Conservation of Energy Question

In summary, according to the conservation of energy principle, the kinetic energy and potential energy of the system at point A will be equal to the kinetic energy and potential energy at point B. Therefore, using this principle, we can determine the speed of the masses after the 2kg mass has dropped 25 cm to be 1.57 m/s.
  • #1
SoulEater
4
0

Homework Statement



In the absence of friction, how fast will the masses move after the 2kg mass has dropped 25 cm? [answer: v = 1.57 m/s]


Homework Equations



Conservation of Energy


The Attempt at a Solution



KE2F + KE1F = PE2I + PE1I

.5*m2*vf2^2 + .5*m1*vf1^2 = m2*g*h2 + m1*g*h1

.5 *2*vf2^2 + .5*1*vf1^2 = 2*9.8*.25 + 1*9.8*?

vf2 = vf1

3/2*vf^2 = ?
 

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  • #2
Hi Souleater, welcome to PF. Conservation of energy is the right approach, but
SoulEater said:
KE2F + KE1F = PE2I + PE1I
is not correct. The correct form is
KEI+PEI=KEF+PEF.
 
  • #3
But shouldn't I combine the total energy from both masses?
 
  • #4
Yes, and you should also combine the total potential energy for both masses.

Mechanical energy conservation says that

Kinetic plus potential energy of the system at point A is the same as kinetic plus potential energy at point B.

When a mass moves from point A to point B it trades one form of energy for the other form in such a way as to keep the sum the same at all times.

It's like taking money out of your left pocket and putting it in your right pocket. As you do this, you have varying amounts of money in each pocket, but the sum on your person does not change.
 
  • #5
But initially, isn't it all potential energy? Therefore the initial kinetic energy for both masses would be 0.
And at the end of the movement, wouldn't both of the masses have converted that potential energy to kinetic energy? Therefore the potential energy at the end would be 0.
 
  • #6
The 1kg block will be gaining gravitational potential energy as it rises.
 
  • #7
Welcome to PF!

Hi SoulEater! Welcome to PF! :wink:

:smile: KE + PE = constant. :smile:
 
  • #8
Thank you. :smile:

So how would the equation look like?
 
  • #9
ke1f + ke2f + pe1f + pe2f = ke1i + ke2i + pe1i + pe2i
 

FAQ: Conservation of Energy Question

What is the law of conservation of energy?

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

Why is conservation of energy important?

Conservation of energy is important because it is a fundamental principle of physics and helps us understand how energy is used and transferred in various processes. It also plays a crucial role in sustainable energy practices and reducing our impact on the environment.

How is energy conserved in everyday life?

Energy is conserved in everyday life through various processes, such as when a ball is thrown into the air, the potential energy of the ball is converted into kinetic energy as it falls back to the ground. In household appliances, energy is conserved by using more efficient devices and turning off unused electronics.

Can energy be lost or wasted?

Energy cannot be lost, but it can be wasted. When energy is transformed from one form to another, some of it may be lost as heat or sound. This is why it is important to use energy efficiently and reduce waste.

What are some examples of energy conservation in action?

Some examples of energy conservation in action include using renewable energy sources, such as solar or wind power, using energy-efficient appliances and vehicles, and implementing energy-saving practices in industries and buildings, such as insulation and LED lighting.

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