Are the energy requirements the same for moving masses in different scenarios?

[Fizzics]

Here there are two scenarios for comparison.

Scenario 1: We move two connected masses which are Constantly 3 metres apart on a friction free surface using the same force and acceleration in a straight line.

Scenario 2: We move two connected masses which are Constantly 3 metres apart over an elevated friction free pulley using the same force and acceleration as above.

Question: Is the energy required to move scenario 1 the same in scenario 2? and can the 2 masses moving over a pulley be considered the same as the 2 masses moving in a straight line?

 

[berkeman]

Here there are two scenarios for comparison.

Scenario 1: We move two connected masses which are Constantly 3 metres apart on a friction free surface using the same force and acceleration in a straight line.

Scenario 2: We move two connected masses which are Constantly 3 metres apart over an elevated friction free pulley using the same force and acceleration as above.

Question: Is the energy required to move scenario 1 the same in scenario 2? and can the 2 masses moving over a pulley be considered the same as the 2 masses moving in a straight line?

Over a pulley implies they are being raised against the force of gravity, versus your horizontal frictionless table. Is that really the comparison you are asking about?

 

[Fizzics]

Over a pulley implies they are being raised against the force of gravity, versus your horizontal frictionless table. Is that really the comparison you are asking about?

As one mass is going up the other mass is going down the other side of the pulley

 

[Fizzics]

 

[berkeman]

As one mass is going up the other mass is going down the other side of the pulley

Then how are they always 3 meters apart and connected? Sorry that I'm not getting the setup for the question.

 

[berkeman]

Oh, I see the figure now. You mean "along the rope" a constant distance apart.

 

[Fizzics]

Oh, I see the figure now. You mean "along the rope" a constant distance apart.

That's right

 

[berkeman]

Can you draw free body diagrams (FBDs) for each situation? That may help you to figure out the answer.

Also, does it make any difference if a force F is applied left to the leftmost mass in the upper diagram and down on the left mass in the pulley diagram, versus applying F/2 to each mass?

 

[anorlunda]

You can solve this problem by simply comparing the final energies (potential energy proportional to height above the ground, and kinetic energy proportional to the square of speed) with the initial energies.

What happens between initial and final, the masses go up/down sideways or in circles, doesn't matter.

 

[Fizzics]

Can you draw free body diagrams (FBDs) for each situation? That may help you to figure out the answer.

Also, does it make any difference if a force F is applied left to the leftmost mass in the upper diagram and down on the left mass in the pulley diagram, versus applying F/2 to each mass?

The equal forces would be applied to mass A sideways and Mass A downwards

 

[Fizzics]

You can solve this problem by simply comparing the final energies (potential energy proportional to height above the ground, and kinetic energy proportional to the square of speed) with the initial energies.

What happens between initial and final, the masses go up/down sideways or in circles, doesn't matter.

Sorry but I don't understand what you are saying, Maybe I should say that the initial force is applied to Mass A in both diagrams and mass B follows because it is connected by a belt.

 

[anorlunda]

Your question was how much energy does it take to ...

Conservation of energy is a wonderful principle. It permits huge simplifications of problems like this. Conservation of energy gives the answer to your question as:

$E_{net.added}=E_{final}-E_{initial}$

The details of how and when the energy was added, are irrelevant. All forces and directions of forces are irrelevant. No matter how complex the problem, conservation of energy requires that the answer is reduced to that simple equation. That's why I say that it simplifies.

 

[Fizzics]

Your question was how much energy does it take to ...

Conservation of energy is a wonderful principle. It permits huge simplifications of problems like this. Conservation of energy gives the answer to your question as:

$E_{net.added}=E_{final}-E_{initial}$

The details of how and when the energy was added, are irrelevant. All forces and directions of forces are irrelevant. No matter how complex the problem, conservation of energy requires that the answer is reduced to that simple equation. That's why I say that it simplifies.

So if it took 50 N initially to move the mass and 45 N Finally to stop the mass the net loss would be 5 N in both cases, is that correct?

 

[A.T.]

So if it took 50 N initially to move the mass and 45 N Finally to stop the mass the net loss would be 5 N in both cases, is that correct?

