a cannon of mass 400kg fires a shell of mass 20kg. if the shell leaves the cannon at 300ms^-1, with what velocity does the cannon recoil?
an a- particle is emitted from a polonium nucleus at a speed of 1.8 x 10^7 ms^-1. the relative masses of the a- particle and the remaining part are 4.002 and 212.0. calculate the recoil speed of the nucleus.
a space satellite has total mass 500kg. a portion of mass 20kg is ejected at a velocity of 10ms^-1. calculate the recoil velocity of the remaining portion (ignoring the initial velocity of the satellite).
two air gliders are at rest with a spring compressed between them. when released, one glider moves away with a speed of 0.32ms^-1 and the other moves ik the opposite direction with a speed of 0.45ms^-1. if the first glider has a mass of 0.4kg, what is the mass of the other?
in an explosion the exploding object breaks up into two parts, A and B. A has three times the mass of B. the speed of A after the explosion is 20ms^-1. calculate the speed of B.
what I got
1. 40v
2. 45.0
3. 35ms
4. 0.6
5. 6.5
honestly,
( Thankfully I got different backup answers on this piece of paper I have )
It was hard to understand my teacher because he can mumble sometimes
To solve these problems, you need to apply the concept of conservation of momentum. Conservation of momentum states that the total momentum before an event is equal to the total momentum after the event if no external forces are acting on the system.
Let's go through each problem step by step:
1. Cannon and shell:
The momentum of the cannon and shell before firing is zero since they are at rest. After firing, the momentum of the shell can be calculated using the formula `momentum = mass x velocity`. Therefore, the momentum of the shell is (20 kg * 300 m/s). According to conservation of momentum, the momentum of the cannon and shell after firing must also be zero. Let's assume the recoil velocity of the cannon is 'v'. The momentum of the cannon is (-400 kg * v). Setting up the equation: (20 kg * 300 m/s) = (-400 kg * v). Solve this equation to find the recoil velocity of the cannon (v).
2. Polonium nucleus:
Similar to the first problem, the total momentum before emission is zero. The momentum of the a-particle can be calculated using the formula. Its momentum is (4.002 * 1.8x10^7 kg * m/s). After the emission, the remaining part (nucleus) recoils in the opposite direction. Let's assume the recoil velocity of the nucleus is 'v'. The momentum of the nucleus is (212.0 * v). Setting up the equation: (4.002 * 1.8x10^7 kg * m/s) = (212.0 * v). Solve this equation to find the recoil velocity of the nucleus (v).
3. Space satellite:
The total momentum before the ejection of mass is zero since the satellite is at rest. The momentum of the ejected mass can be calculated using the formula. Its momentum is (20 kg * 10 m/s). After the ejection, the remaining portion of the satellite (ignoring initial velocity) recoils in the opposite direction. Let's assume the recoil velocity of the remaining portion is 'v'. The momentum of the remaining portion is (480 kg * v). Setting up the equation: (20 kg * 10 m/s) = (480 kg * v). Solve this equation to find the recoil velocity of the remaining portion (v).
4. Air gliders:
Here, we need to find the mass of the other glider. Before the release of the spring, both gliders are at rest, so the total momentum before the release is zero. After the release, the first glider moves with a velocity of 0.32 m/s, and the second glider in the opposite direction with a velocity of 0.45 m/s. Let's assume the mass of the other glider is 'm'. The momentum of the first glider is (0.4 kg * 0.32 m/s), and the momentum of the second glider is (-m * 0.45 m/s). Setting up the equation: (0.4 kg * 0.32 m/s) = (-m * 0.45 m/s). Solve this equation to find the mass of the other glider (m).
5. Explosion:
Before the explosion, the total momentum is zero. After the explosion, object A moves with a speed of 20 m/s. Let's assume the mass of object B is 'm'. Since A has three times the mass of B, the mass of A is 3m. The momentum of A is (3m * 20 m/s), and the momentum of B is (-m * v), where 'v' is the velocity of B. Setting up the equation: (3m * 20 m/s) = (-m * v). Solve this equation to find the velocity of B (v).
Based on these explanations, you can now verify and recheck your answers using the provided formulas and equations.