Ch. 4: Dynamics: Newton's Laws of Motion
Reading
College Physics, Ch. 4
AP Classroom: Unit 2 "Dynamics"
Topics
Labs/projects
College Physics, Ch. 4
AP Classroom: Unit 2 "Dynamics"
Topics
- Newton's three laws of motion
- Solve a variety of problems using mainly the 2nd law: F = ma
Labs/projects
- Newton's 2nd Law lab
- I-35 Bridge Collapse class presentations
Laws of Motion
The Greeks explained motion by saying 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 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.
The Greeks explained motion by saying 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 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."
Newton's 2nd Law: "The acceleration of a body is directly proportional to force and inversely proportional to the mass of the body."
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)".
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 2nd Law" lab
Bring the student handout to lab.
Bring the student handout to lab.
| Newtons_2nd_law_lab__STUDENT HANDOUT |
| 4._newtons_2nd_lab_lab__f_ma__lecture_notes.docx |
| 4._newtons_2nd_law_lab_report_-__STUDENT EXEMPLAR.pdf |
I-35 Bridge Disaster class presentation
| I-35_bridge_collapse_class presentation instructions.docx |
| I-35 Bridge Disaster slides |
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