Coordinate Setup for Multi-Mass Systems: Friction, Tension, and Acceleration

Vocabulary flashcards covering coordinates, masses, net forces, accelerations, tensions, and friction concepts from the lecture.

Coordinates (x1, y1, z1)

The set of position coordinates used to locate block one in 3D space; x1, y1, z1 denote its location along each axis.

Position of block one

The location of block one described by its coordinates (x1, y1, z1).

x1, y1, z1

The x-, y-, and z-coordinates that specify block one’s position in the chosen reference frame.

Mass m1

The mass of block one; determines inertia and appears in Newton’s second law for that block.

Mass m2

The mass of another block in the system (notation used alongside m1).

Net force vector

The vector sum of all forces acting on a block, expressed by components such as F1x, F1y.

Fnetx / Fnety

The x- and y-components of the net force acting on a block, used with the corresponding acceleration components.

a1x / a1y

The x- and y-components of acceleration for block one; used in Fnetx = m1 a1x and Fnety = m1 a1y.

a2y

The y-component of acceleration for block two (or another block) in the system.

Newton’s second law for a block

For each block: Fnetx = m ax and Fnety = m ay, relating net forces to accelerations in each direction.

Tension t1

The tension force in the first connector/string attached to a block.

Tension t2

The tension force in the second connector/string attached to a block.

Static friction

Friction that can prevent motion by opposing the tendency to move; acts to keep the system at rest up to a limit.

Kinetic friction

Friction that acts when there is relative motion between surfaces; opposes the motion and acts during sliding.

Case analysis (friction and tension)

Examining multiple scenarios (e.g., different relative magnitudes of tensions and friction) to determine whether the blocks move or stay stationary.