Kinetic/ Static friction- Newtons 3rd Law

[KingSloth]

Homework Statement

The coefficient of static friction is 0.60 between the two blocks in figure. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force causes both blocks to cross a distance of 5.0 m, starting from rest.
What is the least amount of time in which this motion can be completed without the top block sliding on the lower block?

Homework Equations

The Attempt at a Solution

Fnet Box 1: T-(Fn x 0.6)=ma

Fnet Box 2: T- (Fn x o.2)=ma

Where does static friction play into Fnet of box 2? I almost got it but the only way I could get the answer would be to have static friction in the positve direction. So it would be something like: Fs-Fk=ma . But I don't get how the static friction is in positive direction. please Help!

 

[Delphi51]

T-(Fn x 0.6)=ma

What is the T?
It seems to me the only force acting on the top mass is Fn*0.6 so you can solve for the acceleration directly.

 

[tomcue]

I can provide a response to this content by explaining the concept of static and kinetic friction and how they relate to Newton's Third Law.

Firstly, static friction is the force that prevents two surfaces from sliding against each other when they are in contact and not in motion. It is a reactionary force that acts in the opposite direction of the applied force. In this case, the coefficient of static friction between the two blocks is 0.60, which means that in order for the top block to start sliding on the lower block, a force of at least 0.60 times the normal force between the two blocks must be applied.

On the other hand, kinetic friction is the force that opposes the motion of two surfaces that are in contact and in motion. It is also a reactionary force that acts in the opposite direction of the applied force. The coefficient of kinetic friction between the lower block and the floor is 0.20, which means that a force of at least 0.20 times the normal force between the two surfaces must be applied to keep the lower block in motion.

Now, let's consider Newton's Third Law, which states that for every action, there is an equal and opposite reaction. In this scenario, the action is the force applied to both blocks, and the reaction is the static and kinetic friction forces. These forces are equal and opposite in direction, but they are not necessarily equal in magnitude.

In order for the top block to start sliding on the lower block, the applied force must overcome the static friction force. Once the blocks start moving, the kinetic friction force will come into play and oppose the motion. This is why the coefficient of kinetic friction is lower than the coefficient of static friction, as it takes less force to keep an object in motion than to start it moving from a state of rest.

To determine the least amount of time in which the motion can be completed without the top block sliding on the lower block, we need to consider the forces acting on the system and use the equations of motion to calculate the time. This may involve considering the maximum force that can be applied without causing the top block to slide, and using that to calculate the acceleration and time taken to cover the distance of 5.0 m.

In conclusion, static and kinetic friction are reactionary forces that play a crucial role in the motion of objects. They are related to Newton's Third Law, and understanding their behavior can help us accurately predict and calculate the