In Fig. 6-34, blocks A and B have weights of 44 N and 22 N, respectively. (a) Determine the mini

In Fig. 6-34, blocks A and B have weights of 44 N and 22 N,...

In Fig. $6-34,$ blocks $A$ and $B$ have weights of 44 $\mathrm{N}$ and 22 N, respectively. (a) Determine the minimum weight of block $C$ to keep $A$ from sliding if $\mu_{s}$ between $A$ and the table is 0.20 . (b) Block $C$ suddenly is lifted off $A .$ What is the acceleration of block $A$ if $\mu_{k}$ between $A$ and the table is 0.15$?$

Key Concepts

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It must be overcome by an applied force in order for motion to start, and its maximum value is typically given by the product of the coefficient of static friction and the normal force. This concept is crucial in scenarios where the aim is to prevent relative motion until a threshold is reached.

Kinetic Friction

Kinetic friction is the force that opposes the motion when two surfaces are sliding past each other. Unlike static friction, its magnitude remains constant (often given by the coefficient of kinetic friction multiplied by the normal force) once motion has commenced. Understanding kinetic friction is essential for analyzing systems after an object has overcome static friction and is in motion.

Normal Force

The normal force is the perpendicular contact force exerted by a surface on an object. It plays a critical role in calculating frictional forces, as both static and kinetic friction depend directly on the magnitude of the normal force. In many problems, accurately determining the normal force is key to finding the frictional force acting on an object.

Newton's Second Law

Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This law is fundamental in dynamics, allowing the determination of acceleration given the net force, or vice versa, and is widely used in problems involving forces, masses, and accelerations.

Free-Body Diagrams

A free-body diagram is a graphical representation that depicts all the forces acting on an object. It is an essential tool in the analysis of mechanical systems because it helps isolate the object and clarify the direction and magnitude of forces, making it easier to apply Newton’s laws to solve for unknown quantities.

Transcript

00:01 Hi, here in this given problem this is the table top, a rough table top having a massless frictionless pulley at its edge.

00:16 There is the block a kept over this rough surface of the table tied with a string, a massless string attached with another block b and one more block c has been kept over a.

00:35 Weight of block b, wb acting vertically down, tension t in the string will remain same.

00:45 Weight of block a, wa, as the block a along with the c is having a tendency to move towards right, so force of friction will be acting towards left.

00:59 Weight of block a, wa that is given as 44 newton and this is also given as ma into g.

01:10 So, ma means mass of the block a that will be given by 44 divided by g.

01:16 Similarly for block b, its weight that is 22 newton is equal to mbg.

01:24 So, mass of block b that will be given by 22 by g kilogram.

01:33 In the first part of the problem as a is not sliding on table, it means b will not be falling down.

02:12 So, we can say tension in the string that should be equal to weight of block b and similarly using fbd free body diagram of block a along with c, tension t acting towards right, it should be equal to force of friction and this time it should be static friction as the block is not moving.

02:43 So, using these two equations, equation 1 and equation 2 and we conclude this static friction that should be equal to weight of block b and we know force of friction is given as mu s times the normal reaction and here normal reaction because the weight of block c, it will also be acting vertically down.

03:09 So, normal reaction exerted by the table on both of these blocks that will be n and this n will be equal to wa plus wc is equal to wb.

03:26 We will be plugging in the known values here...

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