Which data are typically needed to solve a two-body Newton's law problem with friction?

Which data are typically needed to solve a two-body Newton's law problem with friction?

• A. Masses, the coefficient of friction (static and/or kinetic), the gravitational acceleration g, external applied forces, and the geometry/direction of motion.
• B. Masses only
• C. The coefficient of friction only
• D. External forces only

Answer: (A)

In problems with friction, you must know how forces balance and how friction arises from contact. The masses give you the inertial terms needed to apply Newton’s second law to each body, so you can relate accelerations to net forces. The friction force is tied to the normal force, which depends on gravity and how the bodies contact each other—so gravity and the setup’s geometry (angles, surfaces, pressurization) are essential to determine that normal force. The coefficient of friction (static or kinetic) tells you how large the friction can be and what regime you’re in, which directly affects the actual friction force. External applied forces change the total forces acting on the system, altering accelerations and possibly whether motion occurs or which friction regime applies. Finally, the geometry and direction of motion set how forces resolve along the directions of motion and determine the friction direction. All of these pieces are typically needed to solve a two-body problem with friction.

In problems with friction, you must know how forces balance and how friction arises from contact. The masses give you the inertial terms needed to apply Newton’s second law to each body, so you can relate accelerations to net forces. The friction force is tied to the normal force, which depends on gravity and how the bodies contact each other—so gravity and the setup’s geometry (angles, surfaces, pressurization) are essential to determine that normal force. The coefficient of friction (static or kinetic) tells you how large the friction can be and what regime you’re in, which directly affects the actual friction force. External applied forces change the total forces acting on the system, altering accelerations and possibly whether motion occurs or which friction regime applies. Finally, the geometry and direction of motion set how forces resolve along the directions of motion and determine the friction direction. All of these pieces are typically needed to solve a two-body problem with friction.