Dynamics in One Dimension

Manual: General · Subject: Physics

Solve force-and-motion problems along a single axis.

Applying Newton’s second law on a line

Procedure

Choose a coordinate axis, draw the free-body diagram, resolve forces along the axis, and write $\sum F = ma$ . The sign convention must be consistent throughout the solution.

Elevator and vertical motion

In vertical problems, the apparent weight can differ from $mg$ . If upward is positive, then $N - mg = ma$ , so $N = m(g+a)$ when accelerating upward and $N = m(g-a)$ when accelerating downward.

Blocks on a line

For connected blocks or objects pushed or pulled along a surface, each object gets its own free-body diagram. Internal forces between objects should not be mixed with forces on the system as a whole unless you are analyzing the combined system.

ℹ️

Solve from the outside in

First solve for the motion of the whole system if that simplifies the unknowns; then solve individual objects to find internal forces like tension.

A 2 kg mass has a net force of 6 N along a line. What is its acceleration?

1\,\text{m/s}^2

2\,\text{m/s}^2

3\,\text{m/s}^2

12\,\text{m/s}^2

If upward is positive, write the force equation for a mass on an elevator accelerating upward.

When a system is accelerating, what must be true about the net force?

It must be zero It must be opposite velocity It must be nonzero It must equal weight

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Dynamics in One Dimension

Applying Newton’s second law on a line

Procedure

Elevator and vertical motion

Blocks on a line