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?
wdawad
To solve questions 17, 18, and 20, we'll be using principles of conservation of momentum and Newton's third law of motion.
17. To find the magnitude and direction of the velocity of recoil, we need to apply the law of conservation of momentum. According to this law, the total momentum before the explosion is equal to the total momentum after the explosion, assuming no external forces are acting.
Since the cannon is at rest initially, its momentum is zero. Therefore, the total initial momentum is only due to the shell, which is given by:
Initial momentum = mass of the shell * velocity of the shell.
The final momentum is the sum of the momenta of the shell and the cannon after the explosion. Since the cannon and the shell move in opposite directions, we can express their momenta as:
Final momentum = mass of the shell * velocity of the shell + mass of the cannon * velocity of the cannon.
By equating the initial and final momenta, we can solve for the velocity of the cannon:
(mass of the shell * velocity of the shell) = (mass of the shell * velocity of the shell) + (mass of the cannon * velocity of the cannon).
Simplifying the equation, we have:
0 = (mass of the shell * velocity of the shell) + (mass of the cannon * velocity of the cannon) - (mass of the shell * velocity of the shell).
Rearranging the equation, we get:
mass of the cannon * velocity of the cannon = mass of the shell * velocity of the shell.
Plugging in the values, we have:
1000kg * velocity of the cannon = 25kg * 500m/s.
Solving for the velocity of the cannon, we get:
velocity of the cannon = (25kg * 500m/s) / 1000kg.
Therefore, the magnitude of the velocity of recoil is (25kg * 500m/s) / 1000kg, and the direction is eastward.
18. To find the ratio of speeds with which the two pieces move apart, we need to apply the law of conservation of momentum. According to this law, the total momentum before the explosion is equal to the total momentum after the explosion, assuming no external forces are acting.
The total initial momentum is zero since the bomb is at rest initially. After the explosion, the two pieces move horizontally in opposite directions. Let's assume the speed of the piece with mass 6kg is v1, and the speed of the piece with mass 2kg is v2.
Therefore, the total final momentum is:
(mass of the piece with mass 6kg * v1) + (mass of the piece with mass 2kg * v2) = 0.
Substituting the values, we get:
6kg * v1 + 2kg * v2 = 0.
Since the mass of the bomb is 8kg, we also have:
mass of the piece with mass 6kg + mass of the piece with mass 2kg = 8kg.
Substituting the values, we get:
6kg + 2kg = 8kg.
Therefore, the ratio of speeds is:
v2 = -(6kg * v1) / 2kg.
Simplifying the equation, we have:
v2 = -3v1.
Therefore, the ratio of speeds with which the two pieces move apart is 1:3.
20. (a) To find the momentum of the second car before the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are acting.
The initial momentum is the sum of the momenta of the two cars, which can be expressed as:
Initial momentum = (mass of the first car * velocity of the first car) + (mass of the second car * velocity of the second car).
Since the cars lock and come to rest at the point of collision, the final momentum is zero.
Therefore, the initial momentum is zero, which means:
(mass of the first car * velocity of the first car) + (mass of the second car * velocity of the second car) = 0.
We are given the mass and velocity of the first car, so let's calculate its momentum:
Initial momentum = (2.0 * 10^3kg * 9m/s).
Thus, the momentum of the second car before the collision is 2.0 * 10^3kg * 9m/s.
(b) Since the cars come to rest after the collision, the velocity of the second car after the collision is zero. Therefore, the velocity of the second car before the collision is the same as the post-collision velocity, which is zero.
Hence, the velocity of the second car before the collision is 0m/s.