forces and free body diagrams

what are the 4 fundamental forces

• strong force

• electromagnetic force

• weak force

• gravitational force

  (listed by strength)

the fundamental forces in nature are all __

• field forces

• means that an object produces a field

field

• an invisible influence that extends through space

• produced by object (field forces)

second object interacting with first object

• the second object also has a field that interacts with the first field to produce a force between the two objects

• because the newtons 3rd law of motion (the second force is equal to the first force in the opposite direction)

newton’s 3rd law

• objects exert equal and opposite forces on each other

• so, the second object has a field that interacts with the first object to produce a force on it as well

we can only see

• what object do to other objects

• ex.: we see the earth moving around the sun

  • because there is a field that keeps it moving

strong force

• strongest force known in the universe

• in the nuclei of atoms to bind nucleons together

• tight binding of quarks to form neutrons and protons

• binding of protons and neutrons “nucleons” to form nuclei

• very short-range (negligible beyond about 10-15 meters)

• carried (mediated) by gluons

• proton example

proton example of strong force

• protons in the nucleus are all positive and should repel each other, but the strong force binds them together, forming nuclei and atoms

• (+ attracts to - not +).

electromagnetic force

• explains electricity, called the “coulomb force”

• exerted between particles that have charge

• strength varies with the inverse square of distance between the charges

• attractive for like charges and repulsive for opposite charges

• long range force (like gravity)

• carried (mediated) by photons

• 1/100 the strength of strong force

why you can’t put your hand through the door

• its actually mostly space, but appears solid because electrons on outside absorb light and the hand has electrons - repel each other

• electromagnetic force

electromagnetic force example

• it’s the force that holds electrons in atoms - attracted by the nucleus

• not JUST in atoms ??

weak nuclear force

• short-range force only found in the nucleus

• carried (mediated) by W=/- and Z bosons

• 1 millionth as strong as strong force

• produces instability in some nuclei to produce radioactive beta decay

• most atoms don’t break down on their own - there would be no life left on the planet if they did

weak nuclear force example

beta radiation from radioactive materials like carbon-14

Gravitational Force

• by far the weakest force, toughest to study

• strength varies as the inverse square of distance

• as far as we know, only an attractive force, if we consider mass to be positive

  • interaction among all objects in the universe

• called “weight” for an object in the gravitational field of another object -

  • W = mg

• carried (mediated) by gravitons (yet undetected)

• LONG RANGE (like the electromagnetic force)

• G vs g

G vs g

• G is the universal gravitational constant which always has the same value

  • 6.67 × 10(-11)

• g is the gravitational field, which varies with distance from a planet

  • (9.8 m/s/s or 9.8 N/kg near Earth)

in the case of FIELD FORCES that interact at a distance

• newton’s 3rd law - objects exert equal and opposite forces on each other

• so the second object has a field that interacts with the first object to produce a force on it, while the first object has a field that interacts with the second object to produce a force on it also

electromagnetic and weak forces

• may be two manifestations of the same force - called “electroweak force”

before we examine how these forces are exerted on objects, we need to first __

• define systems

system

• an object or group of objects that we choose to examine - perhaps because of their motion

• if several objects move together, we might call that a system

• to see how forces affect the system, these forces need to be external to the system.

newton’s first law of motion

• an object or system of objects will maintain in a constant state of motion unless there is an unbalanced or external force exerted on the object or system

  • INNERTIA

constant state of motion

• means motion doesn’t change.

  • if an object or system is at rest, it stays at rest

  • if it is in motion, it does not change speed or direction

equillibrium

• there are no forces on the object or system, or all the forces balance each other

  • the object will not change its motion

• an object in this state can be at rest or at a moving constant velocity

examining what causes a ball to stop rolling after we et it started rolling across a table

1. define our system as just the ball

2. the forces exerted on the ball are all external forces to our system, so we can apply Newton’s 1st and 2nd laws

3. the forces as the ball rolls off the table:

   1. normal force

   2. gravitational force

   3. friction force

normal force

• occurs at surface of contact between two solid objects

• outward from the surface of contact, perpendicular to surface

  • is a type of of electromagnetic (coulumb) force because these are forces between charged parts of atoms

    • ex.: when you sit on chair, the chair also pushes upward on you

• repulsive forces among outer electrons that resist permeation of their electrostatic field

• in math, normal = perpendicular

friction force

• acts along surface of contact, parallel to surface

• acts on an object or system in the direction OPPOSITE to its relative motion to another object or system

• essentially an electrostatic force

• for solids, perpendicular to normal force and coefficient of friction

• for a solid moving in a fluid, proportional to relative velocity

friction force of an object sliding to the left

• friction force of the desk on the object is to the right, it is trying to sow it down

two types of friction force

• static and kinetic

static friction - mu s

• occurs betwee two stationary surfaces trying to slide against each other

• ex.: a box sitting on ram, not sliding

• static friction is proportionate to the normal force

• f_{s    =} mu_s  N

kinetic friction - mu k

• occurs between two objects that are sliding with respect to each other

• this force depends only weakly on speed

• is primarily proportional to the normal force and the coefficient of inetic friction - mu_k

• f_{k    =} mu_k  N

tension force

• occurs in a cord string, cable, rope, etc.

• acts only away from the object, you can’t push with a rope

• if we do not consider the mass of the string itself, then the tension in each direction is the same

• essentially an electrostatic force between molecules holding the rope together

spring or elastic force

• can push OR pull on an object

• the force (F) is in the opposite direction of the displacement of the string (-) and proportional to the amount of displacement

• F = -kx (Hooke’s Law)

• k is the spring or elastic constant

• the smaller the spring constant, the easier it is to stretch or compress the string

hooke’s law for ideal springs

• spring will stretch in proprtion to the force applied to it

• since F = -kx, the slope is equal to the spring constant of the spring

gravitational force on second object

is toward the center of mass of the first object (ex. earth’s force on you is toward the center of the earth, which we call down).

an apple sitting on earth’s surface

• has a gravitational force on it equal to its wieght, mg.

• but an apple in orbit is kept in orbit by a gravitational force that is less than its weight (mg)

  • the apple has the same mass, but g is less

innertia in orbit

• keeps an object moving, and keeps the gravitational force pulling inward to keep it turning so it moves in a circle

free body diagrams

• used to examine all the external forces being exerted on an object/system

• only includes the forces exerted ON the object, not BY the object

net force

unbalanced

ball rolling across table

• normal force upwards, gravitational force downwards

  • equal, so at equilibrium

• friction force backward

• normal force = weight of ball

• friction force = mu times normal force

box sitting on a tilted ramp held in place by static friction force

• since stationary, must be at equilibrium in all directions

• x is up and down the ramp, y is perp. to the ramp

• in x-direction - static friction force balanced by a component of gravitational force that points in +x direction

• in y-direction, normal force is balanced by a component of the gravitational force that points in the y-direction

• if the friction for e is smaller and allows the box to accelerate don the ramp, the forces are in equilibrium in the y-direction, but not x, so the box will accelerate down the ramp

  • newton’s second law of motion