Summary

General Principles

Two Explanatory Models

An object on which there is no net force is in mechanical equilibrium.

Objects at rest.
Objects moving with constant velocity.
Newton’s second law applies with $\vec{a} = \vec{0}$ .

The figure illustrates the free body diagram of an object in mechanical equilibrium.

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An object on which the net force is constant undergoes dynamics with constant force.

The object accelerates.
The kinematic model is that of constant acceleration.
Newton’s second law applies.

The figure illustrates a free-body diagram of an object with a constant force applied on it.

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A Problem-Solving Strategy

Model Make simplifying assumptions.

Visualize

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Solve Use Newton’s second law:

\vec{F}_{net} = \sum_{i}^{} \vec{F}_{i} = m \vec{a}

“Read” the vectors from the free-body diagram. Use kinematics to find velocities and positions.

Review Is the result reasonable? Does it have correct units and significant figures?

Important Concepts

Specific information about three important descriptive models:

Gravity

\vec{F}_{G} = (m g, downward)

Friction

\begin{array}{l} {\vec{f}}_{s} = (0 to μ_{s} n, direction as necessary to prevent motion) \\ {\vec{f}}_{k} = (μ_{k} n, direction opposite the motion) \\ {\vec{f}}_{r} = (μ_{r} n, direction opposite the motion) \end{array}

Drag

Drag is directed opposite the motion with magnitude

F_{drag} = {\begin{array}{l} \frac{1}{2} C_{d} ρ A V^{2} & high R e \\ 6 π η r v & sphere at low R e \end{array}

Newton’s laws are vector expressions. You must write them out by components:

\begin{array}{l} {(F_{net})}_{x} = \sum^{​} F_{x} = m a_{x} \\ {(F_{net})}_{y} = \sum^{​} F_{y} = m a_{y} \end{array}

The acceleration is zero in equilibrium and also along an axis perpendicular to the motion.

The figure illustrates the free-body diagram of forces acting on an object on the x y coordinate plane.

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Applications

Mass is an intrinsic property of an object that describes the object’s inertia and, loosely speaking, its quantity of matter.

The weight of an object is the reading of a spring scale when the object is at rest relative to the scale. Weight is the result of weighing. An object’s weight depends on its mass, its acceleration, and the strength of gravity. An object in free fall is weightless.

An object reaches terminal speed when the drag force exactly balances the applied force.

The figure illustrates drag force and applied force acting on an object.

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{\vec{F}}_{drag} = {\vec{F}}_{applied}