Laws of Motion: Force and Inertia

• Previous lessons described the motion of an object based on displacement, velocity and acceleration.
• This lesson focuses on the Laws of Motion and the concept of Force.
• Muscular activity is involved in actions and its effect is visible.
• Force causes motion and it's fundamental to understanding everyday phenomena.

Objectives

• Explain the significance of inertia.
• State Newton's laws of motion giving examples.
• Explain the law of conservation of momentum giving examples.
• Understand the concept of equilibrium of concurrent forces.
• Define coefficient of friction and distinguish between static, kinetic and rolling friction.
• Suggest methods of reducing friction, highlighting its role in everyday life.
• Analyze situations and apply Newton's laws of motion using free body diagrams.

Concepts of Force and Inertia

• Stationary objects remain where placed unless forced to move.
• Moving objects with constant velocity need force to change their motion.
• Inertia is the property of an object that resists changes to its current state of rest, or uniform motion in a straight line.
• Mass is the measure of a body's inertia.
• Change in velocity of an object can only occur with a net force.

Force

• Force is used in everyday examples like pulling, pushing, kicking, hitting.
• Effects of force can be seen or experienced.
• Different effects include:
  • Changing shape and size of object.
  • Influencing motion by starting or stopping movement.
  • Changing direction/speed of motion.
  • Rotating a body about an axis.

Force and Motion

• Force is a vector quantity.
• Net equivalent force can be calculated by vector addition when multiple forces act on a body.
• Motion is characterized by displacement, velocity.
• Velocity of an object increases or decreases continuously.
• Change the state of a body, the velocity will change depending on the direction of the force acting on it.
• Velocity change depends on the net force acting.
• Velocity of a body changes as long as net force is acting on it.

First Law of Motion

• A marble rolled on the floor stops after some time due to the decrease in velocity.
• To move a trolley at constant velocity, it needs to be pushed or pulled continuously to apply force constantly.
• Galileo proved that a body continues to be in its state of rest or of uniform motion in a straight line in the absence of any external force.
• A body is accelerated moving down an inclined plane and is retarded while moving up.
• Plane surface: a body will move with a uniform speed/velocity (if there is no external force).
• When ball is allowed to roll down a plane it rises to the same height on the face.
• If there is no friction between the plane and the ball, the ball keeps moving.

Issac Newton

• Born in Wollsthorpe, England in 1642.
• Studied at Trinity College, Cambridge.
• Observation of an apple falling towards the ground lead to the law of gravitation and laws of motion.
• Wrote “Principia” in Latin and a book on optics in English.
• Isaac Newton generalized Galileo's conclusions known as Newton's first law of motion.
• Newton's first law of motion states a body continues to be in a state of rest or of uniform motion in a straight line unless acts upon by external force.
• Measurements of changes in position, velocity, acceleration and force recorded with respect to a chosen frame of reference.
• Inertial frame of reference describes a body in translatory motion that has constant velocity if no net external force acts on it.

Concept of Momentum

• Momentum relates to the difficulty in stopping moving objects, which depend on both mass and velocity.
• Linear momentum (p) describes the product of mass (m) and velocity (v): p = mv.
• Momentum is measured in kg ms⁻¹ and it is a vector quantity and its direction follows the velocity vector.
• Momentum changes occur from changes in magnitude or direction.

Second Law of Motion

• A body moving at constant velocity has constant momentum.
• Rate of change of momentum of a body is directly proportional to the net force acting on the body.
• Momentum change occurs in the direction of the force.
• F = k (Δp/Δt), where k is a constant of proportionality.
• Expressing momentum as the product of mass and velocity: F = k m (Δv/Δt) = k m a.
• In SI units where m = 1 kg, a = 1 m/s², the magnitude of force is one unit; k = 1.
• F = m a, where force = 1 kg × 1 ms⁻² = 1 newton.
• Newton (N) is which will produce an acceleration of 1 ms⁻² in a mass of 1 kg.

Forces in Pairs

• When two bodies interact, they exert force on each other.
• One force is defined as 'action,' and the other as 'reaction'.
• Forces always exist in pairs.

Third Law of Motion

• Newton formulated the third law of motion: To every action, there is an equal and opposite reaction.
• Action and reaction mean force.
• Action and reaction forces act on different bodies.
• The action and reaction in a given situation appear as a pair of forces.
• When two objects interact, force exerted by one object on the other equals in magnitude and is opposite in direction to force exerted by the latter object on the former.
• Vectorially, F12 = -F21.

