Newton's Laws of Motion

Newton's Laws of Motion

• Isaac Newton's three laws of motion, published in 1687, explain how forces cause objects to accelerate.
• These laws apply to everyday objects.

Newton's First Law: Inertia

• An object's inertia is its tendency to maintain its current state of motion.
• An object stays in motion or at rest unless acted upon by a net force.
• A net force is required to cause acceleration and change an object's motion.
• Mass is the measure of inertia; greater mass indicates more inertia.

Newton's Second Law: F = ma

• The second law is mathematically expressed as Fnet = ma.
• Fnet represents the net force.
• m represents mass.
• a represents acceleration.
• Net force is the sum of all forces acting on an object.
• Equilibrium occurs when all forces are balanced, resulting in no acceleration.
• An object in equilibrium can still be moving at a constant velocity.
• Unbalanced forces lead to acceleration and changes in motion.

Gravitational Force

• Gravity causes objects to accelerate downwards at 9.81 m/s².
• The force of gravity (FG) is calculated as FG = mg, where m is mass and g is 9.81 m/s².
• The unit of force is the Newton (N).
• Weight is measured in Newtons (N) and mass is measured in kilograms (kg).

Newton's Third Law: Action-Reaction

• Every action has an equal and opposite reaction.
• When a force is exerted on an object, it exerts an equal force back.
• The normal force is the force exerted by a surface on an object in contact with it, perpendicular to the surface.
• The normal force adjusts its magnitude based on the force applied to the surface.
• When a reindeer pulls a sleigh, the sleigh pulls back on the reindeer with an equal force.
• The reindeer can move the sleigh forward by pushing backward on the ground, and the ground pushes it forward.
• If the force from the ground pushing the reindeer forward exceeds the force from the sleigh pulling it back, acceleration occurs.

Free Body Diagrams

• A free body diagram represents an object and all the forces acting on it.
• Steps to create a free body diagram:
  • Draw a rough outline of the object.
  • Place a dot in the center to represent the object's mass.
  • Draw and label arrows representing all forces acting on the object.
  • Choose a direction to be positive.
• For a box sitting on the ground, the diagram includes gravity (downward) and the normal force (upward).
• If the box is stationary, the forces are equal, and the net force is zero.

Tension Force

• Tension force is the force exerted by a rope or cable on an object it is attached to.
• The tension force counteracts the weight of the object, assuming the rope is massless and unbreakable.

Net Force in Elevators

• In an elevator, the net force may not always be zero, leading to acceleration.

Lift Acceleration Calculation

• A lift with a mass of 1,000 kg is controlled by a counterweight of 850 kg.
• The lift accelerates downward because it is heavier than the counterweight.

Free Body Diagram (Lift)

• Positive direction is upward.
• Force of gravity on the lift: 1,000 kg * 9.81 m/s² = 9,810 N (downward/negative direction).
• Force of tension: pulling the lift up (positive direction).
• Net force for the lift: Fnet = T - mlift * g.

Newton's Second Law

• Fnet = m * a, so T - mlift * g = mlift * (-a).

Counterweight Analysis

• Gravity: pulling it down with 850 kg * 9.81 m/s² = 8,338.5 N (downward/negative direction).
• Tension force: pulling it up.
• Net force on the counterweight: Fnet = T - mcounterweight * g.
• Based on Newton's Second Law: T - mcounterweight * g = mcounterweight * a (a is positive because the counterweight is moving upward).

System of Equations

• Two equations with two unknowns (Tension Force, T, and acceleration, a) are established.
• T - mlift * g = mlift * (-a).
• T - mcounterweight * g = mcounterweight * a.

Solving for Acceleration

• Subtracting the first equation from the second eliminates the tension force: (T - mcounterweight * g) - (T - mlift * g) = (mcounterweight * a) - (mlift * (-a)).
• Rearranging to solve for a: a = (difference between the weights) / (total mass).
• The value is essentially a version of Fnet = m * a.
• Solving for a with given values: a = 0.795 m/s².
• This acceleration is relatively low, which indicates a safe descent.