10/14/15 Oregon State University PH 211, Class #8 1

In this course so far, we’ve been learning how to mathematically describe motion. Why?

Because physics is about the universe, where every object apparently has some kind of motion.

Q: How much motion is there in the universe?

To even begin to answer this, we need to make some assumptions and definitions….

10/14/15 Oregon State University PH 211, Class #8 2

The Motion of Real Objects

Up to now, we’ve been learning how to describe the motion of objects—any objects—without much regard to what it takes to get those objects moving in the first place.

Some objects are much more difficult to get moving than others. And then once they’re moving, they’re harder to stop—and harder to turn. That is, you can change the motion of some objects more easily than others:

A rowboat vs. a cruise shipA shotput vs. a softballA pencil vs. a space ship

So does a moving car “have more motion” than a moving skateboard?

10/14/15 Oregon State University PH 211, Class #8 3

Mass: the Inertia of Real Objects

What’s the everyday definition of inertia?

Why do we speak of the inertia of matter? What is it about matter that’s hard to change? Its motion.

Some objects have more of this tendency to resist a change of motion than do other objects. We call this property mass. It is a fundamental dimension (like length and time).

Mass is the measure of an object’s resistance to changing its motion. The more massive the object, the more difficult it is to change its motion. (Q: Is mass a scalar quantity or a vector?)

10/14/15 Oregon State University PH 211, Class #8 4

Units of Mass

The SI unit of mass is the kilogram (kg). This is not a unit of weight

—everyday language is incorrect. Gravitational force happens to

make weight proportional to mass—so, as long as we’re all using the

same planet to measure by, we let weight be a placeholder—an

indicator of mass. But mass is not weight. The same 1 kg melon

that will stretch a hanging spring by 6 cm here on earth will stretch it

by just 1 cm on the moon. But it’s just as difficult to change the

motion of that melon on the moon—or in deep space—as on earth.

Mass is intrinsic to matter. Weight is not. Unless you can create or

destroy matter (ever tried it?), you can’t create or destroy mass. You

can concentrate it or spread it out, but that doesn’t change how much

of it there is. And mass is fundamentally linked to our measure of

motion in the universe….

10/14/15 Oregon State University PH 211, Class #8 5

A thought experiment….

On a level, frictionless table, we’re going to place cart with a remote-control electric fan attached. When the fan spins, it propels the cart across the table—either direction (we can turn the fan around).

We have several such cart-fan sets—all identical—so we have the option to “load” up the original cart with the others (and the extras just ride along as cargo—not using their fans).

Using various “cartloads,” we’re going to do some motion sensor readings (using the same equipment you use in lab)—each trial allowing the cart’s fan to spin for a specific amount of time.

10/14/15 Oregon State University PH 211, Class #8 6

In each trial, the fan blew for 5 seconds (either forward or backward).

1 cart: vi = 1.7 m/s vf = –0.7 m/s (backward fan)

2 carts: vi = 0.3 m/s vf = 1.5 m/s (forward fan)

3 carts: vi = –0.6 m/s vf = 0.2 m/s (forward fan)

4 carts: vi = –0.3 m/s vf = –0.9 m/s (backward fan)

We did the same action (the same fan blew for the same amount of time) in each case. So, is the universe just random —or is there something consistent about all the above results?

Q: What is “the same” about each trial outcome above?

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Mass and Velocity: A Combined Property

Look at those four examples (previous page). The same action apparently does four different things.

Or does it?

Sure, if you look only at the velocity of an object, you could say that. But if you consider the object’s mass, too, look what is revealed.…

The same action consistently gives the same result, if we measure that result using the product of mass and velocity: mv

We call this property momentum—and in the case of straight-line motion, it’s called linear momentum.

10/14/15 Oregon State University PH 211, Class #8 8

Momentum: The Persistence of Motion in Mass

The symbol for momentum is not m, since that’s needed for mass. Instead we use a p, which arose originally because a moving object’s inertia could also be described as persistence: it tends to want to keep on doing whatever it’s now doing.

Q: Is the linear momentum of an object (p = mv)a vector or scalar quantity?

A:

10/14/15 Oregon State University PH 211, Class #8 9

A Fundamental Consistency in the Universe:The Conservation of Linear Momentum

Linear momentum (p = mv) is a property of all matter —every object (anything with mass) in the universe.

And so far as we have observed: The total quantity of this property in the universe is constant. In other words, it cannot be either created or destroyed. It can only be transferred between objects.

Use a helpful analogy: Money (cash currency). Suppose that nobody knows how to make it or destroy it. We just pass it around—via transactions. So, not only does the whole world have a fixed amount of currency, so does any roomful of people within that world—as long as nobody leaves or enters the room.

10/14/15 Oregon State University PH 211, Class #8 10

Exchanges of Linear Momentum

So within any closed room, the total amount of cash doesn’t change, but of course that doesn’t prevent various persons within the room from gaining or losing cash—by taking it from or giving it to, others in the room.

If you take it from another, that person loses exactly what you gain. If you give it to another, that person gains exactly what you lose.

So it is with linear momentum (p): Since we can’t create or destroy it, when two objects interact (make a “transaction”), the amount of p (i.e. the amount of mv) gained by one object is lost by the other.

Let’s look at some common “transactions”….

10/14/15 Oregon State University PH 211, Class #8 11

Explosions and Collisions

An explosion results when internal parts of an object—or a system (collection) of objects interact in ways that separate the parts. But if we analyze the total momentum of all the resulting parts, that total is exactly the same as the total momentum of the original object(s).So long as the transactions were all internal (“within the room”), there’s no change in the overall total vector sum of momentum:

P = Pf – Pi = 0 In other words: Pi = Pf

That is: Pi.x = Pf.x and Pi.y = Pf.y

Collisions result from two or more objects coming together —sometimes staying together, sometimes not. But again, if all the transactions happen “within the room” (the space whose borders are not crossed by other transactions with the outside), then again, there is no change in the system’s overall momentum, P.

Two ice skaters, with masses of 50 kg and 75 kg are at the center of a 60-meter diameter circular ice rink.

The skaters then push off against each other and glide to opposite edges of the rink. If the heavier skater reaches the edge in 20 sec, how long does the lighter skater take to reach the edge?

10/14/15 12Oregon State University PH 211, Class #8