Conservation of Energy initial velocity

In summary, the conversation discusses the impact of initial velocity on the velocity at the bottom of an object's motion. The equation KE_0 + PE_0 = KE + PE is used to determine the velocity at the bottom, taking into account the initial kinetic and potential energies. The confusion arises from the incorrect use of the equations KE = 1/2mv^2 and PE = mgh. After attempting to solve the problem using these equations, it is determined that the correct equation is Vf = Vi^2 + [2 sqrt(2gh)] / m.
  • #1
vesperaka
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I know if there was no initial velocity, the velocity at the bottom would just be sqrt(2gh), but I'm not sure how the initial velocity impacts the velocity at the bottom. I thought just adding the x-component of the velocity would be enough but apparently it's not :\
 
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  • #2
Well if there was an initial velocity, then what was the initial kinetic energy? Just remember:

[tex]KE_0 + PE_0 = KE + PE[/tex]
 
  • #3
Welcome to PF!

vesperaka said:
I know if there was no initial velocity, the velocity at the bottom would just be sqrt(2gh), but I'm not sure how the initial velocity impacts the velocity at the bottom. I thought just adding the x-component of the velocity would be enough but apparently it's not :\

Hi vesperaka! Welcome to PF! :smile:

Yes, do what chislam suggests. :smile:

Another way of looking at it: your equation can be written (1/2)v12 = gh.

So how would you put v0 into that?
 
  • #4
I understand that KE = 1/2mv^2, so when I tinker around with that I get

V = sqrt (2KE/m)

But that equation gives me a problem cause I can't just make KE a variable like that. I do know that all of the energy at the bottom is KE though. So:

1/2mvi^2 + sqrt(2gh) = 1/2mvf^2

When I take that equation and solve for Vf, I get this really long equation

Vf = Vi^2 + [2 sqrt(2gh)] / m


Is that the right answer? If I answer it incorrectly 1 more time I don't get credit so I'm being cautious, but to be honest I don't understand why it wouldn't work (unless I botched the algebra).
 
  • #5
vesperaka said:
… 1/2mvi^2 + sqrt(2gh) = 1/2mvf^2

When I take that equation and solve for Vf, I get this really long equation

Vf = Vi^2 + [2 sqrt(2gh)] / m

Hi vesperaka! :smile:

No, you're very confused.

KE = 1/2 mv^2. PE = mgh (not gh, and certainly not 2gh).

And where did that sqrt come from? :confused:

Try again! :smile:
 

FAQ: Conservation of Energy initial velocity

What is the conservation of energy initial velocity?

The conservation of energy initial velocity refers to the principle that states that energy cannot be created or destroyed, it can only be transformed from one form to another. In the context of physics, it specifically refers to the conservation of mechanical energy, which is the sum of kinetic and potential energies, in a system.

How is the conservation of energy initial velocity applied in real-life situations?

The conservation of energy initial velocity is applied in various real-life situations, such as in the movement of objects, the production of electricity, and the functioning of machines. It is also a key concept in understanding the behavior of natural phenomena, such as the motion of planets in the solar system.

What is the relationship between initial velocity and conservation of energy?

The initial velocity of an object is a crucial factor in determining its kinetic energy, which is a form of mechanical energy. According to the conservation of energy principle, the total mechanical energy of a system remains constant, therefore, the initial velocity of an object directly affects its energy transformation and conservation.

Can the initial velocity of an object change without violating the conservation of energy?

Yes, the initial velocity of an object can change without violating the conservation of energy principle. This is because the change in initial velocity will result in a corresponding change in the object's kinetic energy, which will be compensated by a change in its potential energy to maintain the total mechanical energy of the system constant.

How is the conservation of energy initial velocity related to the law of conservation of momentum?

The conservation of energy initial velocity and the law of conservation of momentum are closely related. Both principles state that in a closed system, the total amount of a particular quantity remains constant. In the case of the conservation of energy initial velocity, it is the total mechanical energy, while in the law of conservation of momentum, it is the total momentum of the system.

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