Lesson 2 - Introduction to Classical Mechanics - Use the Force!

Last lesson, What's the Matter, we introduced the concept of matter and some of its most important characteristics. Some of the definitions and formulas from the last lesson are available below.

• Matter: Anything that has Mass and Volume
  
• Volume: The amount of three-dimensional space a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is used to determine the Density of an object.
  
• Mass: Mass is the amount of material or matter an object is made up of. Ability to resist motion when acted on by a Force due to the quantity of material in the object. Represented by (m) and the unit of measurement is the Gram (g)
  
• Density: Tells us how tightly crammed together matter is. density = mass / volume
  

 

Well if you are reading this then I assume you are ready to learn about the Force. In order to better describe Force and to pay homage to Star Wars, I will offer an example from a relative setting.

You are hanging out in the Millennium Falcon and whatever they use to make artificial gravity has been damaged so that things are floating around in the cabin. In front of you are two floating objects, a blaster helmet and a small droid restraining bolt. You decide in your boredom while the Wookie is repairing the ship to see what would happen if you flick both the bolt and the helmet with your finger in the exact same manner. The bolt flies across the cabin and hits the wall very quickly. However, the blaster helmet takes several minutes to float across to the cabin before it hits the wall. Your finger imparts a force to the bolt and the helmet for only a moment, but the force has a different effect on each object.

The effect of an applied Force on a given mass can be measured. In addition, a Force can be measured by the amount of deflection or distortion it produces in an object that is elastic, such as a spring. Force is typically measured either by a Meter or in comparison to another Force.

Example:

The bathroom scale is a good example of an everyday Force meter. It measures the amount of Force exerted on it in terms of (units of) weight.

Scalars and Vectors

The Mass of an object is a scalar and the unit of measurement is the Gram (g). Scalars are single units of data. In the case of Mass, it has a magnitude which can be measured but has no other quality. Hence, it is a scalar. Force on the other hand is a vector and the unit of measurement is the Newton (N). This is because Force has more than one quality to be measured, magnitude and direction.

If we were to chart Force it would look like a line segment with an arrow, where the line segment length would indicate magnitude, and the arrow would indicate direction.

Question: So what exactly is Force?

Answer: Force is any type of influence that causes a free body to undergo an acceleration.

Displacement

Now that we know about Force, its time to be able to define its type of effects. However, before we can do this we need to learn about the concept of displacement. Displacement is also known as distance. However, there is a slight difference between the two. Displacement is actually the shortest path between two points and thus is always less than or equal to distance. Displacement is a vector quantity because it has magnitude (usually expressed in kilometers) and direction.

Displacement is important because physicists measure work by multiplying the force times the distance over which the force is applied. work = force * displacement

We will return to this formula and concept of work later on.

Speed

One effect a force can have is to change the speed of an object. Speed is the rate (distance & time) at which an object moves relative to some defined reference point of view. The reference frame should be considered stationary (this is relative however). speed = distance / time

Speed is a scalar as it only has magnitude and no other qualities such as direction. The standard unit of speed is meters per second (m/s).

Question: What do you mean the reference point is stationary?

Answer: Lets pretend you are standing on the Earth and watching the movement of the Moon. You measure its speed at a relative stationary point. The point is relative because you are only stationary relative to the Earth, but the Earth is in fact moving as well.

Velocity

Velocity is made up of both magnitude and direction and hence is a vector quantity. The direction can be defined in one or more dimensions. For our purposes currently we will limit the dimensions to three. The formula for Velocity is: Velocity = displacement / time

Acceleration

Acceleration is the rate at which an object changes its velocity. This can occur due to a change in speed, a change in direction, or a change in both. If velocity does not change, then there is no acceleration!

Like velocity it can take place in multiple dimensions and can, but does not have to follow the same direction as the velocity vector. Acceleration magnitude is expressed in meters per second per second. (m/s^2). Acceleration = ∆ Velocity / time

Question: What do you mean per second per second or seconds squared?

Answer: Lets say we have a car that can go from 0 to 60 miles per hour in 5 seconds. A speed of 60 miles per hour is roughly equivalent to 26.8 m/s. Then to calculate the acceleration magnitude: a = 26.8 m/s / 5 s = 5.36 m/s^2