In Fig. 6-48 blocks A and B have weights of 44 N and 22 N, respectively. (a) Determine the min

In Fig. 6-48 blocks A and B have weights of 44 N and 22 N,...

In Fig. $6-48$ blocks $A$ and $B$ have weights of $44 \mathrm{~N}$ and $22 \mathrm{~N}$, respectively. (a) Determine the minimum weight of block $C$ to keep $A$ from sliding if $\mu^{\text {stat }}$ between $A$ and the table is $0.20$. (b) Block $C$ suddenly is lifted off $A$. What is the acceleration of block $A$ if $\mu^{\text {kin }}$ between $A$ and the table is $0.15 ?$

Key Concepts

Force Equilibrium

Force equilibrium occurs when the sum of the forces on an object is zero, indicating that the object is either at rest or moving with constant velocity. In statics problems, establishing force equilibrium is crucial to finding conditions that prevent motion, such as determining the weight needed to counterbalance a potential slip due to static friction.

Newton's Second Law

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law is fundamental in analyzing the motion of objects under various forces, allowing us to set up equations of motion for systems when forces such as friction and tension are present.

Free-Body Diagram Analysis

Free-body diagrams are essential tools in mechanics used to visually represent all the forces acting on a single object. By isolating the object and drawing all the forces, such as gravitational, normal, frictional, and applied forces, one can simplify and solve complex problems involving equilibrium and acceleration.

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. Its maximum value is proportional to the normal force and is determined by the static friction coefficient. In problems involving impending motion, static friction defines the threshold beyond which motion will begin.

Kinetic Friction

Kinetic friction acts on objects that are already sliding relative to one another. It is typically lower than the maximum static friction, meaning that once motion has started, less force is needed to keep the object moving. Kinetic friction is calculated as the product of the normal force and the kinetic friction coefficient.

Transcript

00:01 Hey so we need us first of all draw the diagram so diagram of this question is looking like something like this this is the block a and this is connected via fully and one more block is over here and it is connected like this and this is the second block okay, so this is block b a c and b right so this is a this is c and this is b okay? we have given that the weight of the block b and a and b is 44 and 22 this is weight of block a that is 45 for newton and weight of block b that is 22 newton.

00:34 So what will be the block of block c so that they are present to them, they restrict a to slide, okay, from the slide.

00:42 So basically we know that it will be only happen if the tension t, that means the weight of b equal to the frictional force, that means this friction force, weight of b is 22 equals to 44 plus let's say the weight of c is some weight c into the norm, this is this will the normal force because there is no perpendicular motion and the fictional force will be fixed functional coefficient that is 0 .2 so we can write 0 .2 is 2 upon 10 okay so this will be 11 this will be 110 so weight of c will be 100 110 and the minus of 44 so it will be 70 70 minus 66 newton right 66 newton and in the second part we need to find the acceleration of the block um a block c suddenly a little bit of what is acceleration of block a if kinetic fusion is 0 .15 so acceleration will be when block c it just lifts so acceleration will be nothing but weight b minus of frictional force equal to mass into net force that is a weight to force minus of frictional force that will be mass into acceleration mass into acceleration right so we need to put just value overhead so yeah mass into acceleration so net mass of the system that is mass of a plus mass of b upon into acceleration.

02:24 So over here acceleration a comes out to be weight of b.

02:27 Weight of b is nothing but 22 minus a frictional force...

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