2.+Read+-+The+Physics+of+RC

=Read -- The Physics of Roller Coasters (15 min)=

Have you wondered how a roller coaster works? Do you realise that while you are able to cruise down the track at 100 km/h, the roller coaster actually has no engine! The car is pulled to the top of the first hill at the beginning of the ride, but after that the coaster must complete the ride on its own!

How is this possible? Let's take a look at the physics behind the fun....




 * Work & Energy **

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**__Work Done__** When a force acts upon an object to cause a displacement of the object, it is said that **work** was done upon the object. In order for a force to qualify as having done //work// on an object, there must be a displacement in the direction of the force.

** Work done = Force applied x distance moved by object in the direction of the force ==> Unit for work done is Joules or newton-metre.

** In the case above, the waitress is **__NOT__** doing any work as the tray did not move in the direction of the applied force F (which is upwards, while the tray is being moved horizontally perpendicular to F)! = = == = =

= =

In the case above, as the box slides across the floor 3.0 m to the right, the work done by the force is:

=//** Force x distance = F sin 30o x 3.0 = 2.0 sin 30o x 3.0 = 3.0 J
 * //Work done, W

Since the box only move horizontally, only the horizontal component of the force is considered to have done work! **__

Gravitational Potential Energy __**

Gravitational potential energy (G.P.E) is the energy stored in an object as the result of its vertical position or height from the Earth's surface (an arbitrary point of reference). The energy is stored as the result of the gravitational attraction of the Earth for the object. Mathematically,

= Force x distance moved against gravity = weight x height = mass x acceleration due to gravity x height = mass x g x height ** //where g is the acceleration due to gravity// Unit for G.P.E is Joules. All other terms in S.I units.
 * G.P.E = Work done against gravity
 * => G.P.E = mgh **



Observe the roller coaster in the animation above. When the roller coaster decreases in height, the gravitational potential energy (GPE) it posess also decreases and the kinetic energy (KE) increases.



To determine the G.P.E of the boy in the swing at the three positions shown, a **zero height position** must be arbitarily assigned. The easiest way is to assign the ground as the position with zero height. Then the G.P.E of the boy will be mass x g x height above the ground. This point of reference is arbitary. (can be any point convenient for calculation)


 * __ Kinetic Energy __**


 * Kinetic energy ** (K.E) is the energy of motion. An object which has motion - whether it be vertical or horizontal motion - has kinetic energy. The following equation is used to represent the kinetic energy of an object.

Unit for K.E is Joules. All other terms in S.I units. **
 * where m is the mass of the object and v is the speed.

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**__Conservation of Energy__**

//Introduction to Conservation of Energy// media type="youtube" key="haannJ_7w-k" height="385" width="480" media type="custom" key="6103143" width="170" height="136" = =

// Applying Conservation of Energy // media type="youtube" key="BVxEEn3w688" height="385" width="480"

=__Conservation of Energy in a Roller Coaster__= Click here to learn more about conservation of energy in a roller coaster.


 * __ Power __**

The quantity ** work **has to do with a force causing a displacement. Work has nothing to do with the amount of time that this force acts to cause the displacement.

The quantity which has to do with the rate at which a certain amount of work is done is known as the power. Power is the rate at which work is done. Mathematically, it is computed using the following equation.



The standard metric unit of power is the **watt (W)**. As is implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time. Thus, a watt (W) is equivalent to a **//Joule/second (W = J/s).//**

A person is also a machine which has a //power rating//. For example, a rock climber takes an abnormally long time to elevate her body up a few meters along the side of a cliff. On the other hand, a trail hiker (who selects the easier path up the mountain) might elevate her body a few meters in a short amount of time. The two people might do the same amount of work, yet the hiker does the work in considerably less time than the rock climber.The hiker has a greater //** power rating **// than the rock climber.

Also, a powerful machine is both**// strong (big force) //** and //**fast (big velocity).**// A powerful car engine is strong and fast. A //machine// which is strong enough to apply a big force to cause a displacement in a small mount of time (i.e., a big velocity) is a powerful machine as shown in the equation below:

(Power = Force x velocity only if the velocity is uniform)


 * __​ Efficiency __**

According to the //Law of Conservation of Energy//, the total input energy must equal the total output energy.

**Wo = Wi** or **Wo = Ei**


 * where**
 * **Wi is the input work**
 * **Ei is the input energy**
 * **Wo is work output or work done**

But that is true only in an ideal machine. In reality, some of the output energy does not contribute to the output work and is lost to such things as friction and heat. Hence, a major factor in the usefulness of a machine is its efficiency.

The real situation is:

Note: The total output energy in this case included the energy lost (Wo + EL). Thus energy is still conserved (total input energy = total output energy).**
 * Ei = Wo+ EL **
 * where EL is the energy that is lost.

For example, the energy expended in pushing a box up a ramp is greater than the work done against gravity or the potential energy of having the box at a greater height (at the end of the ramp). This is because useful energy is lost due to the **work done against friction of the box** sliding along the ramp surface. Another example is the output work available from a gasoline engine is less than the input energy of the fuel. Much** heat energy is wasted ** and not used in the output. The efficiency of a machine is the output work or energy divided by the input work or energy multiply by 100. Efficiency is usually expressed in percentage (%) thus the need to multiply by 100.


 * Efficiency = (Wo/Wi) x 100 **

You will be surpised to find that the efficiency of an automobile is only around 15%. About 75% of the energy is lost through wasted heat from the engine and another 10% is lost due to internal friction, including losses from tire friction!

Click here to watch a video on efficiency