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Two masses are connected by a string which passes over a pulley with negligible mass and friction. One mass hangs vertically and one mass slides on a frictionless 30.0-degree incline. The vertically hanging mass is 6.00 kg and the mass on the incline is 4.00 kg. The acceleration of the 4.00-kg mass is

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laurawinter1p43zv5
The tension in the string and the acceleration must be equal for both masses. (See the free body diagrams)





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okpalawalter8

Answer:

  • The acceleration of the 4.00-kg mass is = [tex]3.92m/s^2[/tex]

Explanation:

[tex]m_1 = 6kg\\\\m_2 = 4kg[/tex]

From Newton"s 2nd law

[tex]m_1g - T = m_a[/tex] --------> 1

[tex]T - m_2gsin\theta = m_2a[/tex] ------>

adding equations 1 and 2

[tex]m_2g - m_2gsin\theta = (m_1+m_2)a\\\\a = \frac{g(m_1 - m_2sin\theta)}{m_1+m_2}\\\\a = \frac{9.8(6-4*sin30)}{6+4}\\\\a = 3.92m/s^2[/tex]

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