Elastic and un-elastic collisions

[BananaMan]

well first time i have had to use this forum in a long time, but i am very stuck (i guess being hungover and falling asleep in the lecture didnt help)

but i have 2 problems that i have been playing with for over an hour now and just cannot get any kind of reasonable answer

1) a proton of mass m traveling at 300m/s collides with a stationary carbon nucleus of mass 12m

(a) find the velocity of the centre of mass of the system, for this i got 23.07m/s not sure if this is right or wrong, i simply used conservation of momentum for an imaginary particle of mass 13m
(b) find the velocity of the proton after the collision in the centre-of-mass refrence frame (very lost on this)
(c) find the velocity of the proton after the collision in the lab reference frame, for this i have used conservation of momentum, but with 2 un-knowns and only 1 equation i was thinkin of possibly using the conservation of kinetic energy (with it being an elastic collision) but it didnt work out when i tried





2) A bullet of mass m1 is fired with a speed v into the bob of a ballistic pendulum of mass m2 find the maximum heigh h attained by the bob if the bullet passes through the bob and emerges with a speed v/2

to be honest this is the lecture i was hungover in and do not have a clue on this one

if someone could point me in the right direction on these it would be grately appreciated

thanks :)

 

[Jhero]

First of all, I would like to commend you for seeking help when you are stuck on a problem. It shows that you are determined to find a solution and are not afraid to ask for assistance. I understand the frustration that comes with being stuck on a problem, but I assure you that with the right approach, you will be able to solve these problems.

Now, let's take a look at your first problem. You have correctly used the conservation of momentum to find the velocity of the center of mass of the system. However, for part (b), we need to use the concept of relative velocity. The velocity of the proton after the collision in the center-of-mass reference frame will be equal to the initial velocity of the proton minus the velocity of the center of mass of the system. So, in this case, the velocity of the proton will be 300m/s - 23.07m/s = 276.93m/s.

For part (c), we can use the conservation of momentum and the conservation of kinetic energy to solve for the final velocity of the proton in the lab reference frame. Since we have two equations and two unknowns (final velocity and final velocity of the carbon nucleus), we can solve for the final velocity of the proton. Remember to use the fact that the collision is elastic, so kinetic energy is conserved.

Moving on to your second problem, we can use the principle of conservation of energy to solve for the maximum height attained by the bob. We know that the initial kinetic energy of the bullet will be equal to the sum of the kinetic energy and potential energy of the bob at its maximum height. So, we can set up an equation and solve for the height using the given information.

I hope this helps you in solving these problems. Remember, when solving physics problems, it is important to use the correct equations and concepts and to carefully consider the given information. Don't hesitate to ask for help or clarification if you are unsure about something. Good luck!