Acrate 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?

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:

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

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

Then the condition for not sliding is:

if the person is shown to have +90n, then ans is -10n.

if the person is shown to have -90n, then ans is +10n.