Newton's Laws of Motion

• Isaac Newton's three laws of motion, published in his 1687 book Principia, provide the foundation for describing the effects of forces on objects in everyday life.

Newton's First Law (Inertia)

• An object in motion stays in motion, and an object at rest stays at rest unless acted upon by a net force.
• To change an object's motion (i.e., to accelerate it), a net force is required.
• Inertia is measured by mass: objects with greater mass have greater inertia and are harder to accelerate or stop.

Newton's Second Law

• The net force acting on an object is equal to the mass of the object multiplied by its acceleration: F(net) = ma.
• F(net) refers to the net force, which is the sum of all forces acting on an object after cancellations.
• Equilibrium occurs when all forces on an object are balanced, resulting in no net force and no change in velocity (no acceleration).
• When forces are unbalanced, acceleration occurs

Gravity as a Force

• Gravity is a common example of a force causing acceleration.
• The acceleration due to gravity is approximately 9.81 m/s^2, denoted as 'g.'
• The force of gravity, or weight, can be calculated as F(g) = mg, where 'm' is the mass of the object.
• Weight is measured in Newtons (N, kg*m/s^2), not kilograms (kg).

Newton's Third Law

• For every action, there is an equal and opposite reaction.
• When exerting a force on an object, that object exerts a force back.
• The normal force is the force exerted by a surface on an object, perpendicular to the surface.
• The normal force adjusts its magnitude in response to the force applied to the surface until the surface breaks.

Action and Reaction

• Objects can move despite equal and opposite action-reaction forces because there are other forces at play.
• A reindeer can pull a sled forward because when it steps, it pushes the Earth backward with its foot, and the Earth pushes the reindeer forward.
• The force of the Earth pushing the reindeer forward is greater than the force of the sled pulling it backward, resulting in forward acceleration.

Free-Body Diagrams

• A free-body diagram is a visual representation of all forces acting on an object.
• It involves drawing a point to represent the object and arrows representing the magnitude and direction of each force.

Box on The Ground

• For a box at rest on the ground, the forces are gravity pulling downward and the normal force pushing upward.
• Since the box isn't accelerating, the forces are equal, and the net force is zero.

Box Suspended from The Ceiling

• If the box is suspended from the ceiling, gravity still pulls downward, but the upward force is now tension from the rope.
• Tension adjusts to match the weight of the box (assuming a massless, unbreakable rope).
• Total force is still zero

Elevator Example

• A elevator with a mass of 100 kg is connected to a counterweight of 850 kg via a pulley system.
• We use free-body diagrams for both the elevator and the counterweight, to include tension (T) and gravity.
• For the elevator F(net) = T - m_elevator * g = -m_elevator * a.
• For the counterweight F(net) = T - m_counterweight * g = m_counterweight * a.
• By combining these equations, we can solve for the acceleration which is approximately 0.795 m/s^2.