Algebra Problem

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bigdreamer#1

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Ok, for what ever reason, my brain is not working right.

This is from Kaplan's Physical Science Review book on chapter two of physics "Newtonian Mechanics"
M=mass of block A (15)
A=acceleration of block A (2.5)
mk=coefficient of kinetic friction (0.14)
g=acceleration of gravity (9.8)
T=tension of string

Solving for T, from:

MA=T- mkMg

then the book shows:

T=M(mkg+A)
=15(0.14(9.8)+2.5)
=58.1Newtons

My algebra must be way out of practice because I can't recall how each step of this occurred. Can someone break it down detailed step by step algebra for me, from MA=T-mkMg, I'm confused on what to do algebraically with the variable of "M" on each side so that you end up with the equation for T=M(mkg+A)

Thanks in advance.
 

Drakensoul

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Using the basic F=MA as the start:

F=MA
Forces acting, Tension and Friction in Opposing Directions, Tension leading since it is greater:
T-(mkMg)=MA
Add mkMg to both sides
T=MA+mkMg
Factor out the common M
T=M(A+mkg)
Substitute given information
T=15[2.5+(0.14*9.8)]
Solve
T=58.1 Newtons
 

irie

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I didn't see anything that complicated on the mcat...well, its not complicated but it is time consuming.


M(mkg+A) = M(mkg) + M(A)
 

klonoff

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So you want to go from MA=T-mkMg to T=M(mkg+A)?

Add +mkMg to each side. Get MA + mkMg= T.

MA + mkMg = M(A+mkg) = T
 
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