A 42 -kg slab rests on a frictionless floor. A 9.7-kg block rests on top of the slab, as in Fig.

step 1 So we will be looking at problem 31 of chapter 5 of the physics fifth book. The question says a

A 42 -kg slab rests on a frictionless floor. A 9.7-kg block...

A 42 -kg slab rests on a frictionless floor. A $9.7-\mathrm{kg}$ block rests on top of the slab, as in Fig. 5-40. The coefficient of static friction between the block and the slab is $0.53$, while the coefficient of kinetic friction is $0.38$. The $9.7-\mathrm{kg}$ block is acted on by a horizontal force of $110 \mathrm{~N}$. What are the resulting accelerations of $(a)$ the block and $(b)$ the slab?

Key Concepts

Free-Body Diagram Analysis

A free-body diagram is a graphical representation used to visualize all the forces acting on an object. In problems involving multiple bodies in contact, such diagrams help systematically identify the forces like gravity, normal force, applied forces, and friction, and are essential for setting up the equations needed to solve for accelerations.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the product of its mass and acceleration. This principle is fundamental in analyzing the motion of objects when forces are applied, allowing us to set up equations that relate forces, masses, and resulting accelerations in any physical system.

Static and Kinetic Friction

Static friction is the frictional force that must be overcome to start the motion between two surfaces in contact, and it has a maximum value determined by the coefficient of static friction and the normal force. Once motion begins, kinetic friction—which generally has a lower coefficient—acts to oppose the relative motion between surfaces. Understanding the difference between these frictional forces is crucial when determining whether an applied force will actually move one object relative to another.

Relative Motion in Connected Systems

When multiple objects are in contact, as in a block resting on a slab, the forces acting on one object can cause it to accelerate relative to another. Analyzing the mutual frictional interactions between these objects is key to determining the individual accelerations of each component of the system. This concept involves considering how the movements of the bodies affect each other due to the coupling force provided by friction.

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