Forces and Newton's Laws Notes

Forces

Kinematics: Describes the directions of displacement, velocity vectors, and acceleration vectors.
Dynamics: Explains the physics behind the motion, requiring the concept of force to explain the reason behind object motion.

There are three fundamental forces in nature. All other forces can be explained through these.
Gravitational Force: Discussed in the current chapter.
Strong Nuclear Force: Plays a primary role in the stability of the nucleus of the atom.
Electroweak Force:
- One manifestation is the electromagnetic force that electrically charged particles exert on one another (dealt with in P202).
- The other manifestation is the weak nuclear force, which plays a role in the radioactive disintegration of certain nuclei.
Forces discussed in P201 (except gravitational force) are nonfundamental because they can be explained by fundamental forces.

Right after the Big Bang, the Universe was very hot and dense.
It expanded rapidly, becoming cooler and less dense over time.
The separation of forces occurred at different energy and temperature levels as the universe cooled.

Natural states of motion for any object in the absence of external force:
- State of rest
- Uniform motion in one dimension
An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a net force.
It's not necessary to apply any force to keep an object moving with constant velocity (i.e., same speed in the same direction).
Newton’s 1st Law is also known as Inertia.

To change the state of motion of an object, a force needs to be applied.
Force produces acceleration and changes the state of motion of an object.
F = ma
SI unit of force: Newton (N)
Acceleration is produced when a net force acts on a mass.
The greater the mass of the object, the greater the amount of force needed to accelerate the object.

FORCE: Push or pull; SI Unit: N
INERTIA: Natural tendency of an object to remain at rest or in motion at a constant velocity unless an external force is applied.
MASS: The mass of an object is a quantitative measure of inertia, i.e., how much it resists a change in motion when force is applied. It can also be thought of as the quantity of matter contained in the object; SI Unit: Kg

We must always find the “total force” on an object (also known as “Net force” or “resultant force”), and then find the acceleration.
If the force acts in two dimensions (x and y), we must calculate the total force in the x-direction (\Sigma Fx = max), and then the total force in the y-direction (\Sigma Fy = may), and finally add them vectorially to find the net force (\vec{F} = m \vec{a}).
F{x, net} = \Sigma Fx = ma_x
F{y, net} = \Sigma Fy = ma_y
Magnitude and direction of total/net/resultant force:
F^2 = Fx^2 + Fy^2
tan(\theta) = \frac{Fy}{Fx}
Similarly, if we are asked to find the acceleration in two-dimensional motion, we need to find the accelerations in x and y directions separately and then add them vectorially.

Every particle in the universe exerts an attractive force on every other particle (Newton's Law of Universal Gravitation).
The force of gravity between two objects gets weaker as the objects move further away from each other and falls as 1/r^2
F = G\frac{m1 m2}{r^2}, where G is the universal gravitational constant.
The gravitational force due to Earth on an object always acts towards the center of the Earth, i.e., perpendicular to sea level and downwards.
On Earth, gravity/gravitational force causes a downward acceleration of g = 9.8 m/s^2

The weight of an object exists because of the gravitational pull of the earth.
The weight of an object on or above the Earth is the gravitational force that the Earth exerts on the object.
The weight of an object decreases as it gets farther from the Earth. The distance from the center of the earth to the object is r.
W = Fg = G\frac{M{earth} m_{object}}{r^2}
SI Unit of Weight: Newton (N)
Very close to the surface of Earth, r = R. Hence:
W = Fg = G\frac{M{earth} m{object}}{R{earth}^2}
W = m_{object} g