0924

Weekend tasks:

• Redraw your rubber band calibrations in Newtons.  If you don't have your graph assume that it starts at (8 cm, 0 units) and follows a pretty straight line to (10 cm, 5 units); draw the original graph and then draw the graph again with forces in Newtons.

• Master the first 12 problems in Introductory Problem Set 3 (http://vhmthphy > Physics I > Prob Sets > Introductory Problem Sets > Set 3).  Introduction to ideas of work, energy, power is below

Hereabouts, weight is the force of attraction exerted by gravity between the Earth and whatever mass you wanna weigh.

We aren't even gonna use the word 'weight' at this point.  When we mean 'weight of' we're gonna say 'the gravitational force on' or something very similar.  If 'the gravitational force on' doesn't make a lot of sense in the situation you're probably trying to say 'weight' when you should be saying 'mass'.

Mass is what resists acceleration (inertial mass), and what interacts with other mass to create gravitational force (gravitational mass).  Inertial mass and gravitational mass are, for a reason, the same.

Newton's Second Law relates force, mass and acceleration:

• Force = mass * acceleration

If you drop something its acceleration is 9.8 m/s^2.  If you're good enough with a pendulum timer you can verify this.

Mass is an undefined unit in physics, along with distance, time and charge.

The MKS unit of distance is the meter.

The MKS unit of mass is the kilogram.

The MKS unit of time is the second.

The unit of acceleration is the meter / second^2.

(The unit of velocity is the meter / second, but that's not directly related to force).

The unit of mass is the kilogram (abbreviated kg).

The unit of force is whatever you get when you multiply the unit of mass by the units of acceleration. Thus

• The MKS unit of force is the kg * meter / second^2.

We give this force a name.  We call it a Newton.

• A Newton is a kilogram meter / second^2, abbreviated N or kg m / s^2.

A milliliter of water has a mass of 1 gram.

How many units of force does gravity exert on the standard 50-milliliter water chunk you used to calibrate your rubber band?

50 milliliters has a mass of 50 grams.

A kilogram is, as the prefix kilo- should tell you, 1000 grams.

So 50 milliliters has a mass of .050 kg.

If we dropped that 50 milliliter water chunk it would accelerate at 9.8 m/s^2. 

The force exerted by gravity doesn't care whether that chunk is accelerating or not; it's the same either way.

The gravitational force on this mass is therefore

• Force = mass * acceleration = .050 kg * 9.8 m/s^2 = .49 Newtons.

I delivered enough energy in .02 seconds that the cart was able to coast a distance of .8 meters against a frictional resistance estimated to be about 30,000 Newtons.

Definition:  work = force * displacement

Caveat:  In this definition the force and the displacement must be along the same line and in the same direction.  Otherwise we gotta talk in terms of force and displacement components.

How much work did I have to do?

Enough to overcome a 30,000 Newton frictional resistance through a displacement of .8 meters.  So I had to do

• work = 30,000 Newtons * .8 meters = 24,000 Newton meters.

At what average rate was I doing work with respect to clock time?

The average rate is work / change in clock time = 24,000 N m / (.02 s) = 1,200,000 N m / s.

The unit of work is the N m, also called a Joule, abbreviated J.

J = N m = kg m/s^2 * m = kg m^2 / s^2.

The rate at which work is done is called power, which is measured in units of N m / s, or J / s, or (kg m^2 / s^2) / s = kg m^2 / s^3. 

This unit of work is called the watt.