17. A shell having a mass of 25kg is fired horizontally eastward from a cannon with a velcoity of 500m/s. If the mass of the cannon is 1000kg, what is the magnitude and direction of the velocity of recoil?
18. A bomb having a mass of 8kg explodes into two pieces that fly out horizontally in opposite directions. One piece is found to have a mass of 6kg and the other a mass of 2kg. What was the ratio of speeds with which the two pieces moved apart immediately after the explosion occurred?
20. When a car of mass 2.0 * 10^3 moving at 9m/s collides head on with a second car having a mass of 1.5 * 10^3, the cars lock and come to rest at point of collision. (a)What was the momentum of the second car before the collision? (b) what was the velocity of the second car before the collision?
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17. To find the magnitude and direction of the velocity of recoil, we can use the principle of conservation of momentum. According to this principle, the total momentum before the firing of the shell is equal to the total momentum after the firing.
First, let's find the initial momentum of the system. The momentum of the cannon can be calculated by multiplying its mass by its velocity. So, the initial momentum of the cannon is 1000 kg * 0 m/s = 0 kg*m/s.
The momentum of the shell is the product of its mass and velocity. So, the initial momentum of the shell is 25 kg * 500 m/s = 12,500 kg*m/s.
Since the cannon and the shell are initially at rest, the total initial momentum is the sum of their individual momenta, which is 0 + 12,500 kg*m/s = 12,500 kg*m/s.
To find the final momentum of the system, we need to consider the recoil of the cannon. Let's assume the velocity of recoil is v. Again using the principle of conservation of momentum, the final momentum of the system should be equal to the initial momentum. Since momentum is a vector quantity, we need to consider both magnitude and direction.
The final momentum of the cannon is the product of its mass and velocity, which is 1000 kg * (-v) = -1000v kg*m/s. Note that the negative sign indicates the opposite direction of the cannon's velocity.
The final momentum of the shell is the product of its mass and velocity, which is 25 kg * (500 m/s) = 12,500 kg*m/s.
To find the final momentum of the system, we add the individual momenta of the cannon and the shell: -1000v kg*m/s + 12,500 kg*m/s = 12,500 - 1000v kg*m/s.
Since the total initial momentum is equal to the total final momentum, we have:
12,500 kg*m/s = 12,500 - 1000v kg*m/s.
Simplifying the equation:
12,500 = 12,500 - 1000v.
Solving for v:
1000v = 0.
Therefore, the magnitude of the velocity of recoil is 0 m/s, indicating that the cannon does not recoil.
18. To find the ratio of speeds with which the two pieces move apart immediately after the explosion, we can use the principle of conservation of momentum. This principle states that the total momentum before the explosion is equal to the total momentum after the explosion.
Let's assume the speed of the first piece is v1 and the speed of the second piece is v2.
The initial momentum of the system is the sum of the individual momenta of the two pieces. The momentum of an object can be calculated by multiplying its mass by its velocity.
The initial momentum of the first piece is 6 kg * (v1) = 6v1 kg*m/s.
The initial momentum of the second piece is 2 kg * (v2) = 2v2 kg*m/s.
Since the two pieces move in opposite directions horizontally, their momenta have opposite signs.
So, the total initial momentum is 6v1 kg*m/s - 2v2 kg*m/s.
According to the conservation of momentum, the total initial momentum is equal to the total final momentum.
Since the explosion occurs, we can assume that the pieces move freely without any external forces acting on them after the explosion.
Therefore, the total final momentum is the sum of the individual momenta of the two pieces, which is the sum of their masses multiplied by their respective speeds.
The final momentum of the first piece is 6 kg * (v1) = 6v1 kg*m/s.
The final momentum of the second piece is 2 kg * (-v2) = -2v2 kg*m/s.
Adding these momenta together, we have 6v1 kg*m/s - 2v2 kg*m/s.
Since the total initial momentum is equal to the total final momentum, we have:
6v1 - 2v2 = 6v1 - 2v2.
Simplifying the equation, we get:
4v1 = 2v2.
Dividing both sides of the equation by 2v2, we find:
v1/v2 = 1/2.
Therefore, the ratio of speeds with which the two pieces moved apart immediately after the explosion occurred is 1/2.
20. (a) To find the momentum of the second car before the collision, we can use the equation: momentum = mass * velocity.
The mass of the second car is given as 1.5 * 10^3 kg. To find the momentum, we need to know the velocity of the second car before the collision, which is not provided in the given information. Therefore, we cannot calculate the momentum of the second car before the collision.
(b) Since we don't know the velocity of the second car before the collision, we cannot calculate its value.