A tetherball leans against the smooth, frictionless post to...

A tetherball leans against the smooth, frictionless post to which it is attached. (See Figure $5.50 .$ ) The string is attached to the surface of the ball such that a line along the string passes through the center of the ball. The string is $1.40 \mathrm{~m}$ long, and the ball has a radius of $0.110 \mathrm{~m}$ with mass $0.270 \mathrm{~kg} .$ (a) Make a free-body diagram of the ball. (b) What is the tension in the rope? (c) What is the force the pole exerts on the ball?

Key Concepts

Frictionless Contact Constraint

In the absence of friction, as with a frictionless surface, the only force that the surface can exert on an object is normal to the surface. This simplifies analysis by eliminating the need to account for frictional forces, leaving only the normal (reaction) forces during force balance calculations.

Free-Body Diagram

A free-body diagram is a schematic representation of an object and all the forces acting on it. It helps in visualizing forces like gravity, tension, and contact (normal) forces, and is the starting point for applying Newton’s laws in static or dynamic problems.

Static Equilibrium

Static equilibrium occurs when an object is at rest with no net force or moment acting on it. This concept is used to set up equations by ensuring that all forces and torques balance, allowing for the determination of unknown forces, such as tension or reaction forces.

Tension Force

The tension force is the pulling force transmitted along a string, rope, or cable. It acts along the length of the string and is crucial in problems involving connected bodies, where it directly affects how forces are distributed throughout the system.

Normal (Reaction) Force

The normal force is the contact force exerted by a surface perpendicular to the object in contact with it. In scenarios involving smooth, frictionless surfaces, the normal force is the only reactive contact force and is essential for maintaining equilibrium by counteracting other forces.

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