Question 373.
Determine the distance h to which a hole must be bored into the cylinder so that the center of mass of the assembly is located at
x = 64 mm.
Answer 373.
As the cylinder is of uniform density, the center of mass = center of volume.
Volume of cylinder before drilling,
V1 = π * 4^2 * 12 = 192π cc
Volume of drilled hole,
V2 = π * 2^2 * h = 4πh cc
Center of mass = center of volume
=> 6.4 = (V1*6 - V2*(h/2) / (V1 - V2)
=> 6.4 = [192π * 6 - 4πh * (h/2)] / (192π - 4πh)
=> 6.4 * (192 - 4h) = (1152 - 2h^2)
=> 3.2 * (192 - 4h) = (576 - h^2)
=> h^2 - 12.8h + 38.4 = 0
=> (h - 8) (h - 4.8) = 0
=> h = 4.8 cm or 8 cm.
Link to YA!
Determine the distance h to which a hole must be bored into the cylinder so that the center of mass of the assembly is located at
x = 64 mm.
As the cylinder is of uniform density, the center of mass = center of volume.
Volume of cylinder before drilling,
V1 = π * 4^2 * 12 = 192π cc
Volume of drilled hole,
V2 = π * 2^2 * h = 4πh cc
Center of mass = center of volume
=> 6.4 = (V1*6 - V2*(h/2) / (V1 - V2)
=> 6.4 = [192π * 6 - 4πh * (h/2)] / (192π - 4πh)
=> 6.4 * (192 - 4h) = (1152 - 2h^2)
=> 3.2 * (192 - 4h) = (576 - h^2)
=> h^2 - 12.8h + 38.4 = 0
=> (h - 8) (h - 4.8) = 0
=> h = 4.8 cm or 8 cm.
Link to YA!
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