PHY2053: Chapter 4: Forces and Newton's Laws of Motion

1 pound =

0.454 kg

We know that 1 lb corresponds to?

0.454 kg meaning that the wight of a mass of 0.454 kg is 1 lb

Unit of Force

1 Newton = 1kg x m/s^2 1 Newton = 0.2248 lb

Problem solving strategy: Objects in Equilibrium

1. Draw sketch showing all dimensions & angles 2. Identify object in equilibrium 3. Draw free body diagram for each object 4. Choose coordinate system and represent each force by its components

Net Force

R = F1 + F2 •R = resultant/net force •F1 and F2 are components

As for other vector quantities, the magnitude and direction of the force can be found from?

R = sqrt (Rx^2 + Ry^2) tan theta = Ry/Rx

Weight

Force exerted on an object by gravitation

SI system for force

1N = 1 kg * 1m/s^2

Any force can be presented by?

3 components •Here we will consider only 2 dimensions, the x and y component do not have to be horizontal and vertical but they should be perpendicular to each other

Inertial frame of reference

A frame of reference in which Newton's first law is working

Force causes?

Acceleration

Newton's third law holds regardless of?

Acceleration. •when two objects interact, they exert the same force on each other, equal in magnitude and opposite in direction •acceleration of each of two objects will be determined by respective mass

Any force can?

Act on an object ex: the weight of the object is not constant, it depends on where the object is

The two forces in an action-reaction pair never?

Act on the same object

If Newton's first law is obeyed in one particular frame of reference, it is?

Also valid in every other reference frame that moves with constant velocity relative to the first

By definition, the normal and frictional forces are?

Always perpendicular to each other

Tension

An object (rope) that has pulling forces applied at its ends •magnitude of force acting at that point

Gravitational forces are always?

Attractive •gravitational forces between two objects always obey Newton's third law

Mass

Characterized the inertial properties of an object ex: object's tendency to keep it velocity constant

Friction Force

Component of force parallel to the surface

A constant force causes a?

Constant acceleration

Mass is a?

Constant, intrinsic property of an object, it doesn't change depending on location

You apply a constant force on a hockey puck which accelerates in a straight line. Your opponent applies an equally strong force on the puck but of the opposite direction. In effect, the puck will?

Continue to move with constant velocity

Acceleration of an object is?

Directly proportional to the force acting on it

Doubling the force

Doubles the acceleration

Newton's First Law

Every object continues either at rest or in constant motion in a straight line, unless it is forced to change that state by forces acting on it •When no force acts on an object, or when the vector sum of all forces is zero, the object either remains at rest or moves with constant velocity (no acceleration)

Gravitation

Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them

The effect of simultaneous actions of Fx and Fy is the same as the effect of?

F

Newton's second law

F = ma

When the same force is acted on two different masses then

F1 = F2 and therefore m1a1 = m2a2

Newton's third law can be expressed as?

Faonb = -Fbona

Inertial mass

For a given object, the ratio of the magnitude of force to the magnitude of acceleration is constant and is called the inertial mass or simply the mass of an object

Halving the force

Halves the acceleration

Coefficient of rolling friction

In a wheeled vehicle, this is the ratio of the horizontal force needed for a constant speed on a flat horizontal surface to the upward normal force due to the vehicle's weight

The maximum static friction, fsmax, increases with?

Increasing weight of the object, i.e. with the normal force n •proportionality coefficient is called the coefficient of static friction

Newton's second law is valid only in?

Inertial frames of reference •The earth is considered a good approximation of an inertial frame in spite of its rotation and orbital motion

Mass is an?

Intrinsic property of an object wherever the object is •scalar, it does not have a direction

The mass is?

Inversely proportional to the acceleration

The weight of an object is determined by?

Its mass. •these two quantities are interrelated through the acceleration due to gravity

Less force is needed to?

Keep an object sliding with constant speed then to start it moving

For an object moving in a plane, each component of the total force equals?

