Conservation of energy, PE & KE problem. help?

[nchin]

Conservation of energy, PE & KE problem. help??

a block is sent sliding down a frictionless ramp. Its speeds at points A and B are 2.00 m/s and 2.60 m/s, respectively. Next, it is again sent sliding down the ramp, but this time its speed at point A is 4.00 m/s. What then is its speed at point B?


I understand the first step is to calculate the KE

KE at pt A:
KEa = (1/2) m(2)^2
KEa= 2m*
calculating the KE at pt B:
KEb = (1/2)mv^2
KEb = 3.38m

This part from the solution guide that I'm confused about:
"the difference between the KE at pt B and at pt A is the gravitational potential energy, therefore
Eg = KEb - KEa
Eg = 3.38 - 2m
Eg = 1.38m (m is the mass)"

I don't understand this part!

So PE = KEa - KEb??

Why is that?


And then (this part I also do not understand)
KEa2 = 1/2m(4.00)^(2) = 8m

To get the answer it would be

8m+1.38m=9.38m

1/2mv^(2) = 9.38m
V= 4.33 m/s



I am very confused. Can someone please explain to one to me. Thanks !

 

[Doc Al]

Point A must be higher than point B. As the block lowers to point B, some PE transforms to added KE.

Mechanical energy is conserved:

KE_A + PE_A = KE_B + PE_B

Rearranging, that becomes:
KE_B - KE_A = PE_A - PE_B

 

[TSny]

Conceptually (no numbers for now), how is the change in KE of the block related to the change in PE when sliding from a to b? [EDIT: Doc Al posted while I was still typing. Beat me to the punch :)]

 

[ak71]

While I was reading your post, it didn't occur to me to use the method you mentioned. If you are keen to take the energy approach and it works for you, by all means do!

However, the answer you quoted can be reached by just using Newton's laws of motion. Perhaps it would be easier for you to see what is going on in the problem this way?

Although it seems at first that you don't have enough information to fill in all the blanks (u,v,a,s and t) consider that you might be able to include some of these generally (just as letters), because they can be canceled out later.

 

[Nickie]

I would like to clarify and explain the concepts of conservation of energy, potential energy (PE), and kinetic energy (KE) in this problem.

Firstly, the conservation of energy states that energy cannot be created or destroyed, it can only be transferred from one form to another. In this problem, the energy of the block is being transferred from potential energy to kinetic energy as it slides down the ramp.

Now, let's break down the solution step by step.

1. Calculating the KE at point A:
The formula for KE is KE = (1/2)mv^2, where m is the mass of the object and v is its velocity. Plugging in the given values, we get KEa = (1/2)(m)(2)^2 = 2m. This means that at point A, the block has a kinetic energy of 2m.

2. Calculating the KE at point B:
Using the same formula, we can calculate the KE at point B as KEb = (1/2)(m)(2.60)^2 = 3.38m. This means that at point B, the block has a kinetic energy of 3.38m.

3. Understanding the difference between KE at point B and A:
The difference between the KE at point B and A is the gravitational potential energy (Eg). This is because as the block slides down the ramp, it is losing potential energy (due to its position on the ramp) and gaining kinetic energy (due to its movement). Therefore, Eg = KEb - KEa = 3.38m - 2m = 1.38m.

4. Understanding the relationship between PE and KE:
As mentioned earlier, energy can be transferred from one form to another. In this case, the potential energy of the block at point A is being converted into kinetic energy at point B. Therefore, we can say that PE = KEa - KEb.

5. Calculating the KE at point A with a different initial velocity:
In the second scenario, the block is sent sliding down the ramp with an initial velocity of 4.00 m/s at point A. Using the same formula, we get KEa2 = (1/2)(m)(4)^2 = 8m. This means that at point A, the block has a kinetic energy of 8