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There are uniform cubes in a toy box, a child makes a pillar using these cubes on a rough plane which is inclined to the horizontal at angle theta. The cubes do not slide on each other. If tan theta = 1/8, the max no. of cubes that can be stacked is,
A. 4
B. 5
C. 8
D. 16

Please explain the methods of obtaining the ans . Will mark the brainliest for the best ans

Sagot :

Onyebuchinnajiidn

The maximum number of cubes that can be stacked on the inclined plane without sliding is determined as 8.

Net force on the box

The net force on the box can be used to determine the maximum number of cubes that can be stacked without sliding.

The stack cubes must be at equilibrium.

∑Fx = 0

nW - μFₙ = 0

where;

  • n is number of the cubes
  • Fₙ is the normal force of the cubes
  • W is the weight of the cubes acting parallel to the plane

n(mg)sinθ - μmgcosθ = 0

n(mg)sinθ  = μmgcosθ

nsinθ  = μcosθ

  • let the coefficient of friction = 1

nsinθ  = cosθ

n = cosθ/sinθ

n = 1/tanθ

n = (1)/(1/8)

n = 8

Thus, the maximum number of cubes that can be stacked on the inclined plane without sliding is determined as 8.

Learn more about cubes here: https://brainly.com/question/1972490

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