total momentum after the firing:
m1 x v1 = m2 x v2
Plugging in the given values:
(0.40 kg) x (400 m/s) = (5.0 kg) x v2
160 kg·m/s = 5.0 kg x v2
To solve for v2, divide both sides of the equation by 5.0 kg:
v2 = (160 kg·m/s) / (5.0 kg)
v2 = 32 m/s
Therefore, the speed of the recoil of the gun is 32 m/s.
To find the speed of the recoil of the gun, we can use the principle of conservation of momentum. According to this principle, the total momentum before the firing of the bullet and gun is equal to the total momentum after.
The momentum of an object is given by the product of its mass and velocity: momentum = mass × velocity.
Let's denote the mass of the bullet as m1, the velocity of the bullet as v1, the mass of the gun as m2, and the velocity of the gun as v2 (which is what we want to find).
Before the firing:
The momentum of the bullet is given by m1 × v1.
The momentum of the gun is given by m2 × 0 (since the gun is not moving initially).
After the firing:
The momentum of the bullet is given by m1 × (−v1) (since the direction of the bullet is opposite to its initial velocity).
The momentum of the gun is given by m2 × v2.
Using the conservation of momentum principle, we can write the equation:
m1 × v1 + m2 × 0 = m1 × (−v1) + m2 × v2
Simplifying the equation, we get:
m1 × v1 = m2 × v2
Now, we can substitute the given values:
m1 = 0.40 kg (mass of the bullet)
v1 = 400 m/s (initial velocity of the bullet)
m2 = 5.0 kg (mass of the gun)
Plugging these values into the equation, we have:
(0.40 kg) × (400 m/s) = (5.0 kg) × v2
Now, we can solve for v2, the speed of the recoil of the gun:
v2 = (0.40 kg × 400 m/s) / 5.0 kg
v2 = 32 m/s
Therefore, the speed of the recoil of the gun is 32 m/s.