Physics: Algebra & Static Friction

[Winterbourne]

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I'm trying to solve the following problem. Not sure why I am not getting the correct answer. The problem seems to be with my algebra, but I am not sure where I am going wrong. Is there anyway someone can help me by doing a step by step rearrangement of this equation? Please & Thank you.

Solve for Us

F= Usmgcos(45) + mgsin(45)


* I have shown all my work in the replies. I am clearly having trouble with the algebra because I have tried three different ways to simplify and I need getting the wrong answer according to the review book. * None of my work brings me to the review book answer.

I have shown my work in "term-by-term" simplification. I am sorry if it is annoying to look at. the notation. It was jus the best way I could do it on the computer.

 

[6FFF]

F - mgsin45 = Usmgcos45

(F - mgsin45)/mgcos45 = Us

 

[Winterbourne]

Yes,

F - mgsin45 = Usmgcos45

(F - mgsin45)/mgcos45 = Us

Thanks. I can do all of this, but it has to be totally simplified using the numerical value of sin45 and cos 45 (√2/2). And simply all terms (mg and mg) ect.


So:

1. F = Usmgsin45 + mg cosg45
2. F= Usmg (√2/2) + mg(√2/2)
3. F=(√2/2)(Usmg +mg)
4. 2F/√2 = Usmg +mg
5. 2F/√2 = mg(Us + 1)
6. 2F/mg√2 = Us+1
7. (2F/mg√2) - 1 = Us

This is what I am doing, but it is not correct

If I use your work

1. (F-mgsin45)/(mgcos45) = Us
2. (F-mg(√2/2)/ mg(√2/2) = Us
3. (2/√2) [(F-mg(√2/2)/mg] = Us
4. (2F-(mg)√2)/ (mg√2) = Us
5. (2F/mg√2) - [(mg√2)/mg√2)]
6. (2F/mg√2) - 1

or


1. (F-mgsin45)/(mgcos45) = Us
2. (F-(√2/2)(mg) / (√2/2)mg
3. [F/ √2/2mg] - [ (√2/2)mg/(√2/2)mg]
4. [F/ (√2/2)mg] - 1
5. (2F/mg√2) - 1


ANSWER IN REVIEW BOOK: (√2F/mg) -1

 

[Winterbourne]

Also, you can solve (according to me)

1. F = Usmgcos45 + mgsin45
2. F = Usmg(√2/2) + mg(√2/2)
3. F = [mg(√2/2)] [Us +1 ]
4. (F/mg) = (√2/2)[Us +1]
5. 2F/(mg√2) = Us +1
6. (2F/mg√2) -1 = Us

 

[Winterbourne]

I'm trying to solve the following problem. Not sure why I am not getting the correct answer. The problem seems to be with my algebra, but I am not sure where I am going wrong. Is there anyway someone can help me by doing a step by step rearrangement of this equation? Please & Thank you.

Solve for Us

F= Usmgcos(45) + mgsin(45)


* I have shown all my work in the replies. I am clearly having trouble with the algebra because I have tried three different ways to simplify and I need getting the wrong answer according to the review book. * None of my work brings me to the review book answer.

I have shown my work in "term-by-term" simplification. I am sorry if it is annoying to look at. the notation. It was jus the best way I could do it on the computer.

 

[DrknoSDN]

Also, you can solve (according to me)

1. F = Usmgcos45 + mgsin45
2. F = Usmg(√2/2) + mg(√2/2)
3. F = [mg(√2/2)] [Us +1 ]
4. (F/mg) = (√2/2)[Us +1]
5. 2F/(mg√2) = Us +1
6. (2F/mg√2) -1 = Us

This answer is correct.
(2F/mg√2)-1 = US = (√2F/mg) -1
It's the same thing. (2/√2) is equal to √2/1 so it just simplifies down to the equation on the right.

Could also write (2/√2)*(F/mg) = (√2/1)*(F/mg) = √2F/mg

 

[Winterbourne]

This answer is correct.
(2F/mg√2)-1 = US = (√2F/mg) -1
It's the same thing. (2/√2) is equal to √2/1 so it just simplifies down to the equation on the right.

Could also write (2/√2)*(F/mg) = (√2/1)*(F/mg) = √2F/mg

Thank you!!!! I appreciate your help! x

 

[SN2ed]

Thread closed. These types of questions belong in the MCAT Study Q&A forum.