A 25-g bullet is fired with a velocity of 200m/s. If the gun from which the bullet is fired has a mass of 3.5kg,what is the recoil velocity?
PLEASE HELP ME.
To find the recoil velocity of the gun, we can use the concept of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event (assuming no external forces act on the system).
Step 1: Determine the initial momentum of the bullet.
The initial momentum (p1) of the bullet is given by the product of its mass (m1) and velocity (v1).
m1 = 25 g = 0.025 kg (mass of the bullet)
v1 = 200 m/s (velocity of the bullet)
p1 = m1 * v1 = 0.025 kg * 200 m/s = 5 kg*m/s
Step 2: Determine the initial momentum of the gun.
The initial momentum (p2) of the gun is given by the product of its mass (m2) and velocity (v2).
m2 = 3.5 kg (mass of the gun)
v2 = ?
The gun is initially at rest (v2 = 0 m/s).
p2 = m2 * v2 = 3.5 kg * 0 m/s = 0 kg*m/s
Step 3: Determine the final momentum of the system.
Since momentum is conserved, the final momentum of the system is equal to the initial momentum.
p1 + p2 = p3
5 kg*m/s + 0 kg*m/s = p3
p3 = 5 kg*m/s
Step 4: Determine the recoil velocity.
The final momentum (p3) is given by the product of the total mass (m3) of the system (bullet + gun) and the recoil velocity (v3).
m3 = m1 + m2 = 0.025 kg + 3.5 kg = 3.525 kg
v3 = ?
p3 = m3 * v3 = 3.525 kg * v3
Substituting p3 = 5 kg*m/s, we can solve for v3:
5 kg*m/s = 3.525 kg * v3
v3 = 5 kg*m/s / 3.525 kg ≈ 1.42 m/s
Therefore, the recoil velocity of the gun is approximately 1.42 m/s in the opposite direction to the bullet.
To calculate the recoil velocity of the gun, you 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 can be calculated by multiplying its mass by its velocity. Let's represent the bullet's mass as m1, the bullet's velocity as v1, the gun's mass as m2, and the recoil velocity of the gun as v2.
Before the bullet is fired:
Total momentum = (mass of bullet) x (velocity of bullet) + (mass of gun) x (velocity of gun)
= m1 * v1 + m2 * 0 (as the gun is initially at rest)
After the bullet is fired:
Total momentum = (mass of bullet) x (final velocity of bullet) + (mass of gun) x (recoil velocity of gun)
= m1 * 0 (as the bullet is at rest) + m2 * v2
According to the principle of conservation of momentum, the total momentum before and after the bullet is fired should be equal:
m1 * v1 + m2 * 0 = m1 * 0 + m2 * v2
Since the mass of the bullet is 25 g, which is equal to 0.025 kg, and the mass of the gun is 3.5 kg, and the velocity of the bullet is 200 m/s, you can substitute these values into the equation:
0.025 kg * 200 m/s + 3.5 kg * 0 = 0.025 kg * 0 + 3.5 kg * v2
Simplifying the equation, you get:
5 kg * m/s = 3.5 kg * v2
Now, you can solve for v2 by dividing both sides of the equation by 3.5 kg:
5 kg * m/s / 3.5 kg = v2
Calculating the recoil velocity v2, you get:
v2 = 5 kg * m/s / 3.5 kg
= 1.43 m/s (approximately)
Therefore, the recoil velocity of the gun is approximately 1.43 m/s.