How Does Energy Conservation Apply in a Pendulum-Object Collision?

In summary, when the ball is hanging on a pendulum, it has potential and kinetic energy. The object it hits has potential energy and kinetic energy.
  • #1
Cathr
67
3
1. A ball hanging on a pendulum hits an object standing on the table. The interaction is elastic and linear. After that, the object falls on the floor.


Homework Equations


From state 1 to 2, we have the conservation of the potential energy of the pendulum to its kinetic energy, right before it hits the object.
Then it is the kinetic energy conservation, so mv^2=mv1^2+mv2^2, right?[/B]3. How to write the conservation laws of the next states?
 
Physics news on Phys.org
  • #2
Hello Cath, :welcome:

So: state 1 is the ball held at a certain position away from the object. Let go and the moment just before collision is state 2.
You correctly write (the collision is fully elastic): kinetic energy before collision = kinetic energy after collision or $$ {1\over 2} m_1v_2^2 = {1\over 2} m_1v_3^2 + {1\over 2} m_2 v_4^2$$ where I added some subscripts:
##m_1 \quad## mass of ball
##m_2 \quad## mass of object
##v_2 \quad## speed of ball before collision
##v_3 \quad## speed of ball after collision
##v_4 \quad## speed of object after collision

And you are interested in "the next states". Could you describe them ? And perhaps already write down some of the energies that are associated with these staets ?
 
  • Like
Likes Cathr
  • #3
Thank you!
I am interested to know how to write the conservation law when the object just got hit by the ball, and it started falling down.
I guess there's another equation to write before saying that the kinetic energy of the object right before it hits the floor is equal to the potential energy+its initial kinetic energy (I am not even sure that this is correct).
 
Last edited:
  • #4
The ball doesn't hit the floor. It is the object that hits the floor.
 
  • #5
Right! Excuse me, it's my mistake.
 
  • #6
There is conservation of energy until the object hits the floor. From that point, because we cannot account for the energy transferred two the floor (and earth) there is no longer conservation of energy. But you can use both potential energy and kinetic energy of the object the instant before it hits the floor when its height is that of the floor.
 

FAQ: How Does Energy Conservation Apply in a Pendulum-Object Collision?

What is the energy conservation law?

The energy conservation law, also known as the law of conservation of energy, states that energy cannot be created or destroyed, but can only be transformed from one form to another.

Why is the energy conservation law important?

The energy conservation law is important because it helps us understand and predict how energy behaves in different systems and processes. It also highlights the importance of using energy efficiently and sustainably.

How is the energy conservation law applied in everyday life?

The energy conservation law is applied in everyday life in various ways, such as turning off lights and appliances when not in use, using energy-efficient appliances, and using renewable energy sources.

What are some examples of energy conservation in nature?

In nature, energy conservation can be seen in processes such as photosynthesis, where plants convert sunlight into chemical energy, and in the water cycle, where water is conserved and recycled in different forms.

Is the energy conservation law always true?

Yes, the energy conservation law is considered to be a fundamental law of physics and has been proven to hold true in various experiments and observations. However, in some extreme cases, such as in nuclear reactions, a small amount of mass may be converted into energy, but the total energy is still conserved.

Back
Top