Conservation of momentum and frictionless ice

[StephenDoty]

True or False: As a stone slides down a frictionless ice covered hill its mechanical energy is concerved but its momentum is not.

False- if mechanical energy is concerved so is momentum

right??

 

[Shooting Star]

No.

Take into account the PE here.

 

[StephenDoty]

If mechanical energy is concerved then all PE turns into KE and vice versa because of the fictionless ice covered hill which means that the momentum is concerved also,

Right?

 

[StephenDoty]

is the origonal statement true or false?

 

[StephenDoty]

if mechanical energy is conserved then isn't momentum conserved. I mean momentum is always conserved right? Thus the origonal statement is false.

 

[Shooting Star]

I mean momentum is always conserved right?

Momentum of a system is conserved when there are no external forces acting on the system. Here, two forces, gravity and normal reaction, is acting on the stone.

Suppose you just let go of a stone from your hand. Does it acquire any speed and hence momentum when it hits the ground? Is the given case similar to this? I hope you can answer the question definitively now.

 

[StephenDoty]

The plane is frictionless therefore there are no external forces thus mechanical energy is conserved thus momentum is conserved. At least this is what I got out of my teacher's lecture. If this isn't right then I kind of need an explanation.

Shooting star: Since there are no external forces and since mechanical energy is conserved thus all KE turn into PE and PE turns into KE. Because of this fact momuntum must be conserved otherwise all KE would not turn into PE nor PE would turn into KE.

Thus mechanical energy and momentum is conserved.

 

[Shooting Star]

The plane is frictionless therefore there are no external forces thus mechanical energy is conserved thus momentum is conserved.

The mechanical energy is conserved.

There is another force acting on the stone. Can you name it?

Why don't you just answer the question I asked in my last post? I asked it for a purpose.

 

[StephenDoty]

ok the normal force and weight cancel each other out as far as forces. The only other force working on the object is the initial velocity to make it slide. If the mechanical energy is conserved, which it says in the problem, then all the KE and PE are conserved. So wouldn't Pf = Pi? If not then I do not understand.

 

[Shooting Star]

True or False: As a stone slides down a frictionless ice covered hill its mechanical energy is concerved but its momentum is not.

The stone is sliding down, so the hill must be inclined. Why should the normal reaction and weight cancel each other? It's the component of weight down and along the hill which is accelerating the stone downward, increasing its speed, and thus its momentum.

You could have simply answered my question about letting something drop, and you would have arrived at the correct answer yourself.

The mechanical energy is conserved because there is no friction. The KE increases at the expense of gravitational PE.

 

[StephenDoty]

if a stone is dropped then the stone gains momentum until it hits the ground then the ground "absorbs" the momentum, so isn't momentum conserved just as the momentum is conserved as the stone slides down the hill?

 

[Shooting Star]

if a stone is dropped then the stone gains momentum until it hits the ground then the ground "absorbs" the momentum, so isn't momentum conserved just as the momentum is conserved as the stone slides down the hill?

What about at any point after letting the stone fall and before impact with the ground? Does the stone gain momentum?

When sliding down the hill, the stone is initially at rest. It gains momentum because the component of weight along the plane is accelerating it. Think of it as an endless plane; you have not been asked what happens when the plane ends, but rather what is going on when it is sliding down the plane.