Crates A and B sit at rest side by side on a frictionless...

Crates $A$ and $B$ sit at rest side by side on a frictionless horizontal surface. They have masses $m_{A}$ and $m_{B},$ respectively. When a horizontal force $\overrightarrow{\boldsymbol{F}}$ is applied to crate $A$, the two crates move off to the right. (a) Draw clearly labeled free-body diagrams for crate $A$ and for crate B. Indicate which pairs of forces, if any, are third-law action-reaction pairs. (b) If the magnitude of $\vec{F}$ is less than the total weight of the two crates, will it cause the crates to move? Explain.

Crates $A$ and $B$ sit at rest side by side on a frictionless horizontal surface. They have masses $m_{A}$ and $m_{B},$ respectively. When a horizontal force $\overrightarrow{\boldsymbol{F}}$ is applied to crate $A$, the two crates move off to the right.
(a) Draw clearly labeled free-body diagrams for crate $A$ and for crate
B. Indicate which pairs of forces, if any, are third-law action-reaction pairs. (b) If the magnitude of $\vec{F}$ is less than the total weight of the two crates, will it cause the crates to move? Explain.

Key Concepts

Free-Body Diagrams

Free-body diagrams are schematic representations that depict all the forces acting on an individual object. They are essential tools in mechanics for visualizing forces, understanding the interactions between objects, and setting up the equations of motion based on these forces.

Newton's Third Law

Newton's Third Law states that for every action there is an equal and opposite reaction. This means that if one object exerts a force on a second object, the second object simultaneously exerts a force of the same magnitude but in the opposite direction on the first object. This principle is critical for analyzing paired forces between interacting bodies.

Contact Forces

Contact forces are forces that occur when objects are physically touching each other. Examples include normal forces and friction. These forces are central to understanding how the motion of one object influences another, particularly when analyzing systems where objects push against or support each other.

Frictionless Surfaces

A frictionless surface is an idealized surface where no frictional force exists to oppose motion. This simplification allows for the analysis of objects’ motion by considering only the forces explicitly applied to them, without the complicating effects of friction. It is particularly useful for focusing on the fundamental principles of dynamics in horizontal motion.

Net Force and Acceleration

The net force on an object is the vector sum of all the forces acting upon it, and according to Newton's Second Law, this net force determines the acceleration of the object. Understanding the difference between the magnitude of individual forces and the resulting net force is crucial when analyzing whether an object will move, regardless of comparisons to other forces like weight, which might act in perpendicular directions.

Transcript

00:01 Alright, for this question, we want to get a free body diagram where a force is pushing on block a and pushing it into block b on a frictionless horizontal surface.

00:16 So let's take a look at block a first.

00:21 So let's picture that this little dot is the center of gravity in block a.

00:33 Here we have that there.

00:36 So what we want to do is there is always going to be a normal force.

00:41 The normal force is just perpendicular to the surface.

00:46 So i'll write that as f and to denote normal.

00:51 And remember that is always perpendicular to surface.

00:57 And then obviously the block has some type of weight.

01:01 And weight is equal to mg.

01:05 And here gravity is going down so we have weight down here which is also another force so you have this incoming force here and then causing this to also move so here is going to be the total force right there and we're actually going to call this force the incoming force force a b because it is it is traveling from block a to b so now let's clean that up and make our own little diagram so again here is that center point that we had up there so we have the normal force going up fn we have the net force traveling to block b.

02:04 We'll denote that as just f because that is the total force.

02:10 And then down we have the weight.

02:16 And then this way we have f, a, b.

02:27 Great.

02:28 So now let's take into consideration block b.

02:33 So again, block b will also have a normal force...

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