Another Conversation of Energy Problem

[coldjeanz]

Homework Statement

I already solved Part A so just ignore that. Basically part B is saying that the ramp is no longer frictionless and has a kinetic coefficient of friction of 0.30. The other surfaces are still frictionless. It wants me to figure out how much work is done ON the block by the friction force as it slides up the ramp to the platform

Homework Equations

Wk = F * s

The Attempt at a Solution

Looking at the diagram I can see that there is a Normal force on the ramp, correct? So my Force should be the coeff. of kinetic friction X Normal force and nothing else. Normal force = m*g*cosθ

So I get Muk * mg * cosθ to get my Force. If this is correct can someone clarify as to why it's cosθ? I just kind of assumed that's what it is but I don't know why it actually is.

Ok so after that I still need my "s" to multiply with my Force to get the Work but I don't know how to get it.

 

[thepatient]

The normal force vector is perpendicular to the slope. The angle between north and the normal force vector is equal to theta. It's easier to consider all the energy before and after in order to solve this problem using conservation of energy.

 

[coldjeanz]

Hm I was thinking that initially but I figured it couldn't be done that way. How would I do it using cons. of energy?

 

[coldjeanz]

Well actually I did use cons. of energy to solve part A but I'm having trouble figuring out how to do it here

 

[JHamm]

Use the work energy theorem :)

 

[coldjeanz]

This?

W net = m*vf^2 - m*vo^2

Still confused about how to bring the MuK into consideration then

 

[netgypsy]

You have your vertical height of 3.0 m and the angle so it's very easy to calculate the hypotenuse or ramp length. Otherwise you're fine. You're using work done by friction is the force due to friction times the ramp length. If you draw your components of the force due to gravity you can see which angle to use to get the normal force and from that to calculate the force due to friction. From there you calculate the work done by friction.

You can't use the energy equations because you aren't asked anything other than the work done by friction as it slides up and you aren't told the final velocity at the top so you have to find it directly.

 

[coldjeanz]

^Thanks

But once I calculate my Force due to friction how do I get the "s" that I need to multiply with the Force in order to get the Work. If I just multiply it with the ramp height it doesn't give me the right answer.

 

[netgypsy]

You have the ramp height and the angle the ramp makes with the horizontal. That is enough for you to calculate the ramp diagonal length. Use your definitions of sine and cosine to get the hypotenuse of the right triangle knowing the height and one angle.

 

[thepatient]

You have to include gravitational potential energy; not just kinetic energy.

 

[netgypsy]

You have the vertical height and the angle and from that you can get the diagonal length. You have the coefficient of friction and the weight and the angle so you can get the Fnormal. Force of friction = coefficient of friction time force normal and work done by friction is force of friction times the ramp length. You don't need energy to do it as far as I can see.

As far as using sine or cosine, just draw the vectors and use geometry and trig to get the correct angle that goes with the definition of sine or cosine.

The velocity you found in part A is no longer valid so if you want to find the new velocity you still have to find the work done by friction, so why bother if it isn't asked for ?