Conservation Of Mechanical Energy

In summary, two blocks with different mass are attached to either end of a light rope that passes over a light, frictionless pulley. The more massive block starts to descend after they are released from rest. After the block has descended a distance of 1.30m, its speed is 1.00m/s. The total mass of the two blocks is 18.0kg and the mass of the more massive block is required. Using the equations for kinetic and potential energy, the mass of the more massive block can be calculated as (m1 + m2)v^2/2 = (m1 - m2)gh.
  • #1
tizzful
14
0

Homework Statement


Two blocks with different mass are attached to either end of a light rope that passes over a light, frictionless pulley that is suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended a distance 1.30 , its speed is 1.00 .
If the total mass of the two blocks is 18.0 , what is the mass of the more massive block?
Take free fall acceleration to be 9.80 .
I set the heavier block as m1.

Homework Equations


m1gh1+0.5m1v1^2=m2gh2+0.5m2v2^2

The Attempt at a Solution


They both start at height 0 and velocity 0 and so the initial PE and KE is going to be 0, and so the initial Mechanical energy is also 0 (I'm pretty sure this is wrong but don't know how to fix it). Then m1 drops 1.30m so that's h1 and m2 goes up -1.30m=h2. v should be equal between both, m1=1, m2=-1.

m1(gh1+0.5v^2)=m2(gh2+0.5v^2)
m1/m2=(gh2+0.5v^2)/(gh1+0.5v^2)
=(9.8*-1.30+1/2*-1^2)/(9.8*1.30+1/2*1^2)
Therefore
m1=-m2

So its wrong ahah I was wondering if someone could help me?
Thanks in advance!:shy:
 
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  • #2
tizzful said:
m1/m2=(gh2+0.5v^2)/(gh1+0.5v^2)
=(9.8*-1.30+1/2*-1^2)/(9.8*1.30+1/2*1^2)

Hi tizzful! :smile:

erm … it's not "-1^2" … :redface:

No wonder they came out minus each other! :rolleyes:
 
  • #3
tiny-tim said:
Hi tizzful! :smile:

erm … it's not "-1^2" … :redface:

No wonder they came out minus each other! :rolleyes:

actually the -1 gets squared and so it becomes one.. Its negative because the height is negative because down is positive and up is negative.. But from what you're saying why isn't it -1? It's also in the opposite direction...
 
  • #4
tizzful said:
… why isn't it -1? It's also in the opposite direction...

Noooooo … the kinetic energy mv^2/2 is always positive!

It depends only on speed, not direction!

You have too much imagination! :smile:
 
  • #5
ahahah thank you! But I know KE is always positive because if velocity is negative it gets squared making it positive.. And that's what happened in this case.. But i still can't figure out the answer.. I think there's something wrong with me saying initial ME = 0...
 
  • #6
tizzful said:
m1(gh1+0.5v^2)=m2(gh2+0.5v^2)
m1/m2=(gh2+0.5v^2)/(gh1+0.5v^2)

ah … I see now … your basic equation is wrong …

KE gained is (m1 + m2)v^2/2

PE gained is (m1 - m2)gh. :smile:
 
  • #7
When you have gotten the answer using that method (which is probably the easiest), you can also try doing it by finding the acceleration on the big mass, and then use s=(at^2)/2. You will end up with the exactly same equation. :)
 

1. What is conservation of mechanical energy?

The 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, but can only be transferred or converted from one form to another.

2. How is mechanical energy conserved?

Mechanical energy is conserved through the principle of work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy. This means that if there are no external forces acting on a system, the total amount of mechanical energy will remain constant.

3. What are some examples of conservation of mechanical energy?

Examples of conservation of mechanical energy include a pendulum swinging, a rollercoaster moving along its track, and a ball rolling down a hill. In all of these cases, the total amount of mechanical energy (kinetic energy + potential energy) remains constant throughout the system.

4. Can mechanical energy be transformed into other forms of energy?

Yes, mechanical energy can be transformed into other forms of energy such as thermal energy, sound energy, and electrical energy. This is because energy cannot be created or destroyed, but can only be converted from one form to another.

5. How is conservation of mechanical energy important in everyday life?

Conservation of mechanical energy is important in everyday life because it helps us understand and predict the behavior of objects in motion. It also allows us to design and build machines and structures that utilize and conserve mechanical energy, such as cars, elevators, and bridges.

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