Connected Particles

This section is all about force (force = mass x acceleration)

Equilibrium of a particle under concurrent forces, including friction.

Mass is the amount of matter in a body,

Momentum is a measure of the unstoppableness of a body (pmomentum = mv)

Acceleration is the rate of change in the velocity and is described by 3 equations.

You need to know about acceleration before knowing much about forces, it is the controlling variable for moving force.

Acceleration and force as vectors.

Motion in a straight line under uniform acceleration

more on Forces here

Newton's First Law (also known as the Law of Inertia) states that an object at rest tends to stay at rest and that an object in uniform motion tends to stay in uniform motion unless acted upon by a net external force.

Thats all fine and good for a definition but what does it mean?

  1. Something that is not moving will only begin moving if a force is applied to it.
  2. Something that is moving will only change its velocity (and stop) if a force stops it.
\vec{F}
\vec{p}

Newton's Second Law states that an applied force, , on an object equals the rate of change of its momentum, , with timeThis means that

F = mv - mu / t

F = m x (v-u)/t

F = ma

In S.I. Units they declared the Newton to be the force required to accelerate a 1kg mass by 1ms-2, this makes our lives very convenient because now we can write,

the Net Force on an object is all the various force vectors (we will see more of these later) added up.

Q3) A car is moving at a constant velocity of 20 m/s. How much net force is required to raise its velocity to 50 m/s in 30 seconds? Suppose the car has a mass of 150 kg.

Newton's Third Law states that for every action there is an equal and opposite reaction

Guns recoil back after launching a projectile (bullet), a book sitting on a table has a weight down and the table stops it from falling with a force equal in size but opposite in direction to the weight (i.e. upwards). Therefore the net force on the book is zero, which means the book does not fall.

Look at the diagram on the left, the mass of 2kg hangs by a very thin and light string. You agree there is a force downward caused by gravity. As we know W = mg. If there is a force on an object why does it not fall (move), Newton says so in his 1st law !?!?!

Okay if there is no motion it must due to another force being equal in magnitude to the weight. In order for the Net force to combine to be zero, the direction of this other force must oppose the direction of the first force.

This Force due to the string is known as Tension. These strings support weights up as far as their tensile breaking point, they can support any weight up to this point, but the Tension force is ONLY capable of supporting the weight and no more therefore

T = W

This leads us to reconsider many things .... a book resting on a table, it has weight, so why does this not fall ??

Reaction or Normal force

We call this force the Resultant, this acts like the tension force in the previous example. Anything resting on another object has a Resultant force R counteracting the objects Weight, W, thereforeR = W

This Resultant force only holds if the combination of forces that hold the table together hold, beyond this and the table no longer supports W,

this is the idea of a limit. So as long as W < Rmax

R = W

The resultant acts at right angles to the surface. Weight always acts down. If we have a sloped surface then R = W sin/cos ...