Is Momentum Conserved in a Two-Object Collision?

[sweedeljoseph]

Homework Statement

Two objects of masses M₁ = 1 kilogram and M₂ = 4 kilograms are free to slide on a horizontal frictionless surface. The objects collide and the magnitudes and directions of the velocities of the two objects before and after the collision are shown on the diagram below. (sin 37$$\circ$$ = 0.6, cos 37$$\circ$$ = 0.8, tan37$$\circ$$ = 0.75).

*PICTURE ISNT WORKING SO HERES THE LINK*
http://img359.imageshack.us/img359/1051/probfk9.jpg

a) Calculate the x and y components (p_x and p_y, respectively) of the momenta of the two objects before and after the collision.
b) Show, using the data from the previous question, that linear momentum is conserved in this collision.
c) Calculate the kinetic energy of the two-object system before and after the collision.
d) Is kinetic energy conserved in the collision?

Homework Equations

p=mv
m₁*v₁+m₂*v₂=m₁'*v₁'+m₂'*v₂'
ke=1/2mv²

The Attempt at a Solution

i don't have all the answers from the teacher. i know how to do part a. but that's it. i don't know what else I am supposed to do after that.

the answer to part a is:
http://img262.imageshack.us/img262/4028/charttw5.jpg
you just use the p=mv to solve for everything.

i don't know how to do the rest. i think youre supposed to use the other formula i gave but i don't know. i need a lot of help.

thank you!
sweedeljoseph

 

[Hootenanny]

You simply need to do what the question says, can you calculate the kinetic energy of the system before the collision?

 

[thomate1]

Hello sweedeljoseph,

Thank you for your question. I will provide a response to the content you have provided.

Firstly, for part a, you have correctly calculated the x and y components of the momenta of the two objects before and after the collision. These values will be useful for the rest of the problem.

For part b, you are correct in thinking that you need to use the conservation of linear momentum. This law states that the total momentum before a collision is equal to the total momentum after the collision. In this case, the total momentum before the collision is the sum of the momenta of the two objects, and the total momentum after the collision is the sum of the momenta of the two objects after the collision. To show that momentum is conserved, you can simply compare the values of the total momentum before and after the collision. If they are equal, then momentum is conserved. In this case, you should find that the values are the same, thus showing that momentum is conserved.

Moving on to part c, you are correct in thinking that you need to use the kinetic energy formula, ke=1/2mv^2. For this problem, you will need to calculate the kinetic energy of each object before and after the collision, and then add them together to get the total kinetic energy of the system. You can then compare the values of the total kinetic energy before and after the collision to see if kinetic energy is conserved.

Lastly, for part d, you can compare the total kinetic energy before and after the collision to see if it is conserved. If the values are the same, then kinetic energy is conserved. If not, then it is not conserved. This is an important concept to understand, as it helps us understand the behavior of objects in collisions.

I hope this response helps you. If you have any further questions or need clarification on any of the steps, please do not hesitate to ask. Good luck with your homework!

Sincerely,