(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In the figure (sorry for that quick drawing with paint) m_1 (first block) = 4.0kg, m_2 = 5.0kg and the coefficient of kinetic friction between the incline plane and the first block is \mu_k = 0.24. Incline = 30 degree with horizontal

Find the magnitude of the acceleration of the masses and the tension of the cord

2. Relevant equations

(1) [tex]\sum Fnet = ma[/tex]

(2) [tex]f_k = \mu_k*F_n[/tex]

3. The attempt at a solution

I applied (1) to the first block in the x-direction and then in the y-direction

Found:

[tex]F_n - m_1*g*\sin\theta = 0 (a_y = 0) => F_n = m_1*g*\sin\theta[/tex] [a]

[tex]T - f_k - m_1*g*\cos\theta = m_1*a_x[/tex]

I applied (1) to block 2

[tex]m_2*g - T = m_2*a_y [/tex]

Added [a] to

[tex]m_2*g - f_k - m_1*g*\cos\theta = m_1*a_x + m_2*a_y[/tex]

<=>[tex]m_2*g - \mu_k *m_1*g*\sin\theta - m_1*g*\cos\theta = (m_1+m_2)a[/tex]

<=>[tex]g*\frac{m_2 - \mu_k *m_1*\sin\theta - m_1*\cos\theta}{m_1+m_2}=a[/tex]

What am I doing wrong?

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# Homework Help: Incline plane + friction

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