Egg Crate on Pickup Truck: Maximum Speed?

[bumblebeeliz]

Homework Statement

A crate of eggs is located in the middle of the flatbed of a pickup truck. The truck is negotiating a curve in the road that may be considered as an arc of a circle of
radius 35 m. If the coefficient of static friction between the flatbed and the crate is 0.66, with what maximum speed can the truck negotiate the curve without the crate sliding out during cornering?

Homework Equations

Ffr=\mus Fn = \mus mg

The Attempt at a Solution

I started by finding the v by:

= \sqrt{}rg
= \sqrt{}35m * 9.80 m/s2
= 18.52 m/s

After this, I have no idea how to use the static coefficient in order to find the maximum speed. Any clues?

 

[RTW69]

The force that allows the car to remain in its circular path is the force of static friction. Newton's second law along the radial direction is fs=(m*v^2)/r but fs=N*U-static. A free body diagram of the crate will give you the equation for N. Hint: maximum speed does not depend on the mass of the car.

 

[Doc Al]

I started by finding the v by:

= \sqrt{}rg
= \sqrt{}35m * 9.80 m/s2
= 18.52 m/s

Where did you get that formula? It doesn't apply here. Instead, use Newton's 2nd law.

After this, I have no idea how to use the static coefficient in order to find the maximum speed. Any clues?

As RTW69 said, it's static friction that provides the force that you'll use in applying Newton's 2nd law. What's the maximum value of static friction? (Symbolically, not numerically.) That will allow you to solve for the maximum speed.