Chapter 4 Forces and Newton’s Laws of Motion

Newtonian mechanics Describes motion and interaction of objects Applicable for speeds much slower than the speed of light Applicable on scales much greater than the atomic scale Applicable for inertial reference frames – frames that don’t accelerate themselves Sir Isaac Newton (1643 – 1727)

Force What is a force? Colloquial understanding of a force – a push or a pull Forces can have different nature Forces are vectors Several forces can act on a single object at a time – they will add as vectors

Force superposition Forces applied to the same object are adding as vectors – superposition The net force – a vector sum of all the forces applied to the same object

Newton’s First Law If the net force on the body is zero, the body’s acceleration is zero

Newton’s Second Law If the net force on the body is not zero, the body’s acceleration is not zero Acceleration of the body is directly proportional to the net force on the body The coefficient of proportionality is equal to the mass (the amount of substance) of the object

Newton’s Second Law SI unit of force kg*m/s 2 = N (Newton) Newton’s Second Law can be applied to all the components separately To solve problems with Newton’s Second Law we need to consider a free-body diagram If the system consists of more than one body, only external forces acting on the system have to be considered Forces acting between the bodies of the system are internal and are not considered

Newton’s Third Law When two bodies interact with each other, they exert forces on each other The forces that interacting bodies exert on each other, are equal in magnitude and opposite in direction

Forces of different origins Gravitational force Normal force Tension force Frictional force (friction) Drag force Spring force

Gravity force Any two (or more) massive bodies attract each other Gravitational force (Newton's law of gravitation) Gravitational constant G = 6.67*10 –11 N*m 2 /kg 2 = 6.67*10 –11 m 3 /(kg*s 2 ) – universal constant

Gravity force at the surface of the Earth g = 9.8 m/s 2

Gravity force at the surface of the Earth The apple is attracted by the Earth According to the Newton’s Third Law, the Earth should be attracted by the apple with the force of the same magnitude

Weight Weight (W) of a body is a force that the body exerts on a support as a result of gravity pull from the Earth Weight at the surface of the Earth: W = mg While the mass of a body is a constant, the weight may change under different circumstances

Tension force A weightless cord (string, rope, etc.) attached to the object can pull the object The force of the pull is tension ( T ) The tension is pointing away from the body

Free-body diagrams

Chapter 4 Problem 54 The steel I-beam in the drawing has a weight of 8.00 kN and is being lifted at a constant velocity. What is the tension in each cable attached to its ends?

Normal force When the body presses against the surface (support), the surface deforms and pushes on the body with a normal force that is perpendicular to the surface The nature of the normal force – reaction of the molecules and atoms to the deformation of material

Normal force The normal force is not always equal to the gravitational force of the object

Free-body diagrams

Chapter 4 Problem 61 The drawing shows box 1 resting on a table, with box 2 resting on top of box 1. A massless rope passes over a massless, frictionless pulley. One end of the rope is connected to box 2, and the other end is connected to box 3. The weights of the three boxes are W 1 = 55 N, W 2 = 35 N, and W 3 = 28 N. Determine the magnitude of the normal force that the table exerts on box 1.

Frictional force Friction ( f ) - resistance to the sliding attempt Direction of friction – opposite to the direction of attempted sliding (along the surface) The origin of friction – bonding between the sliding surfaces (microscopic cold-welding)

Static friction and kinetic friction Moving an object: static friction vs. kinetic

Friction coefficient Experiments show that friction is related to the magnitude of the normal force Coefficient of static friction μ s Coefficient of kinetic friction μ k Values of the friction coefficients depend on the combination of surfaces in contact and their conditions (experimentally determined)

Free-body diagrams

Chapter 4 Problem 117 The three objects in the drawing are connected by strings that pass over massless and friction-free pulleys. The objects move, and the coefficient of kinetic friction between the middle object and the surface of the table is (a) What is the acceleration of the three objects? (b) Find the tension in each of the two strings.