Answers to Idea 2 Study Questions -- 7 Ideas Sec. 005

**1.** As far as we are concerned, "deterministic" means that the behavior of everything in the system is ENTIRELY determined by a certain specific set of rules. The Universe of Newton

is one built on specific laws that, in principle, completely determine how everything moves.

**2.** Speed is how far something goes in a given time, e.g., miles per hour.

**3.** Velocity is two pieces of information: speed and direction. Two cars, both having a speed of 60 mph and going in opposite directions, are an example of two objects with the same speed but different velocities.

**4.** It is a straight line.

**5.** It is also a straight line of course, but twice as steep (with twice the "slope").

**6.** The velocity of something depends on who observes it. For example, in class we had two students walking at the same speed next to each other. Relative to us, both were moving fairly fast. To them, however, they were stationary since they were moving together.

**7.** He had a complex, odd idea about air moving behind the object and pushing it.

**8. ** Newton's first law - if no forces act, object move with uniform (unchanging) velocity. Makes sense.

**9.** When forces are applied objects accelerate (change velocity - either change speed, direction, or both). The amount they accelerate is determined by their mass.

**10.** An inclined plane (a tilted table) allows gravity to accelerate an object but slower than if the object were in free fall. This enabled researchers of old to measure speeds and accelerations using their primitive clocks and instruments.

**11.** Acceleration is any change in velocity. If I twirl an object on a string around my head at constant speed, it is still accelerating because it is constantly changing direction. Forces cause accelerations.

**12.** See 9.

**13.** The third law says that for every force, there is another force equal in magnitude but pointing in the opposite direction. As an example, in a rocket engine all the heat exerts a force on gases and whatnot, causing them to fly out of one end (the exhaust). The third law says that there is therefore another force, just as big, that pushes the other way. It is this force that causes the rocket to fly.

**14. ** The same - the mass of an object does not depend on where it is. The WEIGHT does however, because weight is simply the force of gravity acting on the object and that depends on how massive the planet is. In deep space (with no other objects nearby), there is no gravity and the weight is zero.

**15.** Both fall at the same speed.

**16.** The force of gravity gets bigger as the mass gets bigger. However, according to Newton's second law, the acceleration of an object gets SMALLER as the mass gets bigger. These two factors cancel and all object fall at the same acceleration (in the absence of air resistance and stuff).

**17. ** In liquid or gas, there is a force that is due to the object shoving the liquid aside as it falls. This force (unlike gravity) gets bigger the faster the object goes. Thus at the start of the fall, it is small and only gravity acts. As it goes faster, the force pushing back gets bigger and the net force that pulls down is decreased. Thus at first the object falls with high acceleration, then with less acceleration, then with none (constant velocity - the "terminal" velocity). This confused Aristotle and friends and pushed our understanding of motion back quite a bit.

**18.** Projectile motion is made up of horizontal and vertical motion. Galileo's big insight was that these two kinds of motion occur independently - the vertical motion (due to the force of gravity) does not know that the horizontal motion (due to whatever force threw the object) is occurring. Note that the vertical motion is therefore uniformly accelerated (like all things that are falling) and the horizontal motion is uniform velocity since no force acts horizontally (ignoring air resistance of course).

**19. **See 18 - the horizontal motion continues just as if I had held onto the object (Newton's first law - no force acts so the motion is uniform velocity).

**20. **This is much easier mathematically. In any case, the force depends on the mass of BOTH objects that are pulling on each other - on M1 x M2. the force decreases the greater the distance between the objects - it depends on 1/(r*r).

**21.** Actually this is pretty simple - since the force depends on the product M1 x M2, the force with which object 1 pulls on object 2 is equal to the force with which object 2 pulls on object 1.

**22.** The whole point of an orbit is that the falling object manages to move to the side enough that it keeps missing the object that it is falling towards. Obviously for this to happen it has to have enough horizontal velocity (which is, after all, independent of the uniformly accelerated falling motion) to move to the side far enough to miss the object it is orbiting. Try drawing some pictures where you move the object a little bit over and a little bit down.

**23.** They are not actually weightless like they would be in deep space where there is no gravity. In fact, they are so close to the Earth that the force of gravity is almost the same as it is for us on the surface! What is happening is that they are simply in free-fall (as are all orbiting things). Imagine being on a bathroom scale and getting pushed off a cliff - the scale falls with exactly the same acceleration as you do and so you exert no force on the scale - according to the scale you are weightless!

**24.** We introduced momentum as simply a measure of the "amount of force". We then studied the conservation of momentum (with colliding air carts) where we found that

momentum = mass x velocity.

**25.** In a closed system (no external forces acting on it), the total momentum (sum of all the momenta of each object) is always exactly the same. An example is the collision of two air carts in class with each going with equal velocity in opposite directions - before the collision the total momentum was zero since the masses were equal and the velocities canceled out (opposite directions). After the collision, the total velocity was zero so the momentum was still zero. Now apply the same reasoning to the other collisions of carts we did in class (one moving and the other stationary).

**26.** The reasoning went like this: Since objects fell faster in thinner liquids (remember he made the mistake of studying motion in liquids - see #17), if he removed the liquid altogether (a vacuum), it would fall infinitely fast. Since infinite speed was, to Aristotle, silly, there could be no vacuum. The mistake here is in thinking that objects fall infinitely fast in a vacuum - of course they don't - they all fall with exactly the same finite acceleration.

**27.** Newton did something very cool - he thought up his law of gravitation (see #20) that EXPLAINED Kepler's laws! That is, he now could, from one universal (same across the Cosmos) law explain why objects move in elliptical orbits, why they sweep out equal areas in equal times, and so on.