A bullet with a mass of 28 g is fired from a 2.8-kg gun that is stationary, but free to recoil. After the bullet is fired, the gun is observed to be moving at 1.4 m/s [left]. What is the velocity of the
bullet?
let left be negative.
initial (before shooting, momentum was zero, so after shooting, the sum of the bullet and gun momentum has to be zero
28*V +2800*(-1.4)=0
solve for V
To solve this problem, we can start by applying 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 of an object is given by the equation:
momentum = mass × velocity
Before the bullet is fired, the gun is stationary, so its momentum is zero. Therefore, the total momentum before the bullet is fired is also zero.
After the bullet is fired, the gun recoils with a velocity of 1.4 m/s to the left. We can consider this as the final momentum of the gun and bullet system. Let's denote the mass of the bullet as m and the velocity of the bullet as v.
Now we can apply the principle of conservation of momentum:
Total momentum before = Total momentum after
(0 kg) × (0 m/s) = (28 g + 2.8 kg) × (1.4 m/s)
Converting the mass of the bullet from grams to kilograms:
(0 kg) = (0.028 kg + 2.8 kg) × (1.4 m/s)
Simplifying the equation:
0 = (2.828 kg) × (1.4 m/s)
Now we can solve for the velocity of the bullet:
0 = 2.828 kg × v
Since the product of any number and zero is always zero, we can conclude that the velocity of the bullet is zero.
Therefore, the velocity of the bullet is 0 m/s.
To find the velocity of the bullet, 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 of an object is given by the product of its mass and velocity. Let's represent the mass of the bullet as "m1" and its velocity as "v1". The mass of the gun is given as "m2", and its velocity is "v2". Since the gun is initially stationary, its velocity is 0.
We can set up the equation as follows:
(mass of bullet * velocity of bullet) + (mass of gun * velocity of gun) = 0
Given:
Mass of the bullet (m1) = 28 g = 0.028 kg
Mass of the gun (m2) = 2.8 kg
Velocity of the gun (v2) = -1.4 m/s (negative sign indicates left direction)
Substituting the given values into the equation, we get:
(0.028 kg * v1) + (2.8 kg * -1.4 m/s) = 0
Now, we can solve for v1, which is the velocity of the bullet:
(0.028 kg * v1) - (2.8 kg * 1.4 m/s) = 0
0.028 kg * v1 = 3.92 kg*m/s
v1 = (3.92 kg*m/s) / (0.028 kg)
v1 ≈ 140 m/s [right]
Therefore, the velocity of the bullet is approximately 140 m/s to the right.