The maximum speed the truck can go without sliding

[goli12]

Homework Statement

A crate of eggs is located on the back of a truck. The truck rounds a circular bend in the road with radius of 35 meters. If the coefficient of static friction between the crate and the truck is 0.6, what is the maximum speed the truck can go without the crate sliding?

Homework Equations

F=mv²/r
Fs=μ_sn

The Attempt at a Solution

Hey guys, can you please check my answer for this question, I'm not entirely sure it is correct...

Firstly, I took the normal force of the truck to get n=mg, as it is not moving vertically. This results in the force of static friction (Fs) to be: Fs=μ_smg.

Secondly, this static friction is providing the centripetal force of the truck to go around in a circular motion and so resulting in the following equation: Fs=F=mv²/r = μ_smg.

So with algebra I made velocity the subject. The masses cancel out leaving: v²/r = μ_sg and so resulting in v=√(μ_sgr)

Now I enter the variables v=√(0.6*9.8*35), giving the velocity of 14.35ms^-1.

 

[Zatman]

Looks fine to me :)

 

[PhanthomJay]

Solution looks ok, however, substitute the word 'truck' with 'crate' in your attempt.

 

[goli12]

Solution looks ok, however, substitute the word 'truck' with 'crate' in your attempt.

Ahh yes, my mistake many thanks :tongue:

 

[Nickie]

This means that the maximum speed the truck can go without the crate sliding is 14.35 meters per second.

Your answer appears to be correct. Good job using the equations for centripetal force and static friction to solve for the maximum speed. However, it would be helpful to explain why this is the maximum speed and what would happen if the truck were to go any faster.

The maximum speed the truck can go without the crate sliding is determined by the balance between the centripetal force required to keep the truck moving in a circular motion and the force of static friction between the crate and the truck. If the truck were to go any faster, the centripetal force would exceed the maximum static friction force, causing the crate to slide. Therefore, the maximum speed calculated is the threshold for the truck to maintain circular motion without the crate sliding. Going any faster would result in the crate sliding, potentially causing damage or loss of the eggs.