Understanding Work and Energy: Solving a Physics Problem

[kixtoby]

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 u_k = F_k/F_N
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?

 

[QuantumQuest]

and that Fd = 1/2mv(initial)^2

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

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

 

[kixtoby]

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

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.

 

[QuantumQuest]

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.

Is the substitution you do correct? Please check it again

 

[kixtoby]

Is the substitution you do correct? Please check it again

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

 

[QuantumQuest]

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...

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?

 

[kixtoby]

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?

Find a way to cross it out?

 

[QuantumQuest]

Find a way to cross it out?

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

 

[Chestermiller]

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

 

[kixtoby]

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

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...

 

[kixtoby]

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

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

 

[QuantumQuest]

Can I multiply mass on each side to cancel them out?

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?

 

[haruspex]

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

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 F_N to mass.

 

[kixtoby]

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

Original

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 F_N to mass.

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

 

[QuantumQuest]

Original

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?

 

[haruspex]

Original

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

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

 

[kixtoby]

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?

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.

 

[Chestermiller]

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)?

 

[haruspex]

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

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?

 

[QuantumQuest]

I am still not understanding how to go about this without knowing the mass. Is there another hint you could give me?

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.