# TPR Chapter 3 FSQ #4

#### today15

I realize some has already posted a thread about this question, however I'm still having trouble getting the answer algebraically and it's really getting on my nerves :/.

Question: A box of mass m is sitting on an incline of 45 degrees and it requires an applied force F up the incline to get the box to begin to move what is the maximum coefficient of static friction?

a) [sqrt2*F / mg] - 1
b) [sqrt2*F / mg]
c) [sqrt2*F / mg] + 1
d) [2F / mg] - 1

I can get up to all this:

Since the force of friction as well as force of gravity is opposing the movement:

F = mgSin 45 + (mu) mg Cos 45

F = mg/sqrt2 + (mu)mg/sqrt2

mu = (F - mg/sqrt2) * sqrt2/mg

From this point I cannot seem to get the answer (a)...my algebra is not so great so if you could break it down that would be fantastic! Thank you!

#### aHealthNut

Ahhh was just working through this Q last night.

The set-up got me a little, but since you understand that, the work for the rest is, like you said, all algebra. From your last line:

mu = (F-mg/sqrt2)*sqrt2/(mg) ----> Multiply the sqrt2/(mg) to both terms inside the paranthesis

mu = (F*sqrt2/(mg))-(mg/sqrt2)*(sqrt2/(mg)) -----> the second term reduces to 1

Now you have: mu = (F*sqrt2/(mg)) - 1

Which is ans (a)

• today15
OP
T

#### today15

Appreciate you help! However, I still have a problem in one of those small pesky algebra steps.

This step:
mu = (F-mg/sqrt2)*sqrt2/(mg) ----> Multiply the sqrt2/(mg) to both terms inside the parenthesis

Correct me if I'm wrong, but we can rewrite (F-mg/sqrt2) to ((F/sqrt2) - (mg/sqrt2)) and then multiplying both terms by (sqrt2/mg) would yield:

(F*sqrt2/sqrt2*mg) - (mg*sqrt2/mg*sqrt2)

which simplifies to:

(F/mg) - 1

Obviously, I'm doing something wrong algebraically, I just don't see it?

#### aHealthNut

Ok, so the main thing is you can't rewrite (F-mg/sqrt2) to ((F/sqrt2) - (mg/sqrt2))

-Think PEMDAS for order of operations! Paranthesis, Exponents, Mult/Division, Add/Subtraction. Think of the term
(F-mg/sqrt2) as (F) - (mg/sqrt2) because the division of mg/sqrt2 happens before you subtract that quantity from F.

This way you can mult. ((F) - (mg/sqrt2)) * (sqrt2/(mg)) (I'm ALL about dem paranthesis)
and you will come up with F*(sqrt2/(mg)) - (mg/sqrt2)*(sqrt2/(mg)) ---> F(sqrt2/(mg)) - 1

-Aside note: since mg is 2 quantities, sqrt2/mg = (sqrt2/m) * g!!!!! NOT what you want. You need to make sure that you put parths around the mg quantity (this is for more calculation type things) -----> sqrt2/(mg) Hope this clears it up

#### medickdb

5+ Year Member
Shouldn't this be in the MCAT section?

• Haxx