In Fig. 6-33, a 2.0 kg block lies on a 20 kg trolley that...

In Fig. 6-33, a 2.0 kg block lies on a 20 kg trolley that can roll across a floor on frictionless bearings. Between the block and the trolley, the coefficient of kinetic friction is 0.20 and the coefficient of static friction is 0.25. When a horizontal 2.0 N force is applied to the block, what are the magnitudes of (a) the frictional force between the block and the trolley and (b) the acceleration of the trolley?

In Fig. 6-33, a 2.0 kg block lies on a 20 kg trolley that can roll
across a floor on frictionless bearings. Between the block and the
trolley, the coefficient of kinetic friction is 0.20 and the coefficient
of static friction is 0.25. When a horizontal 2.0 N force is applied to
the block, what are the magnitudes of (a) the frictional force
between the block and the trolley and (b) the acceleration of the
trolley?

Key Concepts

Newton's Second Law

This law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). It is fundamental for analyzing the motion of objects when forces, such as friction and applied forces, are acting on them. In problems like this, Newton's Second Law applies separately to each part of the system, as well as to the system as a whole, to determine accelerations and interactions.

Static and Kinetic Friction

Friction is the force that opposes the relative motion between two surfaces in contact, and it comes in two forms: static and kinetic. Static friction prevents motion up to its maximum value, which is determined by the coefficient of static friction; once this is exceeded, slipping occurs and kinetic friction, characterized by a typically lower coefficient, takes over. Understanding the difference between these two is essential for determining whether bodies remain in relative rest or begin to slide against each other.

Relative Motion Analysis

In systems where multiple objects interact, such as a block on a trolley, the analysis of relative motion becomes important. The frictional force often depends on the relative acceleration or tendency of relative motion between the objects. Analyzing relative motion helps to establish if one part of the system will remain in static contact with another or if kinetic friction will be activated, informing the subsequent calculation of net forces and acceleration.

Free Body Diagram Analysis

Drawing free body diagrams (FBDs) is a critical technique in mechanics used to visualize and isolate all forces acting on an individual object. For complex systems, separate FBDs for each component allow for a clear identification of forces such as gravity, normal, frictional, and any applied forces. FBDs aid in setting up the equations based on Newton's Second Law and in systematically solving for unknowns like frictional force and acceleration.

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