Block A rests on top of block B as shown in Fig. E4.26. The...

Block $A$ rests on top of block $B$ as shown in Fig. E4.26. The table is frictionless but there is friction (a horizontal force) between blocks $A$ and $B .$ Block $B$ has mass $6.00 \mathrm{~kg}$ and block $A$ has mass $2.00 \mathrm{~kg} .$ If the horizontal pull applied to block $B$ equals $12.0 \mathrm{~N},$ then block $B$ has an acceleration of $1.80 \mathrm{~m} / \mathrm{s}^{2}$. What is the acceleration of blosk $A$ ?

Key Concepts

Free Body Diagrams

Free body diagrams are graphical representations that isolate an object and illustrate all external forces acting upon it. They are essential tools in solving dynamics problems as they help in identifying and analyzing the forces, including friction and applied forces, thus facilitating the application of Newton's laws.

Newton's Second Law

This fundamental law of motion states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. It is used to calculate the acceleration of objects when forces, including applied forces and friction, are known, allowing for a quantitative analysis of motion in mechanical systems.

Friction

Friction is the resistive force that opposes the relative motion between two surfaces in contact. In this context, it pertains specifically to the friction between two objects, which affects how forces are transmitted between them and can cause different accelerations when friction is present or absent.

Static Friction

Static friction is the frictional force that must be overcome to initiate relative motion between two surfaces. It is key in multi-body systems where one body rests on another, determining whether the bodies move together or slide relative to each other when a force is applied.

Transcript

00:01 So for this problem, we have two blocks stacked on top of each other, block a being the smaller one stacked upon block b.

00:08 On a frictionless plane, frictionless horizontal plane, there is a horizontal friction between block a and b, so that they stay stuck on each other for now.

00:21 And we want to know the acceleration of block a when block b is pulled horizontally, resulting in force fb.

00:33 So how do we go about doing this? so we're going to use newton's second law, and we are going to write in terms of block b first, taking into account the force of friction.

00:49 So that is just the total force minus the force of friction, which will denote as f subf.

00:56 And now we can write this in terms of block a, which is going to be mass science acceleration of a equals the force of friction, which is going to be a result from the first equation.

01:15 So if we act in object b with force f, it starts its motion.

01:20 It is the cause of friction of the friction force that acts on object b.

01:26 So due to newton's second wall where every action has an equal and opposite reaction, f sub f, the force of friction, must act on object a as well.

01:40 And for here, the acting force on object a is the frictional force, f of sub s.

01:49 So that's how we get this equation here.

01:54 So doing the math, we can add.

01:57 Our first equation here and add it to here...

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