Two masses hanging from a pulley (conservation of energy)

In summary, the conversation discusses using conservation of energy to determine the speed of a 22.5 kg mass when it hits the ground, with the masses connected by a string and hanging over a frictionless pulley. The conversation mentions finding the potential energy and kinetic energy of each mass and the pulley, and suggests creating an energy equation to relate them. It also addresses the concept of potential energy being zero at the ground.
  • #1
khannon5
24
0

Homework Statement


Two masses are connected by a string that hangs over a frictionless pulley with mass 8kg, radius .25m, and moment of inertia .5mr^2. One mass lays on the ground and has mass 15kg. The other mass is 22.5 kg and is 2.75 m above the ground. Use conservation of energy to determine the speed of the 22.5 kg mass when it hits the ground

Homework Equations


Ke final = pe initial
Ke=.5mv^2 + .5Iw^2

The Attempt at a Solution


I found the pe of the 22.5 mass using pe=mgh. I made that equal the ke equation but I'm not sure whether to combine masses or what to use
 
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  • #2
The system loses gravitational PE. The first question is to ask where does this energy go?
 
  • #3
There are three elements to the system, the two masses and the pulley. Consider the total energy (KE and PE) of each at start and again at the moment of impact.
 
  • #4
PeroK said:
The system loses gravitational PE. The first question is to ask where does this energy go?
Kinetic energy of each mass and the rotation of the pulley
 
  • #5
khannon5 said:
Kinetic energy of each mass and the rotation of the pulley

Can you write down an energy equation involving all the energies gained and lost?
 
  • #6
PeroK said:
Can you write down an energy equation involving all the energies gained and lost?
Ke=.5mv^2 of mass 1 + .5mv^2 of mass 2 + .5Iw^2 of pulley
 
  • #7
khannon5 said:
Ke=.5mv^2 of mass 1 + .5mv^2 of mass 2 + .5Iw^2 of pulley

OKay, but there's no PE there.

You're also going to have to find a relationship between the various KE's. So, you need to think about that as well.
 
  • #8
PeroK said:
OKay, but there's no PE there.

You're also going to have to find a relationship between the various KE's. So, you need to think about that as well.
Would the pe just be the mgh of the weight above the ground?
 
  • #9
khannon5 said:
Would the pe just be the mgh of the weight above the ground?

There are two masses involved.
 
  • #10
PeroK said:
There are two masses involved.
But why does it have pe if it's on the ground
 
  • #11
khannon5 said:
But why does it have pe if it's on the ground

Does it stay on the ground?
 
  • #12
PeroK said:
Does it stay on the ground?
No but in the beginning it has no pe
 
  • #13
khannon5 said:
No but in the beginning it has no pe
Right (assuming ground is taken as the reference point for PE). So post the initial energy = final energy equation.
 

Related to Two masses hanging from a pulley (conservation of energy)

1) How does the conservation of energy apply to two masses hanging from a pulley?

The conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. In the case of two masses hanging from a pulley, the potential energy of the masses at different heights is transformed into kinetic energy as the masses move towards equilibrium.

2) How does the height of the masses affect the conservation of energy in this scenario?

The height of the masses plays a crucial role in the conservation of energy. The higher the masses are suspended, the greater the potential energy they possess. As the masses move towards equilibrium, this potential energy is converted into kinetic energy, resulting in the masses moving faster.

3) Is the conservation of energy the only principle at play in this scenario?

No, the conservation of energy is not the only principle at play in this scenario. The principle of mechanical advantage also comes into play as the pulley system reduces the amount of force needed to lift the masses, but this does not affect the overall conservation of energy.

4) How does friction affect the conservation of energy in this scenario?

Friction can affect the conservation of energy in this scenario by dissipating some of the energy as heat. This can result in a loss of energy and the masses may not reach the same height as they were initially suspended at. However, in an ideal scenario with no friction, the conservation of energy still holds true.

5) Can the conservation of energy be used to predict the final velocity of the masses?

Yes, the conservation of energy can be used to predict the final velocity of the masses. By using the equations for potential and kinetic energy, the final velocity of the masses can be calculated based on their initial heights and masses. This is assuming no external forces or friction are acting on the system.

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