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Nuetrik [128]
3 years ago
15

A crate of eggs is located in the middle of the flat bed of a pickup truck as the truck negotiates a curve in the flat road. The

curve may be regarded as an arc of a circle of radius 36.1 m. If the coefficient of static friction between crate and truck is 0.570, how fast can the truck be moving without the crate sliding?
Physics
1 answer:
spayn [35]3 years ago
8 0

Answer:

v_{max}=14.2\frac{m}{s}

Explanation:

Hi!

If the crate is not sliding, its trajectory is the arc with 36.1 m radius. Then the crate  has a centripetal acceleration:

a_c= \frac{v^2}{r} \\r = radius\\v = tangential \; velocity

The centripetal force acting on the crate is the static friction force between crate and truck. The maximum value of this force is:

F_{max} = \mu N\\\mu = 0.570=static\;friction \;coefficient\\N =normal\; force\\

The normal force has a magnitude equal to the weight of the crate:

N=mg

Then the condition for not sliding is:

F_{centripetal} = M\frac{v^2}{r}

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