Question

A 200-N crate rests on an ramp; the maximum angle just before it slips is 25 ∘ with the horizontal. What is the coefficient of static friction between crate and ramp surfaces?

Answer 1

Answer:

coefficient of static friction = tan a

where a is the angle of repose.

Explanation:

coefficient of static friction= tan25

Answer 2

The correct answer is 0.47.

Given: Weight of crate = 200N.

Maximum angle just before it slips = 25°.

To Find: The coefficient of static friction between ramp surface and crate.

Solution:

As we know the equation.

F = ma

mgSinФ is the weight along horizontal direction opposite friction.

Let the friction = f.

So the resultant will be difference of both the forces.

mgSinФ - f = 0

mgSinФ - цN = 0

Normal(N) will be equal to mgCosФ. As vertical component of weight is perpendicular to the crate.

mgSinФ - цmgCosФ = 0

SinФ - цCosФ = 0

ц = $\frac{SinQ}{CosQ}$

ц = tanФ

ц = tan25°

ц = 0.47.

Hence, the coefficient of static friction between ramp surface and crate is 0.47.

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