Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 10

Dynamics Connection between force and motion The concept of force gives us a quantitative description of the interaction between two bodies or between a body and its environment

Newton’s Laws 1st Law: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration 2nd Law: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. 3rd Law: For every action there is an equal, but opposite reaction

Newton’s law of gravitation

Falling with air resistance

Terminal Velocity with Coffee Filters where is the resistance force. 1.A penny and a quarter dropped from a ladder land at the same time (air resistance is negligible). 2.A coin dropped in a coffee filter from a ladder lands later than a coin without coffee filter (the terminal velocity is smaller for larger cross-section area). 3.A quarter dropped in a coffee filter will land faster than a penny in a coffee filter (the terminal velocity is larger for larger mass) 4.Two identical coins dropped in coffee filters of different diameters land at different times (the terminal velocity is smaller for larger cross-section area).

Resistance force: A – area of the projectile For a spherical projectile in air at STP: Terminal velocity: A 70-kg man with a parachute: v T ~ 5 m/s A 70-kg man without a parachute: v T ~ 70 m/s

Newton’s 1 st Law A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration

Aristotle: a natural state of an object is at rest; a force is necessary to keep an object in motion. It follows from common sense. Galileo: was able to identify a hidden force of friction behind common- sense experiments B.C.

Galileo: If no force is applied to a moving object, it will continue to move with constant speed in a straight line Galilean principle of relativity: Laws of physics (and everything in the Universe) look the same for all observers who move with a constant velocity with respect to each other. Inertial reference frames

Newton’s second law The vector acceleration of an object is in the same direction as the vector force applied to the object and the magnitudes are related by a constant called the mass of the object.

A faulty model rocket moves in the xy-plane (the positive y- direction is vertically upward). The rocket’s acceleration has components a x (t)=  t 2 and a y (t)=  -  t, where  =2.50 m/s 4,  =9.00 m/s 2, and  =1.40 m/s 3. At t=0 the rocket is at the origin and has velocity with and a)Calculate the velocity and position vectors as functions of time. b)What is the maximum height reached by the rocket? c) What is the horizontal displacement of the rocket when it returns to y=0?

First exam Tuesday, September 23, 7 – 8 pm Sections 549, HELD Sections 551, HELD Section HELD

All liquids, gels and aerosols must be in three-ounce or smaller containers. No calculators and cell phones BRING YOUR STUDENT ID!

What is included? Chapters 1-4 Kinematics, vectors

Kinematics

In components:

If is given, you can find and

Vectors

Friendly advice DO NOT…

DO NOT use Const acceleration case formulas when acceleration is a function of time. You have to integrate or differentiate! What are the Const acceleration case formulas?

DO NOT write the vector sign over a projection!

Do Not Forget to Write down what is given and express the answer in terms of what is given Box the answer Indicate the origin and positive x and y

Have a great day! Reading: Chapter 5