# Tension between two sliding blocks

1. Sep 16, 2014

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1. The problem statement, all variables and given/known data

The problem:

Two blocks made of different materials connected together by a thin cord, slide down a plane ramp inclined at an angle θ to the horizontal as shown in the figure (block B is above block A). The masses of the blocks are mA and mB and the coefficients of friction are μA and μB.

If mA=mB=5.5kg, and μA = 0.19 and μB = 0.30, determine the tension in the cord, for an angle $θ = 28^{\circ}$

2. Relevant equations

Newton's Laws

3. The attempt at a solution

My Attempt:

After setting up free body diagrams (not shown), I found the acceleration $a\approx2.5~\frac{m}{s^2}$ along with the following equation for T:

$$sin(\theta )mg-T-\mu _acos(\theta)mg=ma$$

$$\Rightarrow T=m(sin(\theta)g-\mu _acos(\theta)g-a)\Rightarrow$$

$T\approx 2.722 ~\textrm{N}$ in magnitude

2. Sep 17, 2014

### ehild

The solution is correct in principle, but you rounded off the acceleration too much, therefore the second digit of T is inaccurate. You could have cancelled a and get T directly.

ehild