class 050928

Write down

050928

and your name.

Write down the definition of acceleration.

Write down the four equations of uniformly accelerated motion.

Check units on every equation.

Solve the following:

A car starts up a hill, inclined at a uniform angle with horizontal, with unknown initial velocity.  The magnitude of its acceleration is assumed to be a constant 1.2 m/s^2, and it coasts the first 100 meters in 5 seconds.  What is its initial velocity, and if the hill continues forever how far will the car travel up the hill before coming to rest?

One lesson of rubber bands and dominos:

The more mass we have for the same force, the less the acceleration.  If we have four dominoes as opposed to two, the same pullback gives us less velocity and also takes longer to snap back. 

Less change in velocity in greater time implies less acceleration:  smaller `dv makes `dv / `dt smaller, and greater `dt makes `dv / `dt smaller. 

This is consistent with Newton's Second Law, which says that

• net force = mass * acceleration

or in symbols

• F_net = m a.

It follows that

• a = F_net / m.

Substituting this into the fourth equation of uniformly accelerated motion we get

• vf^2 = v0^2 + 2 (F_net / m) `ds

which we can rearrange to give us

• F_net * `ds = 1/2 m vf^2 - 1/2 m v0^2

If we define kinetic energy (KE) as 1/2 m v^2 and net work as `dW_net this can be written

• `dW_net = `d(KE).

This is the first form we will see of the work-energy theorem.

Where F_net is constant, the region below the F_net vs. `ds curve is just F_net * `ds, consistent with the area-beneath-the-curve procedure we used for finding the energy in the rubber-band 'slingshot'.

See Introductory Problem Set 3 for detailed development of these ideas.