A uniform ladder of mass and length leans at an angle against a frictionless wall .If the coefficient of static friction between the ladder and the ground is , determine a formula for the minimum angle at which the ladder will not slip.

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Answer:A uniform ladder of mass and length leans at an angle against a frictionless wall .If the coefficient of static friction between the ladder and the ground is , determine a formula for the minimum angle at which the ladder will not slip.

Explanation:

A uniform ladder of mass and length leans at an angle against a frictionless wall .If the coefficient of static friction between the ladder and the ground is , determine a formula for the minimum angle at which the ladder will not slip.

The max angle for not to slip ladder is 48°.

According to the question,

Coefficient of friction,

u = 0.45

  • Mass of ladder = m
  • Length of ladder = L
  • Vertical force = mg
  • Horizontal force = u.mg

As the ladder is stable, the moment is zero.

Now,

→ [tex]u\times mgL\times sin(theta) - \frac{mgL}{2}\times cos(theta) =0[/tex]

→ Tan(theta) = [tex]\frac{1}{2} u[/tex]

By putting the values, we get

→                    = [tex]\frac{1}{2}\times 0.45[/tex]

→                    = [tex]48^{\circ}[/tex]

Thus the answer above is right.

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