Friday's Physical Law - Work Work Work

As we have previously seen force impacts a lot on motion. Today I want to look at how we apply forces, or rather what allows us to apply forces, and as you may have guess by the title this involves the concept of work.

When we exert a force on an object what we are doing is work on that object. And by work we don't mean what one does 9 to 5 but rather transferring energy. To be precise work W is done on an object when ever and object is moved a distance d parallel to a force F acting on the object

• W = F d cosθ

when F and d are parallel θ = 0 and then cosθ = 1 and the work is maximum when the angle (θ) between F and d is 90° then they are perpendicular and cosθ and hence W = 0.

Well that can all be a little complicated and daunting, but essentially you can think of it in terms of a box, if I push the box across the floor I give it motion and hence energy (by doing work: force across direction across), however if I hold it while walking across the room the box itself is only in motion because I am and as such is not getting any energy from me (so no work done: force up direction across).Of course while I was lifting the box (before I carried it across the room) then I was doing work on it.

So as you an see (hopefully) work is done and energy transferred when giving an object motion or changing its position with respect to gravity. We refer to these forms of energy as kinetic energy and gravitational potential energy, respectively.

So we will now look at these a bit closer. Firstly, kinetic energy occurs when anything has velocity (is moving), and is dependant only on the mass of the object and the velocity it has:

• E = ½mv²

And gravitational potential energy, is a form of potential (or stored) energy which depends on position with a gravitational field, and it depends on height (above ground), the mass of the object, and gravity (on Earth the acceleration due to gravity, g, is about 9.8 at the surface of the Earth, but this will vary for other planets and heights, at this stage I plan to deal with this next week):

• E = mgh

There are many other types of energy that we will get to in the fullness of time, such as the potential energy of a spring, thermal energy (heat), electrical energy, nuclear energy etc, but the important thing to note is that energy can never be created or destroyed only converted (transferred) from one form to another (this incidentally is the first law of thermodynamics).

And when it comes to motion this idea of conservation of energy can simply be put as:

• ½mv²_f + mgh_f = ½mv²_i + mgh_i + W

where the _f indicates the object in a final state and the_i indicates the object in an initial state. And we can see that friction is a case of work acting against the motion of an object, reducing its kinetic energy and creating heat (thermal energy).