Crate off Eggs: Maximum speed

[cbrowne]

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 the truck can negotiate
the curve if the crate is not to slide out during cornering?

Homework Equations

The Attempt at a Solution

Can someone please confirm this answer.

a(c) = v^2/r = v^2/35

You want to find the maximum 'acceleration' your friction can give you, and set it equal to that centripetal acceleration to find the corresponding velocity.

Mu=Friction Force/Normal Force
Mu*Fn=Ff
Mu*m*g=m*a(friction)
.66*g=a(friction)

Now back to original.

v^2/35=.66*g
v=15 m/s

 

[LowlyPion]

Seems OK.

 

[baba89]

I can confirm that your solution is correct. In order for the crate of eggs to not slide out during cornering, the maximum speed of the truck must be 15 m/s. This is because the maximum acceleration provided by the coefficient of static friction is equal to the centripetal acceleration needed to keep the crate in place on the truck bed. Great job using the equation for friction and solving for velocity!