Chapter 4

Dynamics: Newton’s Laws of Motion

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Definition of Force

A force is a push or pull.

Forces can be :

Contact Forces

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Newton’s First Law

(Often called the “Law of Inertia”):

Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no

net force acts on it.

Inertia: Tendency of an object to resist a change in its motion

Mass: Proportional to the inertia of an object

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Newton’s Second Law

Newton’s second law is the relationship between acceleration and force:

Acceleration is proportional to net force on an object and inversely proportional to its mass.

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Equilibrium

A condition in which the net force on an object is equal to zero.

According to Newton’s 2nd Law, if FNet = 0, then a = 0 m/s. Object is:

a) at rest (v = 0 m/s)

b) moving with constant velocity

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Newton’s Third Law

Any time a force is exerted on an object, that force is caused by another object:

Whenever one object exerts a force on a second object, the second exerts an equal force in the

opposite direction on the first.

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Weight – the Force of Gravity

Weight is the force exerted on an object by gravitational attraction. Close to the surface of

the Earth, where the gravitational force is caused by the Earth and is nearly constant, the

weight of an object is:

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The Normal Force

The force exerted perpendicular to a surface is called the normal force.

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FrictionOn a microscopic scale, most surfaces are rough.

For kinetic (sliding) friction:

is the coefficient of kinetic friction, and is different for every pair of surfaces.

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Static Friction

Static friction is the frictional force between two surfaces that are not moving along each other. Static friction keeps objects on inclines from sliding, and keeps objects from moving when a force is first applied.

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Hooke’s Law

Fs = kx

k: spring constant

x: stretch distance

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Tension and Pulleys

Tension is uniform within a cord/string, pulleys are frictionless.

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“Apparent Weight”: Normal Force

Scales/Normal Force

- Measure the normal force - Scale reading is equal to weight on a flat, stationary surface

- Scale reading will change if surface is tilted or accelerating

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Terminal Velocity

For an object in free-fall, when frictional force of air resistance (“drag force”) is equal to object’s weight, object is in equilibrium and will maintain constant velocity.

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Forces at Angles

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Solving Problems with Newton’s Laws: Free-Body Diagrams

1. Draw a sketch.

2. For one object, draw a free-body diagram, showing all the forces acting on the object. Make the magnitudes and directions as accurate as you can. Label each force. If there are multiple objects, draw a separate diagram for each one.

3. Resolve vectors into components.

4. Apply Newton’s second law to each component.

5. Solve.

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Example 1 (g = 9.8 m/s2)

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Example 2

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