Impulse

• Is the effect of force applied for a short duration.
• Impulse is the product of force (F) and the the time duration (Δt) for which the force is applied i.e., Impulse = F.Δt
• Impulse = Δp, that is, impulse equals change in linear momentum.
• Impulse is a vector quantity; measured in kgms⁻¹ (or N s).

Conservation of Momentum

• If two bodies interact, the vector sum of their momenta remains unchanged if the mutual interaction forces are the only forces acting.
• A system is a number of bodies interacting with each other.
• An isolated system describes the bodies in a system do not interact with bodies outside the system.
• The law of conservation of momentum exists that in an isolated system, the vector sum of the momenta of bodies remains constant.
• The total momentum of the bodies in an isolated system remains unchanged, momentum of individual bodies may change.
• Changes in momentum of individual bodies in an isolated system due to mutual interactions/strengths.
• Conservation of linear momentum applies to collisions, explosions, nuclear reactions and radioactive decay etc.

Newton’s Law consequence

• Change in momentum Δp of a body when a force F acts on it for time Δt is: Δp = F Δt
• Implies that if no force acts on body, its momentum remains unchanged as the change in momentum of the body will be zero.

Illustrations

• Recoil of a gun has the velocity v₂ of the recoil of the gun found using the law of conservation of momentum.
• Collision describes the colliding bodies as a system.
• In the absence of any external force on such system, this system can be described as an isolated system.

Equilibrium of Concurrent Forces

• Concurrent forces describes a number of forces acting simultaneously at a point.
• With concurrent forces, they are said to be in equilibrium if the resultant is zero.

Friction

• A ball rolling along the ground stops because the momentum of the ball tends to be zero.
• Frictional force causes this change in its momentum.
• Frictional force exists whenever bodies tend to move in contact with each other.
• Overcoming the force of friction occurs when pushing or pulling a body along the floor to change its position.
• Friction is a contact force and its opposite to the direction of the body’s motion.
• Friction results from roughness of the surfaces in contact.
• Efforts can be made to make surfaces rough or smooth based on what is needed.
• Friction opposes the motion of objects, causes wear and tear and is responsible for loss of mechanical energy.
• Friction plays a dual role that allows us to walk, drive vehicles and stops moving vehicles; it is a necessary evil.

Static vs Kinetic Friction

• Static friction: a minimum force is required to move an object over a surface.
• With static friction as external force Fext. is applied to the block, initially the block does not move if some other force is acting on block.
• Force of static friction is represented by symbol fs.
• As Fext. increases, fs also increases until it reaches a critical value fmax.
• Kinetic friction: When Fext. is further increased, block starts to slide, faces kinetic friction.
• The force needed to set an object in motion is larger than needed to keep it moving at a constant velocity.
• Maximum value of static friction fmax between a pair of surfaces in contact is larger than the force of kinetic friction fk between them.
• fmax is directly proportional to the normal force FN i.e. fmax α FN.
• Coefficient of static friction, μs.
• Normal force FN on the block will be mg i.e. where m = mass of the block.
• Maximum force of static friction between a pair of surfaces is independent of the area of contact.
• fk = μkFN, where μk is the coefficient of kinetic friction; generally, μs > μk.
• μs/μk are not really constants for any pair of surfaces.

Rolling Friction

• Pushing/pulling objects on wheels is easier; rolling motion.
• Rolling friction the the friction in the case of rolling motion.
• Rolling friction is smaller than sliding friction for same normal force.
• steel wheels on steel rails, rolling friction ≈ 1/100th of sliding friction
• coefficient of rolling friction μr ≈ 0.006 for steel on steel and 0.02 – 0.04 for rubber on concrete

Methods of Reducing Friction

• Wheel is considered to be greatest invention of mankind for simple reason rolling is easier than sliding.
• Ball bearings are used in machines to reduce friction; placed between two co-axial cylinders.
• Rotation of the balls is almost frictionless.
• Applications of ball-bearings are found in all types of vehicles and in electric motors e.g. electric fans.
• Lubricants reduce friction by Use of grease or oil between the surfaces in contact.
• The presence of lubricants changes nature of friction from dry friction to fluid friction, which is smaller than the former.
• Fluid friction depends on the shape of the bodies.
• Give Stream-line shapes.
• Fluid friction increses rapdily with speed.

Free Body Diagram Technique

• It becomes easier by use for application of Newton's laws to solve problems in mechanics.
• Free body diagram (FBD) shows all forces acting on a body in a given situation.
  • Draw a simple neat diagram.
  • Isolate the object of interest as the free body.
  • Mark all the external forces acting on the free body via arrows.
  • Apply Newton’s second law ΣF = ma (or ΣFx = ma and ΣFy = ma) to get the acceleration of gravity.