A cannon is mounted on a railroad car. The cannon shoots a 1.75 kg ball with a muzzle velocity if 300 m/s. The cannon and the railroad car together have a mass of 4500 kg. if the ball, cannon, and railroad car are initially at rest, what is the recoil velocity of the car and cannon?
To find the recoil velocity of the car and cannon, we can use the principle of conservation of momentum. According to this principle, the total momentum before the cannon is fired is equal to the total momentum after the cannon is fired.
The momentum of an object is given by the product of its mass and velocity (p = mv).
Let's denote the recoil velocity of the car and cannon as V.
The total initial momentum is zero because the ball, cannon, and railroad car are initially at rest:
Total initial momentum = 0 kg m/s
The total momentum after the cannon is fired can be calculated as follows:
Momentum of the ball: m_ball * V (since the ball is moving in the opposite direction)
Momentum of the cannon and car: (m_cannon + m_car) * (-V) (since the cannon and car move together as a unit in the opposite direction)
Total final momentum = (m_ball * V) + ((m_cannon + m_car) * (-V))
According to the principle of conservation of momentum, the total initial momentum should be equal to the total final momentum:
0 kg m/s = (m_ball * V) + ((m_cannon + m_car) * (-V))
Substituting the given values:
0 = (1.75 kg * V) + ((4500 kg) * (-V))
Now, let's solve for V:
0 = 1.75V - 4500V
Combining like terms:
-4500V = -1.75V
Divide both sides of the equation by -1.75 to solve for V:
V = -4500 / -1.75
V ≈ 2571.43 m/s
Therefore, the recoil velocity of the car and cannon is approximately 2571.43 m/s in the opposite direction of the ball's velocity.
To find the recoil velocity of the car and cannon, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the cannon is fired should be equal to the total momentum after the cannon is fired.
The total momentum before the cannon is fired is zero since both the cannon and the railroad car are at rest. So, we can set the initial momentum (before firing) equal to zero:
Initial momentum = 0 kg.m/s
After firing the cannon, the ball is given a certain momentum in one direction, while the cannon and the railroad car gain momentum in the opposite direction. Let's assume the recoil velocity of the cannon and the car is v (in m/s).
The momentum of the ball can be calculated using the formula:
Momentum of ball = mass of ball × velocity of ball
So, the momentum of the ball after firing is:
Momentum of ball = 1.75 kg × 300 m/s = 525 kg.m/s
According to the conservation of momentum, the total momentum after the cannon is fired (considering the ball, cannon, and railroad car together) should be equal to the initial momentum (zero). Since the momentum of the ball is in the opposite direction of the momentum of the cannon and the car, we can write the equation as follows:
Momentum of ball = - (momentum of cannon + momentum of car)
Substituting the values we have:
525 kg.m/s = - [(mass of cannon + mass of car) × v]
Now we can solve for v:
v = - (525 kg.m/s) / (mass of cannon + mass of car)
v = - (525 kg.m/s) / (4500 kg)
v ≈ -0.117 m/s
Therefore, the recoil velocity of the cannon and the railroad car would be approximately -0.117 m/s in the opposite direction to that of the ball. The negative sign indicates that the car and cannon are moving in the opposite direction to the ball's motion.
which way is the cannon pointed? Especially the shooting angle.
If horizontal, along the direction of the tracks...
momentumcannon+momentumcar=zero
1.75*-300=4500V