**Unit 4: Dynamics****:** Newton's Laws of Motion

**Unit 4: Dynamics**

__Reading (weeks 7 & 8)__

BJU book: Ch. 6 "Dynamics"

AP students additional reading: Princeton Review "Newton's Laws" - read applicable sections

__Topics__

- Newton's three laws of motion
- Solve a variety of problems using mainly his 2nd law: F=ma

__Lab__

Newton's Second Law lab. See instructions below.

Below: Roller coaster illustrates "Newtonian mechanics" better than anything

__Laws of Motion__

The

**Greeks**held that objects seek to be "at rest" in their "natural place". That's why rolling rocks eventually slowed down and stopped, and why an arrow stopped moving upward in the air and came back down to earth. The "natural place" of the rock and the arrow was at rest, on the ground. For objects that seek to be in water (liquids or dissolved substances) or in the air (steam or smoke), then water and air was their "natural place" of rest. This view pretty much explained the motion of everything. A heavy rock falls faster than a feather, because it 'more vigorously' wants to return to its place of rest. Using this reasoning, a heavy rock should therefore fall faster than a light rock; and a rock falls downward through water because, after all, it's just trying to return to its natural place - the earth.

Amazingly, this view held sway for 2,000 years, from

**Aristotle**until the time of Galileo in the 1500's. One reason for this is that we simply didn't have clocks which could measure small time intervals with precision and accuracy.

**Galileo**conducted motion experiments using ramps and dripping water as a timing device. A ramp with a groove cut in it slows down the rolling bronze sphere just enough so that consistent measurements can be made; then basic trigonometry can used to back out the forces and acceleration of the object.

In this way, Galileo developed the idea of

__Inertia__; an object will

__continue in its straight-line motion__until some outside force acts upon it! That 'outside force' could be gravity, or friction, or wind, or gunpowder, or the arm or bow-and-arrow of a person launching it. So there was no longer any need to think of an object 'seeking to return' to its natural place and ceasing motion.

**Isaac Newton**was born, as people are fond of pointing out, in the same year Galileo died. Newton built upon the work of Galileo, as well as Tycho Brahe and Johannes Kepler, who had by this time (1600's) spent much time & effort studying the motion of the planets and working out the laws of celestial mechanics (basically how the solar system operates).

4._newtons_laws_of_motion_-_class_notes.docx |

__Lecture outline:__

Newton's 1st Law: "Every body continues in a state of rest, or of uniform motion in a straight line, unless acted upon by outside forces."

- An object just stays in its present state until acted upon by an outside force.
- This seems obvious to us; but it was revolutionary in the 1600's for the reasons given in the section above
- You can see this is just a restatement of Galileo's idea of Inertia. No force = No acceleration. No force = No change in direction or velocity.
- The hurdle in the 1600's was that people had to accept the
__existence of forces they couldn't see__.... gravity, magnetism, friction, etc. This was difficult for them!

Newton's 2nd Law: "The acceleration of a body is directly proportional to force and inversely proportional to the mass of the body."

- Written as an equation, this is simply
**F=ma**(Force = mass X acceleration) - Newton had to invent the concepts of mass and "inertia". The "force" has to push on "something", after all.
- If you're willing to accept the 2nd Law, then you don't need the 1st Law. The 1st Law is simply the 'special case' where the force is zero (F=0). The 2nd Law is the "general case".

Newton's 3rd Law: "Whenever one body (a horse) exerts a force on a second body (a cart), the second body exerts an equal and opposite force on the first body (i.e. the cart also pulls on the horse)".

- Forces always come in pairs. Forces do not exist in isolation.
- The 3rd Law is called "The law of interaction" or "The law of action and interaction"
- Think: If the horse and cart were standing on ice, the cart wouldn't move no matter how much struggling the horse did. But since there is friction between the earth and the horse's hooves, the cart moves forward. In essence, the cart pulls the earth backward through the horse's efforts (but it's too small to measure the effect on the earth, of course).

Friction:

- Friction is the 'normal' force multiplied by the coefficient of friction.
- 'Normal' in Physics means "perpendicular".

__"Newton's Second Law" lab__

Basic instructions: Set up a track at different angles. Accelerate the cart up the track using a known weight suspended from a string running through one or more pulleys (depends on how elaborate we want to get). Use a stopwatch to measure the time required. Compute the cart's acceleration using Big Five equation #4 (delta-x = v1t + 1/2at2). Use trigonometry (SOH-CAH-TOA) together with Newton's 2nd law to compare the observed acceleration to the predicted acceleration. Discuss the results.

We will also perform experiments on "friction", by sliding an object (a book or block of wood) across a surface, with and without weights.

Your lab report must contain all 5 of these elements:

We will also perform experiments on "friction", by sliding an object (a book or block of wood) across a surface, with and without weights.

Your lab report must contain all 5 of these elements:

- Carefully sketch all three track 'scenarios' and label all components, including track angle, length, mass of cart, mass of weight, etc.
- Calculate the cart's 'predicted/theoretical' acceleration up each of the 3 tracks, using F=ma and the requisite trigonometry.
- Then calculate the 'measured/observed' acceleration for each of the 3 tracks, using the correct Big Five equation and the requisite trigonometry.
- Compare the 'predicted/theoretical' value to the 'measured/observed' values for each scenario. Compute the % error for all 3 scenarios.
- Discuss the results. Why are your measured results so far off? ....or, why are they close? What are the sources of error in this lab? How could you improve the experiment to get better results?

__Newtons Laws homework problems__

4._newtons_laws_problems.docx |