We take for granted that Carbon atoms in a log of wood just stick together. Whereas Oxygen atoms from the air also stick together. But the air does contain Carbon Dioxide, which is nothing but Carbon and Oxygen combined together. However, you never see Carbon from the wood moving out in large quantities and sticking with the oxygen in the air to spontaneously form Carbon Dioxide gas. Thing about how absurd that would look - anytime you had a log of wood it would keep dissolving into Carbon Dioxide gas! Or the other way - if Carbon Dioxide from the air were to abruptly form lumps of coal which are essentially made of Carbon again, watch out for the next time it rains Carbon! So why do the atoms in a log of wood stick together so cohesively? It turns out nature is composed of various kinds of forces, which determine how objects at various scales interact together. There are four fundamental forces in nature. These are gravity, electromagnetism, strong nuclear, and weak nuclear forces.

# Newton's laws of forces

Newton's laws tell us how motion is 'created' from force. In particular, - force is related to the mass(m) and acceleration (a) of an object as:

Newton's 2nd law
, where acceleration is the change in velocity divided by the time interval. The two videos below do a great job in illustrating the concept of acceleration, as well as measuring acceleration from graphs.

The table below, shows how instantaneous acceleration can be calculated from a moving object, whose position changes in time. Notice that if the velocity is constant, v is the same at all times, which gives a zero acceleration. Since instantaneous velocity is calculated between two successive displacement intervals, there is one less value for velocity. Since instantaneous acceleration is calculated between two successive velocity intervals, there is one less value for acceleration as compared to velocity.

Position, velocity, and acceleration

# The force of gravity

Gravity is the weakest of the four fundamental forces, yet it is the dominant interaction at the macroscopic scale, and is the cause of the formation, shape and trajectory of astronomical objects. The universal law of gravitation shows that objects attract each other proportional to their masses and inversely proportional to the distance squared between them (inverse square law force).​

Gravitational Force

In addition, as mentioned earlier - Newton's 2nd law states that any object of mass m1 with a Force F acting on it, experiences an acceleration a=F/m1. As an exercise, you can put in values for the mass of the Earth and radius of the Earth in SI units to find the aceleration due to gravity, g= F/m1=G ME/rE2 for any object of mass m1 on the surface of the Earth, which turns out to be 9.8m/s2

You might notice that this value of acceleration due to gravity is independent of the object. This leads us to a conundrum. Don't some objects fall faster than others? If you drop a feather vs a ball from the same height, would one fall faster than the other? Check this video to see why it depends on what sort of environment the objects are in:

On an inclined surface, the acceleration due to gravity depends on the angle as shown in the image below. When the angle is 0 degrees, the object does not move, since sin(0)=0 and there is no effective gravitational force. But when the angle is 90 degrees, the object falls down with an acceleration g=9.8m/s2 since sin(90)=1. However, most often there is friction between the moving object and the surface, resulting in a lower acceleration than that due to only gravity acting on the object. This is also the reason many objects moving on a surface eventually slow down after they are given an initial push.

Gravitational force on a sliding surface

# The electromagnetic force

The electromagnetic force is the force between charged particles (electrostatic) and moving charges (magnetic). It is the electromagnetic force that holds atoms, molecules, and ultimately, materials together. Similar to the gravitational force, the electrostatic force is inversely proportional to the square of the distance, between charges (rather than masses). The constant of proportionality k depends on the material in which the charges are.

Electric Force
Coulombs law
Coulombs constant

# The weak and strong nuclear forces

The strong nuclear force is what holds the nucleus together against strong repulsions from all the protons contained within. It is an extremely short range force, that binds protons and neutrons, acting over 10-15m, the size of the nucleus. The strong nuclear force is what gives an atomic bomb its power.

Strong Nuclear Force

You might have heard about recent uncovering of painting forgeries through radiocarbon dating. This is possible through the weak nuclear force. The weak nuclear force is a weak force that binds a neutron together. Because this force is weak, neutrons of unstable atoms spontaneously decay, and an electron is released in the process, known as beta decay, or more generally, radioactive decay. In the example of Carbon, Carbon in the atmosphere is composed of two isotopes: 12C and 14C. 14C contains 6 protons and 8 neutrons, and is radioactive. 14C has a half life of 5730 years, meaning that during this time, half the amount of 14C would have decayed by the process of releasing an electron, and transforming into 14N which has 7 neutrons and 7 protons. Whereas 12C contains 6 protons and 6 neutrons, and is stable. A painting freshly made would have the same ratio of the two isotopes. From the mass of the object, it is possible to estimate how much 14C it had originally (N0). Comparing with the measured amount of 14C from a sample, the age of the sample can be obtained.

Beta Decay

In order to measure the age, we need to know the original amount (N0), and the half life (T1/2=5730 years for14C). From the half life we can obtain the decay constant λ, and obtain the age of the sample, t in the exponential decay.

Half Life
Exponential Decay

# Example Problems

## Additional Resources

Forces

Gravity

Radioactive Decay

# Slides

# Lab Activities