Tension between two sliding blocks

[END]

Homework Statement

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 $θ = 28^{\circ}$

Homework Equations

Newton's Laws

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

Is this the correct answer?

 

[ehild]

Homework Statement

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 $θ = 28^{\circ}$

Homework Equations

Newton's Laws

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

Is this the correct answer?

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 canceled a and get T directly.

ehild