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The cylinder in the picture is rotating at 500 RPMs. The friction coefficients between the cylinder and block B are static=0.5 and kinetic=0.3. Assume both blocks are attached together. Determine if the block system will slide down or not.

The cylinder in the picture is rotating at 500 RPMs The friction coefficients between the cylinder and block B are static05 and kinetic03 Assume both blocks are class=

Respuesta :

  • Coefficient of static friction = 0.5
  • Coefficient of Kinetic friction = 0.3
  • Angular velocity = 500 RPMs

The Radius of the System

Let R be the radius of cylinder

[tex]m_a + m_b = 4 + 3 = 7kg[/tex]

The angular velocity is 500 RPMs

[tex]\omega ^2 = \frac{500 * 2\pi}{60} rad/s\\N = (M_a + M_b)\omega ^2 R[/tex]

The normal force

[tex]f = \mu N = (M_a + M_b) g\\\mu (M_a + M_b) \omega ^2 R = M_a + M_b\\R = \frac{1}{\mu \omega ^2 R}\\\mu_s = 0.5\\R = \frac{1}{0.5 * (\frac{500 * 2\pi}{60})^2 }\\R = 0.0073m\\R = 7.3mm[/tex]

Since the radius is very little for two block to execute circular motion so system will slide down.

Learn more on coefficient of static friction here;

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