A cannon, mass 500kg, fires a bullet, mass 100kg, horizontally so that the velocity of the bullet is 100m.s^-1 to the right. calculate the recoil velocity of the bullet
To calculate the recoil velocity of the bullet, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the firing is equal to the total momentum after the firing.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v), i.e., p = m * v.
Before the firing, the cannon and the bullet are at rest; therefore, their initial momentum is zero.
After the firing, the bullet moves with a velocity of 100 m/s to the right. To maintain the conservation of momentum, the cannon must move in the opposite direction, with a velocity we need to calculate.
Let's denote the recoil velocity of the cannon as V.
Since the total momentum before the firing is zero, the total momentum after the firing should also be zero:
(Initial momentum of the cannon) + (Initial momentum of the bullet) = (Final momentum of the cannon) + (Final momentum of the bullet)
0 + 0 = (mass of the cannon) * (recoil velocity of the cannon) + (mass of the bullet) * (velocity of the bullet)
0 = (500 kg) * V + (100 kg) * (100 m/s)
0 = 500V + 10000
500V = -10000
V = -20 m/s
The negative sign indicates that the cannon moves in the opposite direction to the bullet. Therefore, the recoil velocity of the bullet is 20 m/s to the left.
To calculate the recoil velocity of the cannon, we can apply 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.
Given:
Mass of the cannon (m1) = 500 kg
Mass of the bullet (m2) = 100 kg
Velocity of the bullet (v2) = 100 m/s (to the right)
Step 1: Calculate the initial momentum before the firing.
The initial momentum (P_initial) is given by:
P_initial = m1 * v1
Since the cannon is initially at rest, the initial velocity (v1) is 0 m/s. Therefore:
P_initial = m1 * v1 = 500 kg * 0 m/s = 0 kg⋅m/s
Step 2: Calculate the final momentum after the firing.
The final momentum (P_final) is given by:
P_final = (m1 * v1) + (m2 * v2)
Since the bullet is moving horizontally to the right, the final velocity (v1) of the cannon will be in the opposite direction (to the left). So, v1 = -v_1.
Substituting the given values:
P_final = (500 kg * -v_1) + (100 kg * 100 m/s)
P_final = -500v_1 + 10000 kg⋅m/s
According to the principle of conservation of momentum, the initial momentum should be equal to the final momentum, hence:
P_initial = P_final
0 kg⋅m/s = -500v_1 + 10000 kg⋅m/s
Now, we can solve this equation to find the value of v_1 (recoil velocity of the cannon):
-500v_1 = -10000 kg⋅m/s
v_1 = (-10000 kg⋅m/s) / -500
v_1 = 20 m/s (to the left)
Therefore, the recoil velocity of the cannon is 20 m/s to the left.