# A-level Physics/Forces and Motion/Dynamics

Dynamics is the study of why objects move, and the effects of forces on moving objects.

## Mass

When you are standing on a bus, and the bus starts very quickly, your body seems to be pushed backward, and if the bus stops suddenly, then your body seems to be pushed forwards. Notice that when the bus turns left, you will seem to be pushed to the right, and when the bus turns right, you will seem to be pushed to the left.

Also consider a full shopping cart. If you try to push it from a stationary position, it will take some effort to get it moving. The same is true if you try to stop it when it is moving at a high speed, or try to turn it left or right.

In both cases, an object with mass is opposing a change in motion. In the first case, it is your body that tries to stay moving as it was before the change. Your body also tries to stay in a straight line when the bus turns, although it appears to be moving to the side. What is really happening is that your body is still moving straight and the bus turns in the opposite direction. The shopping cart exhibits the same behaiviour. When it is stationary, it tries to stay stationary, and when you try to stop it moving, it will try to continue. Your body and the cart both have mass.

From this, we can define a property of mass:

Mass will resist changes in motion.

This says that any object with mass will resist any change in motion. Objects with greater mass will resist change in motion more than objects with less mass. It is like having the shopping cart only half full and finding that it is much easier to change its movement. This is Newton's first law of motion: An object at rest will remain at rest unless acted upon by an outside force. Conversely: An object in motion will remain in motion unless acted upon by an outside force.

In the SI system, the unit of mass is the kilogram (kg).

## Force

We all have an innate understanding of forces. To put quite simply, a force involves a push or a pull. Exerting a force on an object will cause that object to accelerate.

Try pushing your finger against a wall. By doing this, you are said to exert a force on the wall. You will feel the wall 'pushing' back on you. The wall is said to exert a force on you. The force you exert on the wall always equals the force with which the wall exerts on you (Newton's Third Law).* Note that the forces are acting on different bodies. Because the wall is heavy, the force you exert on it does not move the wall noticeably. However, being much lighter, you will be probably be moved by the force that the wall exerts on you. Try it!

A force can be applied to an object in different directions. Force is said to be a vector quantity.

### Force and Acceleration

Exerting a force on an object causes the object to accelerate. The same force applied on objects of different masses causes different accelerations in each object. We observe that a force applied on a light object causes greater acceleration than the same force applied on a heavier object. We also observe that the acceleration of an object is proportional to the force exerted on it.

This is summarized by the formula F = kma, where F=force, k=some constant, m=mass and a=acceleration.

### Defining the Newton

In the SI unit system, force is measured in Newtons. One Newton is the force required to accelerate a mass of 1 kg at $1{\rm {ms^{-2}}}$ . Therefore, we have defined the unit of force in such a way that the value of k in F = kma is 1, thereby reducing the equation to F = ma.

1 N = 100000 dynes = 0.101971621298 kgforce = 0.2248089431 lbforce

1 dyne = 1E-5 Newtons, 1 kgforce=9.80665 Newtons, and 1 lbforce=4.44822161526 Newtons

### Weight

The weight of an object is defined as the gravitational force acting on the object, and is dependent on the mass of the body. Note that the acceleration due to gravity (or acceleration of free-fall, usually denoted by g) is taken as the constant $9.81{\rm {ms^{-2}}}$ for all bodies, although it varies slightly from place to place. The direction of that force (weight) is always toward the center of this planet. We can calculate the weight of an object from its mass by the equation W = mg, where W=weight, m=mass and g=acceleration of free fall. In rough terms, an apple weighs approximately one Newton.

• Newton's third law: For every action, there is an equal and opposite reaction.

## Motion of particles through fluids

Mechanics of particle motion.

There are three forces acting on particles in motion through a fluid;

1) The external force (gravitational or otherwise);

2) The drag force (apparent when there is relative motion between a particle and a fluid);

3) The buoyant force (acting parallel to the external force, but in the opposite direction).

## Density

$Density={\frac {Mass}{Volume}}$ ## Viscosity

Viscosity of a fluid is a measure of its resistance to flow. Objects drag fluid along near its surface. The faster the object moves, the bigger the viscous drag.