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Newtonian Dynamics Applications

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Newtonian Dynamics Applications

Why It Matters

Newtonian dynamics turns a force diagram into predictions about motion. It is the main bridge between Forces and Kinematics.

Definition

Newtonian dynamics applies Newton’s laws to bodies or systems of bodies. The central idea is that a resultant force causes acceleration, not velocity.

Key Representations

For constant mass:

In components:

The component equations use signed components after axes and positive directions have been chosen. In one-dimensional problems, this reduces the vector equation to a single signed-component equation.

Weight in a gravitational field:

In magnitude form:

For apparent weight in vertical motion, the vector equation is reduced to a one-dimensional signed equation. Taking upward as positive:

Mass, Weight, and Inertia

Mass is a scalar measure of inertia, meaning resistance to changes in velocity. It does not depend on location.

Weight is the gravitational force on a body. It is a vector and depends on the local gravitational field strength.

For the same resultant force, a larger mass gives a smaller acceleration, showing greater inertia.

Force Analysis Workflow

  1. Define the body or system.
  2. Draw a free-body diagram.
  3. Choose axes and positive directions.
  4. Resolve forces along the chosen axes.
  5. Apply Newton’s second law along each axis.
  6. Combine with kinematic equations if motion variables are required.

The mass in must correspond to the chosen body or system.

Equilibrium vs Acceleration

If the resultant force is zero:

then:

The body is either at rest or moving with constant velocity. A non-zero velocity does not require a continuing force; a non-zero acceleration does.

Connected Particles and Tension

Connected-particle problems involve bodies linked by strings, rods, or contact. For an ideal light inextensible string over a smooth pulley:

  • Tension has the same magnitude throughout the string.
  • Connected bodies have the same acceleration magnitude along the string.
  • Newton’s second law is usually applied separately to each body.

Typical equations are:

The equations are solved simultaneously for acceleration and tension.

Apparent Weight and Lift Problems

Apparent weight is the normal contact force exerted by a support on a body. A weighing scale reads , not .

With upward positive:

  • Upward acceleration:
  • Downward acceleration:
  • Constant velocity:
  • Free fall:

Apparent weightlessness means there is no normal contact force. It does not mean gravity is absent.

Common Exam Points

  • Force is linked to acceleration, not velocity.
  • Draw separate free-body diagrams for connected bodies.
  • Tension always pulls away from the body along the string.
  • Do not assume normal contact force equals weight unless justified.
  • Use consistent signs for acceleration and force components.

Graph View

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