How Does Friction Affect the Acceleration of a Truck Carrying a Heavy Crate?

[homyungtj]

Homework Statement

You and a friend have just loaded a 200 kg crate filled with priceless art objects into the back of a 2000 kg truck. As you press down on the accelerator, force F(surface on truck) propels the truck forward. To keep things simple, call this Ft. What is the maximum magnitude Ft can have without the crate sliding? The static and kinetic coefficients of friction between the crate and the bed of the truck are 0.8 and 0.3.

That is the original question.

My question is when I look at the free body diagram of the truck on the x axis, Ft is moving forward (towards east). That I understand.
But friction by crate on truck is moving backward (towards west of FBD).

I'm thinking the crate is on the truck. IN terms of Newton's third law, yes it makes sense.
But when you're thinking the crate is on the truck, how could it pull (force definition) the
truck backwards, affecting Ft?

Thanks in advance for your answers.

Homework Equations

The Attempt at a Solution

 

[ehild]

If the crate does not slip it has to move together with the truck. The truck is accelerating. So does the crate, and its acceleration is the same as that of the truck. What force accelerates the crate? The same force, but with opposite sign acts at the truck from the crate.

ehild

 

[homyungtj]

If the crate does not slip it has to move together with the truck. The truck is accelerating. So does the crate, and its acceleration is the same as that of the truck. What force accelerates the crate? The same force, but with opposite sign acts at the truck from the crate.

ehild

First of all, thanks for the reply ehild.
your explanation helps me better to understand this problem,

let me just paraphrase what you explained just so I understand your point.

1) crate moves together with the truck. So it has to have same acceleration
2) because it's accelerating, there must be force.
3) so what is that force?

and I don't think I understand
"The same force, but with opposite sign acts at the truck from the crate."

because what I don't understand is how can a crate "on the truck"
possibly pull the truck backwards (according to FBD of the textbook)
when it makes sense explained by your way (Newton's third law).

 

[ehild]

Yes, it is Newton's third law. There is an interaction between the truck and the crate through static friction. This force acts against the accelerating force in case of truck. At the same time, the force of static friction accelerates the crate.

ehild

 

[rwisz]

As a scientist, it is important to understand the concepts of Newton's laws of motion and how they apply to this situation. In this problem, the crate is on the truck, which means that the weight of the crate is acting downwards and the normal force from the truck is acting upwards. These two forces cancel each other out, so they do not affect the motion of the truck.

The only force that can accelerate the truck forward is the force of the engine, which is Ft. However, there is also a force of friction acting in the opposite direction, which is caused by the contact between the crate and the bed of the truck. This frictional force is what prevents the crate from sliding off the truck.

The maximum magnitude of Ft that can be applied without the crate sliding is determined by the coefficients of friction. The static coefficient of friction is 0.8, which means that the maximum force of friction that can be applied before the crate starts to slide is 0.8 times the normal force. In this case, the normal force is the weight of the crate, which is 200 kg multiplied by the acceleration due to gravity (9.8 m/s^2), giving a normal force of 1960 N.

Therefore, the maximum force of friction that can be applied is 0.8 x 1960 N = 1568 N. This means that the maximum magnitude of Ft that can be applied without the crate sliding is 1568 N. If the force of the engine exceeds this value, the crate will start to slide and the truck will accelerate with the crate sliding on its bed.

In summary, the crate on a box problem can be solved by understanding the forces acting on the truck and crate, and applying the concept of coefficient of friction to determine the maximum magnitude of Ft that can be applied without the crate sliding.