Forces

What is dynamics?

• the study of how forces affect the motion of objects

What is a force?

• a push or a pull on an object with a specific magnitude and direction; can be represented by vectors; can be expressed as a multiple of a standard force

What is an external force?

• any outside forces that act on a body

What is a free-body diagram?

• a drawing of all external forces acting on a body

Newton I - Law of Inertia

• a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force
• The net force is the vector sum of all the forces acting on an object

What is inertia?

• the tendency of an object to remain at rest or remain in motion
• related to an object’s mass

What is mass?

• the quantity of matter in a substance

Newton II - Acceleration is due to forces

• $\boxed{F_{net}=ma}$
  • $F_{net}$ = net force = cause
  • $m$ = mass
  • $a$ = acceleration = effect
• An object subject to a net force will accelerate in the direction of the net force at a rate proportional to the force and inversely proportional to the object’s mass

Newton III - Action/Reaction

• For every action, there is an equal but opposite reaction on a different object
• ⚠️ Forces in an action/reaction pair always act on different objects
• For every force on an object, there is a force of equal magnitude but opposite direction on some other object
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Is this an action/reaction pair?

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Weight

• $w=mg$
• If the only force acting on an object is due to gravity, the object is in free-fall
• there is always a weight force on an object, even when it is not accelerating (as long as $g\neq 0$)

Mass vs Weight

Mass	Weight
A measure of the inertia of an object (resistance to acceleration)	The magnitude of the gravitational force exerted on an object
scalar	vector
Depends only on ‘amount of substance’ in an object ($m$)	Depends on both the mass ($m$) and local acceleration due to gravity ($g$)

Spring Forces

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Hookes’ Law

• $\vec{F_{sp}}=-k\Delta\vec{x}$
  • $F_{sp}$ = spring force
  • $k$ = spring constant
    • minus sign($-$) indicates that the spring force is always in the opposite direction to the extension or compression of the spring
  • $\Delta \vec{x}$ = displacement
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Forces on Sam, the trampoliner

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Normal Forces

• Normal force exactly counter-balances weight forces so that objects don’t fall through solids
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• Only solids have normal forces
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• Normal forces are perpendicular to surface
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Tension Forces

• Tension Force = force transmitted through a string or wire
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• Inextensible String Approximation
  • Assumes that the rope doesn’t stretch at all
• Massless String Approximation
  • Assume that tension is equal throughout a rope/string

Using Newton’s Laws to Solve Problems

1. Identify the system of interest (which may include several objects)
2. Draw a diagram of the system of interest and its environment

Equilibrium

Static Equilibrium

• Net force on the object is zero and the object is stationary

Dynamic Equilibrium

• Net force on the object is zero, and the object is moving at constant (non-zero) velocity

Friction

• $\boxed{f\equiv \mu N}$
  • $f$ = friction
  • $\mu$ = coefficient of friction
    • depends on the characteristics of the surface that are in contact
    • no units
  • $N$ = normal force
  • still need to account for static and kinetic friction
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• Friction is a force that opposes the motion past each other of objects that are touching

Textbook Recommended Problems:

• Recommended Problems:
  • Ch4: 1,2,4,6,10,11,16,21,26,33*,36,37,40,49,59*