A solid ball is released from rest and slides down a hillside that slopes downward at 65.0° from the horizontal. (c) In part (a), why did we use the coefficient of static friction and not the coefficient of kinetic friction?

Verified step by step guidance

1. Understand the difference between static and kinetic friction: Static friction acts when an object is at rest and prevents it from starting to move, while kinetic friction acts when an object is already in motion.
2. Recognize that the ball is initially at rest when it is released. This means that static friction is the force that must be overcome for the ball to start sliding down the hill.
3. Consider the role of static friction in preventing the ball from slipping as it begins to move. Static friction is responsible for the initial grip between the ball and the surface, allowing it to roll without slipping.
4. Note that once the ball starts moving, kinetic friction would be relevant if the ball were sliding without rolling. However, in this scenario, the ball rolls, and static friction is crucial for maintaining the rolling motion without slipping.
5. Conclude that the coefficient of static friction is used because it determines the maximum force that can be applied before the ball starts to move, ensuring that the ball rolls down the hill rather than slides.

Key Concepts

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It acts when an object is at rest relative to a surface and prevents it from starting to move. The coefficient of static friction is used when determining the maximum force that can be applied before the object begins to slide.

Kinetic Friction

Kinetic friction, also known as sliding friction, occurs when two surfaces are in relative motion. It is generally lower than static friction and acts to oppose the motion of the sliding object. The coefficient of kinetic friction is used to calculate the force of friction once the object has started moving.

Transition from Static to Kinetic Friction

The transition from static to kinetic friction occurs when the force applied to an object exceeds the maximum static friction, causing the object to start moving. Initially, static friction is considered to determine if the object will move, and once motion begins, kinetic friction takes over to describe the frictional force during motion.