Conservation of a mechanical energy question

In summary, The conversation is about a question regarding an Atwood's machine with two masses initially at rest. The question asks about the height that the heavier mass, m2, will rise to before momentarily coming to rest, given that it has an initial upward speed. The conversation offers tips and hints for solving the problem, such as using conservation of mechanical energy and finding the acceleration and using kinematics to find the distance.
  • #1
wilmerena
11
0
Hi, this is my first time here and Id like to thank in advance for any help offered :smile:
Im having trouble with the following question about 2 masses in an atwoods machine.

2 masses are initially at rest at the same height, if m2 has a given initial upward speed, how high does m2 rise above its initial position before momentarily coming to rest, (masses for each are given with m2 being heavier)

I know that I need to show some work before I should post this, but I embarrased to say I don't know how to even apporach it :frown:

any tips will be greatly appreciated :biggrin:
 
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  • #2
Welcome to PF!
This is a conservation of mechanical energy question.
Set up the initial mechanical energy of the whole system (kinetic+potential)
When the system falls momentarily at rest (assuming that the string remains taut all the time), the system only have potential energy.
As a hint, note that with a taut, inextensible string, the increase of height for m2 must equal the decrease of height for m1
 
Last edited:
  • #3
First, find the acceleration of the masses. Then use some kinematics to find the distance. Should be dead easy.
 

FAQ: Conservation of a mechanical energy question

What is the law of conservation of mechanical energy?

The law of conservation of mechanical energy states that the total amount of mechanical energy in a closed system remains constant over time, ignoring any external forces such as friction or air resistance. This means that energy cannot be created or destroyed, but can only be transferred or transformed from one form to another.

How is mechanical energy conserved?

Mechanical energy is conserved through the exchange of potential and kinetic energy within a system. When an object is at rest, it has potential energy due to its position or state, and when it is in motion, it has kinetic energy. The sum of these two energies remains constant as long as there is no external work or energy loss.

What are some examples of conservation of mechanical energy?

Some examples of conservation of mechanical energy include a pendulum swinging back and forth, a roller coaster going up and down, and a ball rolling down a ramp. In each of these cases, the potential energy at the highest point is converted into kinetic energy at the lowest point, and the total mechanical energy remains constant.

Can mechanical energy be completely conserved?

In theory, mechanical energy can be completely conserved in a closed system. However, in real-world situations, there are always external forces such as friction that cause some energy to be lost. This means that mechanical energy is not completely conserved, but is only conserved to a certain extent.

What are the implications of the conservation of mechanical energy?

The conservation of mechanical energy has important implications in the field of physics and engineering. It allows us to accurately predict the motion and behavior of objects in a closed system, and it also helps us to design and optimize energy-efficient machines and systems. Understanding and applying the law of conservation of mechanical energy is essential in many scientific and technological advancements.

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