Conservation of mechanical energy

In summary, the problem involves two blocks attached by a string over a frictionless and massless pulley. The lighter block is released and the two blocks meet at the same height after a distance of 1m. The problem requires finding the speed at which they meet at that moment. The equations used are based on conservation of energy and the solution involves determining the unknown height at which they meet, with the hint that one block lowers by the same distance that the other rises.
  • #1
nvictor
9
0

Homework Statement



I have two blocks attached by a string (massless) over a pulley (frictionless, massless). Block 2 (which weighs less than block one) is released and the two blocks meet momentarily at the same height. I have the find the speed at which the meet at that moment. The blocks are separated by a distance of 1m.

I have drawn a figure in paint (sorry for this pic): http://i36.tinypic.com/2076at1.png

Homework Equations



Emechf = Emechi
Emech = Ug + K

The Attempt at a Solution



Emechf = Emechi
<=> (m_1gh + m_2gh) + (1/2m_1v^2 + 1/2m_2v^2) = m_1gH (where H = 1m, and h is the height at which they meet)

But then I have this h which is unkown and I can't figure out.

Thanks a lot in advance.
 
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  • #2
If the lower (and lighter) block starts out at height "h", the higher (heavier) block starts out at height "h + 1".

At what height will they meet? Hint: One block lowers by the same distance that the other rises.
 
  • #3
Thanks a lot, I see it clearly now. I really appreciate you help.
 

What is conservation of mechanical energy?

Conservation of mechanical energy is a fundamental principle in physics that states that the total amount of mechanical energy in a closed system remains constant over time. This means that energy cannot be created or destroyed, only transferred or converted from one form to another.

What are the different types of mechanical energy?

The two main types of mechanical energy are kinetic energy and potential energy. Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or configuration.

How is mechanical energy conserved in a closed system?

In a closed system, mechanical energy is conserved because any changes in kinetic energy are always accompanied by equal and opposite changes in potential energy. This means that the total amount of mechanical energy remains constant, even if there is a transfer of energy from one form to another.

What are some examples of conservation of mechanical energy?

A common example of conservation of mechanical energy is a pendulum swinging back and forth. As the pendulum swings, it has both kinetic and potential energy, but the total amount of mechanical energy remains constant. Another example is dropping a ball from a height, where the potential energy is converted into kinetic energy as the ball falls.

What are the real-life applications of conservation of mechanical energy?

Conservation of mechanical energy has many practical applications, such as in the design of roller coasters and other amusement park rides. It is also important in understanding the motion of objects in everyday life, such as the trajectory of a basketball during a shot or the movement of a car on a rollercoaster track.

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