What is the maximum acceleration a truck can have to keep a crate in place?

[FLANKER]

A flatbed truck is carrying a 69.5 kg crate along a level road. The coefficient of static friction between the crate and the bed is 0.400. What is the maximum acceleration that the truck can have if the crate is to stay in place?

 

[chroot]

Can you first calculate the force on the crate due to friction? Hint: F = [mu]_s m g.

Then how about using Newton's second law, F = ma?

- Warren

edit: typo

 

[M98Ranger]

To answer this question, we can use the equation Ff = μN, where Ff is the force of friction, μ is the coefficient of static friction, and N is the normal force. In this case, the normal force is equal to the weight of the crate, which is mg, where m is the mass of the crate and g is the acceleration due to gravity (9.8 m/s^2).

Plugging in the given values, we get Ff = (0.400)(69.5 kg)(9.8 m/s^2) = 271.6 N. This means that in order for the crate to stay in place, the maximum force that can be applied to the crate is 271.6 N.

We can then use Newton's second law, F = ma, where F is the net force and a is the acceleration. Since we know the maximum force that can be applied (271.6 N) and the mass of the crate (69.5 kg), we can solve for the maximum acceleration:

271.6 N = (69.5 kg)a
a = 271.6 N / 69.5 kg = 3.91 m/s^2

Therefore, the maximum acceleration that the truck can have is 3.91 m/s^2. Any acceleration greater than this would cause the crate to start moving and potentially slide off the truck. It is important for the truck driver to be aware of this limit and drive accordingly to ensure the safety of the cargo.