Question

Not understand the steps involved my physics book uses to rearrange an equation. Its to find tension in a string

i have and understand up to this step (w-Tsin(theta) is another way of saying N, the normal force)

Tcos(theta) = "mu k"(w-Tsin(theta)

the next step in the book the equation looks like

T = ("mu k" * w) / (cos(theta) + "mu k"sin(theta)

I dont understand what happend to the T on the right side and how sin(theta) ended up on bottom. I get how cos(theta) ended up on bottom but not sin

Answer 1

Here is a picture of the equation i am talking about

Answer 2

\[Tcos30=\mu_{k}(w-Tsin30)\]and here's what happened;
distributed the mu(k)\[Tcos30=\mu_{k}w-\mu_{k}Tsin30\]and then added mu(k)Tsin30 to both sides\[Tcos30+\mu_{k}Tsin30=\mu_{k}w\]factored out the T\[T(\cos30+\mu_{k}\sin30)=\mu_{k}w\]then divied both sides by cos30+mu(k)sin30\[T=\frac{\mu_{k}w}{\cos30+\mu_{k}\sin30}\]

Answer 3

Thank you. I just noticed the equation button (so icould have done \[\mu\] but dont see how to do a subscript

Answer 4

figured it out \[\mu _{k}\]

Answer 5

oh nice!