# Homework Help: Work and Energy Problem

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1. Nov 21, 2016

### kixtoby

• Misplaced homework moved here by moderator, hence no template.
I have been stuck on this physics question:

An object is sliding along a flat surface with an initial speed of 30 m/s. What must the coefficient of kinetic friction be between the object and the surface if the object slides to a stop in 10m? What would be the speed of the object after it had only slide half that distance?

So I know that uk = Fk/FN
and that Fd = 1/2mv(initial)^2
but for the life of me I cannot figure out how to solve this problem.

Any help at all would be extremely appreciated.

I have done this:
F(10m)=1/2(9.8m/s2)(30m/s)
F(10m)=147m/s
F=14.7m/s

Am I at least on the right track?

Last edited: Nov 21, 2016
2. Nov 21, 2016

### QuantumQuest

Be careful in the substitution. Do it again. Also what are you trying to find by this?

3. Nov 21, 2016

### kixtoby

I am honestly not sure, I guess what I was trying to find was the force? But I need to find the coefficient of kinetic friction between the object and the floor. I guess I'm not sure what direction I need to go to solve this.

4. Nov 21, 2016

### QuantumQuest

Is the substitution you do correct? Please check it again

5. Nov 21, 2016

### kixtoby

I noticed I forgot to square...was that my only error? I also was not sure about plugging in gravity, but no mass was given in the problem...
F(10)=1/2(9.8)(30)^2
F(10)=4410
F=441

6. Nov 21, 2016

### QuantumQuest

Squaring is second. First, you have substituted g for mass. This is wrong. Now, if m is not given, can you think of a way to not have it in your equation?

7. Nov 21, 2016

### kixtoby

Find a way to cross it out?

8. Nov 21, 2016

### QuantumQuest

Cancelling is one way. What can you do and what can you find?

9. Nov 21, 2016

### Staff: Mentor

What is the acceleration of the object? Have you drawn a free body diagram?

10. Nov 21, 2016

### kixtoby

how would I calculate acceleration from the information given? And yes, I did draw one, although I wasn't really sure what values to plug in...

11. Nov 21, 2016

### kixtoby

Can I multiply mass on each side to cancel them out? Then the equation would be: fd=1/2v^2

12. Nov 21, 2016

### QuantumQuest

I don't understand this. Can you elaborate writing the equation?

EDIT: As a hint, what does the initial equation you wrote express in words?

13. Nov 21, 2016

### haruspex

What is f? Previously you used F for force. If f is the same, the left hand side is energy, while right hand side is velocity-squared. That would be dimensionally impossible.
Relate FN to mass.

14. Nov 21, 2016

### kixtoby

Original
I am very lost. I don't think I understand this problem at all.

15. Nov 21, 2016

### QuantumQuest

Original?

EDIT: Try to analyze the equation. What does it express? What can you substitute and what can you find from it in order to proceed to the solution of the problem?

16. Nov 21, 2016

### haruspex

What are the vertical forces? What is the vertical acceleration? If m is the mass, what equation does that give you?

17. Nov 21, 2016

### kixtoby

Sorry, I didn't realize I had replied to you. I started to type and must have hit reply by mistake.
So for this problem, I know that friction does work: f*d which is is equal to the initial kinetic energy (1/2)mv^2
Then, F = mu * mg where my goal is to solve for mu (coefficient of kinetic friction).

I am still not understanding how to go about this without knowing the mass. Is there another hint you could give me? I almost think I am making this harder than it needs to be, but I just don't understand.

18. Nov 21, 2016

### Staff: Mentor

Are you familiar with the SUVAT equations for a body moving with constant acceleration? If so, which one do you think you can you use in this problem to calculate the acceleration of the object (This part of the calculation does not involve Newton's laws. It is totally kinematic)?

19. Nov 21, 2016

### haruspex

Do F and f stand for the same thing here? If so, why not connect those two equations, eliminating it? If not, what are they?

20. Nov 21, 2016

### QuantumQuest

Look at what haruspex asked in #19. You have to understand which force's work is f*d - as you write it, in your initial equation. Also, I recommend looking at it the way Chestermiller suggests in #18.