Kinetic and potential energy and speed

[crpcrpcrp]

Could someone please help me out??!
I'm so confused because we were never taught any of this and i have to hand in this assignment 2morrow

1.An object is dropped from a height of 10m at what height will it s kinetic energy and potential energy be equal?

2.A 100kg roller coaster car starts from rest on the top of a 30m high track.It rolls down to a 10m high deep then back up to a 15m crest. What are the speeds of the cart at (a)the deep and (b)the crest?

Help me pleasezz

 

[crpcrpcrp]

I know i am supposed to at least attempt the problem but I have no idea where to start.We have never been taught this stuff.If i could at least get an equation that can help i would be very grateful.

 

[Hootenanny]

Okay, let's take question one first. If we ignore air resistance we can say that the total energy of the object must remain constant, yes?

 

[Astronuc]

Also, in question 1, the potential energy is taken with respect to 0 m. Presumably, the object starts 'at rest'.

 

[crpcrpcrp]

Okay, let's take question one first. If we ignore air resistance we can say that the total energy of the object must remain constant, yes?

yea.I guess there is constant velocity

 

[Hootenanny]

yea.I guess there is constant velocity

No, the velocity is not constant. I said the total energy must remain constant.

 

[crpcrpcrp]

Oh sry I'm not very good at physics.

 

[Hootenanny]

Oh sry I'm not very good at physics.

No problem, so now we've established the total energy of the object is constant. What types of energy does the object posses?

 

[crpcrpcrp]

Kinetic rite?

 

[Hootenanny]

Kinetic rite?

Are you sure that it only has kinetic energy?

 

[crpcrpcrp]

and potential because it starts at rest

 

[Hootenanny]

and potential because it starts at rest

Yes, it also has potential, but not because it starts at rest. It has potential energy because it is some distance above the ground, does that make sense?

So, now we can say that;

kinetic energy + potential energy = constant

Do you follow?

 

[crpcrpcrp]

yea i get it

 

[Hootenanny]

So, if we want to find the point at which kinetic energy = potential energy we can say that;

potential energy + potential energy = 2*potential energy = constant

 

[crpcrpcrp]

So, if we want to find the point at which kinetic energy = potential energy we can say that;

potential energy + potential energy = 2*potential energy = constant

Ummmm...i don't really follow

 

[Hootenanny]

Ummmm...i don't really follow

Which bit don't you follow?

 

[crpcrpcrp]

This bit:
potential energy + potential energy = 2*potential energy = constant

 

[Hootenanny]

This bit:
potential energy + potential energy = 2*potential energy = constant

Okay, suppose we have an equation;

a + b = c

Now, suppose we say a=b, then we have;

a + a = 2*a = c

Is that a little clearer?

 

[crpcrpcrp]

Okay, suppose we have an equation;

a + b = c

Now, suppose we say a=b, then we have;

a + a = 2*a = c

Is that a little clearer?

Yea i get it now

 

[Hootenanny]

Good . So now we have;

2*potential energy = constant

Now we need to find the constant. How do you suggest we do that?

 

[crpcrpcrp]

use direct variation?

 

[Hootenanny]

If the total energy of the system is constant, what is the total energy of the system before the object is dropped?

 

[crpcrpcrp]

i don't understand the question

 

[Hootenanny]

What is the initial energy of the stone before it is dropped?

 

[crpcrpcrp]

i don't know

 

[Hootenanny]

Okay, before the object is dropped find;

1. The kinetic energy of the object
2. The potential energy of the object

 

[crpcrpcrp]

isn't it 0J

 

[crpcrpcrp]

how do i find it?I was not given to velocity or mass

 

[Hootenanny]

how do i find it?I was not given to velocity or mass

Firstly, what is the velocity of the object before it is dropped?

 

[crpcrpcrp]

the potential energy=mass*gravity*height
=10*10*m
=100m

 

[crpcrpcrp]

is the initial velocity=0ms-1

 

[Hootenanny]

the potential energy=mass*gravity*height
=10*10*m
=100m

Correct! So since the object is at rest before it is dropped, all the energy is in the form of potential energy. So the constant in our equation must be...

 

[crpcrpcrp]

0?

 

[Hootenanny]

0?

If the total energy of the object must be constant then the total energy must be the same as the total energy at the start. Does that make sense?

 

[crpcrpcrp]

I understand

 

[Hootenanny]

Good, so now we have

2*potential energy = constant

2mgh = 20mh = 100m

20h = 100

Can you now go from here?

 

[crpcrpcrp]

i'm still a little confused. so what would be the constant?

 

[crpcrpcrp]

Good, so now we have

2*potential energy = constant

2mgh = 20mh = 100m

20h = 100

Can you now go from here?

what do i do form here?

 

[crpcrpcrp]

wait...
where did u get the 100?

 

[Hootenanny]

i'm still a little confused. so what would be the constant?

The constant would be the 100m as you stated yourself.

what do i do form here?

You should solve for h, the height of the ball when the potential energy is equal to the kinetic energy

wait...
where did u get the 100?

You derived it yourself;

the potential energy=mass*gravity*height
=10*10*m
=100m

 

[wisienkas]

at starting height you know that potential energy = constant

you know the constant is potential energy + kinetic energy.

therefore the potential energy and the kinetic energy is the same if 2*potential energy=constant

you can therefore say constant/2 = potential energy or constant/2= kinetic energy

since you get the potential energy from gravity*mass*height you can simply just isolate the height since you have te energy from the constant.

its more math than physics however. hope it helps for any looking in here