Pendulum collision and elastic collision

[ihateap]

1. Homework Statement
2 pendulums collide and stick together after being released from rest at angle Ø (each one is at Ø)
pendulum 1 mass is 2m, pendulum 2 mass is m
What is the final swing angle of the stuck together masses? in what direction is the swing?

repeat for elastic collision

2. Homework Equations
Ui+Ki+Win-Wout=Kf+Uf (conservation of energy)
conservation of momentum


3. The Attempt at a Solution
a very sad one

sorry i couldn't put a picture up, even though it would help a great deal
but any suggestions would help
and if you couldn't tell it has to be solved symbollically

 

[Dick]

They will collide at angle phi=0 (the lowest point on the pendulum), right? What is the velocity (and hence momentum) of each pendulum just before they collide? If they stick together, then after the collision you have a single object with the same momentum. What's it's velocity? Translate that into to how high it will go, and what the angle is. Try and start answering some of these questions. It will make for a much improved 'attempt at a solution'.

 

[thomate1]

I would like to provide an explanation and solution to the given scenario of pendulum collision and elastic collision.

In the case of pendulum collision, when two pendulums with masses 2m and m collide and stick together after being released from rest at angle Ø, the final swing angle of the stuck together masses can be determined by applying the principles of conservation of energy and momentum.

Firstly, we can consider the conservation of energy, which states that the total energy of a closed system remains constant. This means that the initial kinetic energy and potential energy of the pendulums before the collision should be equal to the final kinetic energy and potential energy of the stuck together masses.

Using the given equation, Ui+Ki+Win-Wout=Kf+Uf, we can equate the initial energy (Ui+Ki) to the final energy (Kf+Uf) and solve for the final swing angle. This would give us a symbolic solution for the final swing angle.

Secondly, we can also apply the principle of conservation of momentum, which states that the total momentum of a closed system remains constant. This means that the initial momentum of the pendulums before the collision should be equal to the final momentum of the stuck together masses.

Using the equation for conservation of momentum, we can equate the initial momentum to the final momentum and solve for the final swing angle. This would also give us a symbolic solution for the final swing angle.

For the case of elastic collision, we can apply the same principles of conservation of energy and momentum. However, in elastic collisions, the total kinetic energy of the system is conserved, which means that the initial kinetic energy should be equal to the final kinetic energy after the collision.

Using the given equations and the information about the masses and angles, we can solve for the final swing angle and direction of the stuck together masses in both the cases of pendulum collision and elastic collision.

In order to provide a more detailed and accurate solution, a diagram or a visual representation of the scenario would be helpful. Additionally, providing the values of the masses and the initial angle Ø would also aid in solving the problem symbolically.