Can Mechanical Energy Be Conserved?

In summary, the two masses are balanced by one spring each, with the mass of A being twice that of B.
  • #1
jack1234
133
0
I have no clue in solving this question, can somebody help me?
http://tinyurl.com/34ax9f
 
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  • #2
what have you tried so far?...
 
  • #3
One has two masses A and B, and the mass of A is twice that of B, i.e. mA = 2*mB.

They are suspended from identical springs and since the mass of A is twice that of B, the deflection of the spring suspending A must be twice that of the spring suspending mass B, because A is twice as heavy.

The force of the spring is F = kx where k is the spring constant and x is the deflection from rest when zero force is applied to the spring.

Now the spring mechanical potential energy is [itex]\int_0^x{F(s)}ds[/itex] = 1/2 kx2, so if the deflection of A is 2x and the deflection of B is x, what can one say about the relationship between the mechanical energies?

Please refer to - http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html
 
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  • #4
Hi, I think I am very confused the sign with total mechanical energy...can see here
https://www.physicsforums.com/showthread.php?t=196128

Hence using what I am understand
Treat downward as negative,
for Mass A
E=1/2k(2x)^2 - mg(-2x)
since mg=k(-x), so E=1/2k(2x)^2 - k(-x)(-2x)
E=6kx^2
for Mass B
E=1/2k(x)^2 - mg(-x)
=1/2k(x)^2 - k(-x)(-x)
=3/2kx^2
so E_A=4E_B

Correct...this is the answer...but this will contradict the answer at
https://www.physicsforums.com/showthread.php?t=196128
the answer is -1/2kx^2, not 3/2kx^2(cases for mass B)
What is the problem? I feel very confuse now:(
 
  • #5
Hi, learningphysics has very kindly posted a long essay in the mentioned thread, will spend some time to digest it, hope that it will shed me some light for this question :)
 
  • #6
Ok, I think the following make more sense after understanding the explanation of learningphysics

for Mass A
(1/2)k(2x)^2-mg(2x)
=2k(x)^2 - k(2x)(2x)
=-2k(x)^2
for Mass B
(1/2)k(x)^2-mg(x)
=1/2k(x)^2-k(x)^2
=-1/2k(x)^2

Hence E_A=4E_B

Is it?
 
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  • #7
By the way, what I understand from the question is:
Two blocks are hung by two springs separately, ie each block is hung by one spring, not sure is it correct...although the answer is correct.
 
  • #8
jack1234 said:
Ok, I think the following make more sense after understanding the explanation of learningphysics

for Mass A
(1/2)k(2x)^2-mg(2x)
=2k(x)^2 - k(2x)(2x)
=-2k(x)^2
for Mass B
(1/2)k(x)^2-mg(x)
=1/2k(x)^2-k(x)^2
=-1/2k(x)^2

Hence E_A=4E_B

Is it?

yes, looks perfect to me.
 
  • #9
jack1234 said:
By the way, what I understand from the question is:
Two blocks are hung by two springs separately, ie each block is hung by one spring, not sure is it correct...although the answer is correct.

yes, each is balanced by one spring separately...

only difference from what you said is that the masses are on top of springs that are being compressed... but that makes no difference mathematically...
 
  • #10
I see, thanks for the confirmation and correction :)
 
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FAQ: Can Mechanical Energy Be Conserved?

What is total mechanical energy?

Total mechanical energy refers to the sum of the kinetic energy and potential energy of a system. It is a measure of the energy present in a system due to its motion and position.

How is total mechanical energy calculated?

Total mechanical energy is calculated by adding the kinetic energy, which is the energy of motion, and the potential energy, which is the energy stored in an object due to its position or configuration. The formula for total mechanical energy is E = KE + PE.

What is the conservation of total mechanical energy?

The conservation of total mechanical energy is a fundamental principle in physics which states that in a closed system, the total mechanical energy remains constant over time. This means that the total amount of energy in a system cannot be created or destroyed, but can only be transformed from one form to another.

What factors can affect total mechanical energy?

The two main factors that can affect total mechanical energy are the mass and velocity of an object. A change in either of these factors can result in a change in the total mechanical energy of a system. Additionally, external forces, such as friction or air resistance, can also affect the total mechanical energy of a system.

Why is total mechanical energy important?

Total mechanical energy is important because it helps us understand and predict the behavior of physical systems. It is used in various fields of science and engineering, such as mechanics, thermodynamics, and electricity, to analyze and solve problems related to motion and energy. It also allows us to make efficient use of energy and design systems that minimize energy loss.

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