Energy is not measured in N.

 

[anorlunda]

So if it took 50 N initially to move the mass and 45 N Finally to stop the mass the net loss would be 5 N in both cases, is that correct?

No, forces don't enter into the problem at all if you use energies.

The energy of each mass is $\frac{1}{2}m*v^2 + m*g*h$ where m is the mass, v is the velocity, g is 9.81 in Earth's gravity. and h is the height above the ground. Compute that for mass 1 and mass 2 both before the experiment starts and after it ends. Subtract initial from final and you have the energy that was put into the system. If the starting or ending velocities are zero, then v=0. You can also choose a reference where h=0 for one of the starting positions.

Be careful with the units if you want the correct answer.

 

[anorlunda]

So if it took 50 N initially to move the mass and 45 N Finally to stop the mass the net loss would be 5 N in both cases, is that correct?

There is another possibility. You original question asked how much energy. Did you mean to say how much force?

 

[Fizzics]

There is another possibility. You original question asked how much energy. Did you mean to say how much force?

I guess I have wandered between force and energy without thinking so to try and clarify let's stick with energy required. So let's say that 100 joules of energy is applied to moving mass A in both scenarios in the direction of the arrows for 2 seconds (= 200 watts) then as a result of this let's say that the straight line masses in scenario 1 move for 2 metres before coming to rest, my question is would the masses moving over the pulley in scenario 2 also move for 2 metres before coming to rest. Thank you in advance for taking the time to consider this.

 

[A.T.]

that 100 joules of energy is applied to moving mass A in both scenarios in the direction of the arrows for 2 seconds (= 200 watts)

200 watts for 2 seconds is 400 joules, not 100 joules

then as a result of this let's say that the straight line masses in scenario 1 move for 2 metres before coming to rest, my question is would the masses moving over the pulley in scenario 2 also move for 2 metres before coming to rest.

What makes them come to rest?

 

[Fizzics]

200 watts for 2 seconds is 400 joules, not 100 joulesWhat makes them come to rest?

They come to rest naturally because of the forces around them such as gravity and air resistance, they are not in a vacuum or perpetual motion. The 2m stopping time is just so that a comparison can be made between the 2 scenarios it could just as easily be a 2 km stopping distance providing there was enough distance between the masses going over the pulley. I guess that my real question is that does gravity have more of an effect in stopping the masses in either of the scenarios because of the way they are set up?

 

[Fizzics]

200 watts for 2 seconds is 400 joules, not 100 joulesWhat makes them come to rest?

My meaning was 100 J per second for 2 seconds = total energy used 200w (1 Watt is the power of a Joule of energy per second ) however this was only an example and not relevant to my questions outcome

 

[A.T.]

They come to rest naturally because of the forces around them such as gravity and air resistance,

Same air resistance at same speed in both scenarios?

I guess that my real question is that does gravity have more of an effect in stopping the masses in either of the scenarios because of the way they are set up?

None in the first case. And none in the second if the masses are equal.

total energy used 200w

Energy is measured in Joule, not Watt.

 

[Fizzics]

Thank you
So two equal masses traveling over a pulley is the same as two equal masses traveling in a straight line if all of the conditions are the same?

 

[anorlunda]

My meaning was 100 J per second for 2 seconds = total energy used 200w (1 Watt is the power of a Joule of energy per second ) however this was only an example and not relevant to my questions outcome

You're getting it backward. 100 watts for 2 seconds = 200 watt seconds = 200 joules

They come to rest naturally because of the forces around them such as gravity and air resistance,

Then your problem is misstated. You must either assume that the objects are in empty space, or you must explicitly include gravity and friction in the calculation. The devil is in the details. If you get the details wrong, it confuses you about the principles.

 

[Fizzics]

You're getting it backward. 100 watts for 2 seconds = 200 watt seconds = 200 joules Then your problem is misstated. You must either assume that the objects are in empty space, or you must explicitly include gravity and friction in the calculation. The devil is in the details. If you get the details wrong, it confuses you about the principles.

Thanks for the feedback I will take it all on board