Mass times the corresponding component of acceleration: •Fx = max •Fy = may

Any force can be?

Replaced by its components, acting at the same point

For two objects to be an action-reaction pair they must

Represent mutual interaction between objects •the forces forming an action-reaction pair should determine and be determined by each other

Superposition of forces

The effect of any number of forces exerted on an object of the resultant of all forces (vector sum)

Weight

The gravitational pull exerted by the earth on an object

When vector R (net force)= sum of Vector F = 0

The object is in equilibrium

When R = sum of F = 0

The object is in equilibrium •this definition is sufficient only if the object can be treated as a particle

The vector sum (resultant) of all forces acting on an object equals?

The object's mass times its acceleration •acceleration has the same direction as the resultant force

Coefficient of kinetic friction

The ratio of Fk/n •when the magnitude of kinetic-friction force is roughly proportional to the magnitude n of the normal force

Dynamics

The relationship between motion and force

The interaction between any two objects having spherical symmetric distribution of mass is?

The same as though all the mass of each were concentrated at its center •this means that gravitational interactions can be modeled by replacing the spherical objects with particles at their center with the same mass

Inertia

The tendency of an object to remain in rest or to keep moving once it is set in motion

The magnitude of the coefficient of kinetic friction depends on?

The two materials and the quality of contact surfaces

friction forces can also depend on?

The velocity of the object relative to the surface

The principles of dynamics are described by?

Three laws known as Newton's laws of motion •they cannot be deduce from or proved by any other principles

Force is always a?

Vector quantity

If the sum of vector F =0 then?

Vector v = constant and a=0

Force is a?

Vector, it has a certain direction

Contact Force

When a force involves direct contact between two objects

Tension

When a rope is attached to an object and pulled

static friction force

When an object is at rest, the associated friction force is called the static friction force

Kinetic-friction force

When an object is sliding on a surface, the associated friction forces are called kinetic-friction force •direction is always opposite to the direction of motion of the object

Normal Force

When an object rests on a surface there is a component of force perpendicular (normal) to the surface

The normal force and the friction force

When an object rests/slides on a surface, the contact force exerted by the surface on the object can be presented by two components, perpendicular and parallel to the surface

Newton's third law

Whenever two objects interact, the two forces they exert on each other are equal in magnitude and opposite in direction

When two objects interact by direct contact, the interaction forms are called?

contact forces •normal and friction forces are both contact forces

At or near the earth's surface, all objects develop what acceleration?

g = 9.8 m/s^2

For any given pair of surfaces, usually?

mu k < mu s •as a result, when sliding starts, the friction force decreases

Fsmax =?

mu(s) n Fs <= mu(s)n •the equality sign holds when the applied force parallel to the surface has reached the critical value at which motion starts

If a rope is in equilibrium

the tension is the same at both ends throughout the rope

Weight

the total gravitational force exerted on the object by all other objects in the universe

The magnitude of kinetic-friction force increases with?

the weight of the object or with the magnitude n of the normal force

Mass of 1 kg

w = 1kg * 9.8 m/s^2 = 9.8 kg * m/s^2 = 9.8N

Weight =

w = mg •acceleration is a vector

Equilibrium of a Particle

•An object is in equilibrium when it is at rest or moves with constant velocity •the vector sum of all forces acting on an object in equilibrium is zero, and therefore the acceleration is zero

Issac Newton

•One of the most influential scientists in human history •Considered father of modern science •Discovered universal gravitation and laws of motion •Invented reflection telescope and developed theory of color •Developed differential and integral analysis (calculus)

Force

•Push or pull on an object •Interaction between two objects or between an object and its environment •Vector quantity with magnitude and direction •whatever can cause an object with mass to accelerate

Fg = G (mme/ r^2)

•This is only correct provided r is larger than the earth's radius •for objects closer to the earth's center than the earth's radius, the gravitational force decreases because the earth's mass above the object exerts gravitational force to the opposite direction

Free body diagrams

•used to identify forces acting on an object