Conservation of energy question

[shuter]

Homework Statement

An 8.70kg block slides with an initial speed of 1.66m/s up a ramp inclined at an angle of 27.4 degrees to the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.3. Use energy conservation to find the distance the block slides before coming to rest.

Homework Equations

I think Wf=/F//delta s/cos(F,delta s) is relevant, but I'm unsure how to apply it.

The Attempt at a Solution

My answers don't really make sense (I have them written down on paper, but are too complicated to write online). I am not really sure how to make use of the coefficient of kinetic friction. Any help would be greatly appreciated.

 

[xcvxcvvc]

W = f dot d

Where is the confusion? Be more explicit (as in show work or ask less broad questions)

 

[shuter]

I apologize for the vagueness of my questions, this was my first time using this forum. So, I essentially know how to do the conservation of energy part of the question (although it would be appreciated if someone could go through it to confirm that my work so far is correct). But I'm not sure what role the coefficient of kinetic friction plays in the answer. So if someone could elaborate on that, I would really appreciate it.

 

[jwxie]

Hi. Let's not let me show all work. Instead, I will walk through the problem.

First look at your triangle. You need to have the right labels for known values (given forces, component forces, and angles). It does not matter whether we will use all of them of not (one or two may not applicable, who knows).

This assumes that you other than the given forces should have 1) horizontal component due to gravity 2) vertical component due to gravity

Let us remember there are two different energy of conversations (actually they are the same equation). The reason I said two are not to confuse you at this point, and not to draw the attention.

If there is no friction involves, we say the system should have energy conserved by
Kf + Uf = Ki + Ui
K is the the kinetic and U is the potential energy

If friction presents, we no longer have a conserved equation, that is
changes of K + changes of U = changes of mechanical energy = - Ff * d

Which in general, is the same form as the first equation. When there is no friction or any nonconservative force presents, we can move some terms over the other side.

Look at your picture again. What do you need for your equations?
Use those components.

Hint and tips: don't worry about the answer yet. I want you to develop the concept before actually finding the right answer (if you fail to do it this time).

Ps: I suggested you make a triangle and attach it (screenshot it, or whatever method...) here if you can't find the right answer after your second attempt

 

[rwisz]

I can provide a response to this conservation of energy question. First, let's define what conservation of energy means. In simple terms, it is the law of physics that states energy cannot be created or destroyed, only transferred from one form to another. In this problem, we can use the conservation of energy principle to find the distance the block slides before coming to rest.

To do this, we need to consider the different forms of energy involved in this scenario. The block has an initial kinetic energy due to its motion, and as it slides up the ramp, this kinetic energy is converted into potential energy due to its change in height. Additionally, there is also the energy lost due to friction between the block and the ramp, which is converted into thermal energy.

Using the conservation of energy principle, we can equate the initial kinetic energy of the block to the final potential energy and the energy lost due to friction. This can be represented as:

Initial kinetic energy = Final potential energy + Energy lost due to friction

We can express these energies in terms of their respective equations:

(1/2)mvi^2 = mgh + Wf

Where m is the mass of the block, vi is the initial velocity, g is the acceleration due to gravity, h is the height the block travels up the ramp, and Wf is the work done by friction.

We can rearrange this equation to solve for the distance traveled, h:

h = (1/2m)(vi^2 - (Wf/m))

To find Wf, we can use the equation:

Wf = μkmgcosθ

Where μk is the coefficient of kinetic friction, m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of the ramp.

Plugging in the given values, we get:

Wf = (0.3)(8.70kg)(9.8m/s^2)cos(27.4°) = 22.23J

Substituting this into our first equation, we get:

h = (1/2)(8.70kg)((1.66m/s)^2 - (22.23J/8.70kg)) = 0.36m

Therefore, the block slides a distance of 0.36m before coming to rest. This is a simplified explanation of the solution, but I hope it helps in understanding how to apply the