Solving Boy's Sled & Hill Homework: Find Friction & Acceleration

[abhikesbhat]

Homework Statement

A boy drags his 60N sled at constant speed up a 15 degree hill. He does so by pulling with a 25N force on a rope attached to the sled. If the rope is inclined at 35 degrees to the horizontal

What is the coefficient of kinetic friction between the sled and snow?

At the top of the hill he jumps on the sled and slides down the hill. What is the magnitude of his acceleration down the slope.

Homework Equations

The Attempt at a Solution

Is the correct answer for part 1 .1197?
Also when he jumps down, do I include his mass also? It does not cancel out at the end so do I keep it in terms of his mass or go without including? If I get it wrong, I will show my steps.

 

[songoku]

I get different answer for part 1...

For the second one, the mass of the man should be included. But if it's not given, then maybe it can be neglected, though I'm not sure...

 

[rock.freak667]

Could you post exactly how you got your answers? You don't need the mass of the person.

 

[songoku]

Oh i get it, thanks rock.freak667 for pointing out my mistake ^^

 

[abhikesbhat]

Ok I found all the forces acting on the sled.
25Cos20(from the boy)-60Sin15(gravity) -f=0 (constant speed, velocity)
f=7.9631 f=un n+25Sin20=60Cos15 n=49.4 u=.1611
Hm I think I calculated wrong last time. Is this right?

 

[RoyalCat]

Ok I found all the forces acting on the sled.
25Cos20(from the boy)-60Sin15(gravity) -f=0 (constant speed, velocity)
f=7.9631 f=un n+25Sin20=60Cos15 n=49.4 u=.1611
Hm I think I calculated wrong last time. Is this right?

Whoops, misread it at first. If you happened to read this post before the edit, ignore everything it said.

That looks correct. :) But I'd just like to make two suggestions.
The first is that you work parametrically, and only substitute for the question values at the very end. This is a skill you'll find very valuable later on.

Another suggestion I'd like to make is that you try and work with a bit more structure.
I might be off here, for all I know, you solved it perfectly on paper, but it just didn't show.

A personal suggestion of mine is that when you analyze the forces acting on an object, as well as its acceleration(s), you draw a clear diagram, and title it. What mass are you referring to, and where are you positioning your observer? Another thing I always try and do is write in bold what parameter I'm trying to isolate. What the variable I'm trying to solve for is.

Write the question data along-side the diagram and make sure you write whatever equations you derive from the free-body diagram.

This might be a bit overkill for simple problems such as these, but it's down-right necessary for multiple-mass problems where you may end up with MANY equations.

Again, these are just suggestions I'll be happy if you adapt, since it'll make your life much easier in the long run. :)

 

[abhikesbhat]

Yea I drew a free-body diagram on paper. I don't understand by what you meant when you said

"The first is that you work parametrically, and only substitute for the question values at the very end."

Thank you for your help.

 

[RoyalCat]

Yea I drew a free-body diagram on paper. I don't understand by what you meant when you said

"The first is that you work parametrically, and only substitute for the question values at the very end."

Thank you for your help.

By that I mean that you work things out without substituting for the numerical values given in the question.

So your final answer would be:
$$\mu_k=\frac{F_{boy}\cos{\beta}-mg\sin{\alpha}}{mg\cos{\alpha}-F_{boy}\sin{\beta}}$$

You'll soon meet questions which ask you about different situations (Things like, what if the boy exerted twice as much force and things like that). They would be painfully frustrating to solve your way, since you'd end up having to solve everything from the start.
But if you solve parametrically, you get a full view of what's at play, and you have an easy way to solve any following questions.

A very powerful tool you then get is a way to analyze your answer for correctness. You can look at extreme cases and compare what you get to what you think should happen.
For instance, in the above question, $$\mu_k$$ is defined as a positive pure number. The first test is dimensional analysis. What you get on the right side has to be the same as what you get on the left, what you get, has to be a pure number.

But the really interesting case is when you consider what happens when the value turns negative. For the value to turn negative, $$\beta$$, which I have defined as the angle of the force relative to the incline, would have to be negative. That means that the boy pushes the sled into the incline harder and hard until the normal is so great, that you would need an infinite coefficient of friction to keep the sled at equilibrium. :)

I may have rambled on a bit, I hope I got my point across. :x

 

[abhikesbhat]

Oh ok, so instead of numbers I should put variables, then substitute back in the end. I usually don't do that unless the problem gives just variables. Thank you and I will change my work-style.