Respuesta :
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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