Lecture 5. (sections )

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1 Lecture 5 PHYSICS 201 (sections ) Instructor: Hans Schuessler Temporary: Alexandre e Kolomenski o

2 Projectile Motion The horizontal and vertical parts of the motion behave independently This is why vectors with their x and y components is a convenient way of description! We will use the same approach for dynamic problems as well!

3 Ball Dropping Analyze Vertical and Horizontal separately!!! a y = g (downwards) d a x = 0 Constant for Both directions!!! V x =0 V x >0

4 A weird consequence Prove that an object projected horizontally will reach the ground at the same time as an object dropped vertically!

5 Main laws of dynamics: Newton s laws Discovered and formulated several fundamental laws of physics. Created related fields of mathematics. Isaac Newton ( )

6 Chapter 4: Newton s Laws Force First of all what is force? How many forces can act on a body? Is it a scalar or a vector? Mass What is mass? Resistance to the force? Vector or scalar?

7 Before we start What is a Force? Vector quantity, that can initiate a motion. Examples: Push Pull Slap Gravity Others?

8 Examples Example of non-zero net forces? Friction: Causing a moving block to come to rest (Net force causes acceleration in the negative direction) Gravity: making a ball fall Example of zero net force Car just sitting on the pavement No acceleration, must tbe no net tforce Spaceship in outer space Nothing to slow it down constant velocity

9 Newton s First Law A body acted on by a zero net force moves with constant velocity (which may be zero), i.e. it moves with zero acceleration

10 In other words Without a Force there is no change in the state of the motion => an acceleration is zero and the velocity is constant But this holds only in special reference frames (systems of coordinates) : inertial systems (to a good approximation the one related to Earth IS such a system) For instance, in rotating reference systems this statement is not valid Force is a Vector! When several forces, need to add up all the forces (vectors) to find the Net (or total) force.

11 Example: inertial and non inertial frames of reference

12 Newton s Second Law If a net external force acts on a body, the body accelerates. The direction of acceleration is the same as the direction of the net force. The acceleration is directly proportional to the net force and inversely proportional to the mass of the body. a F m

13 In other words... To cause an acceleration (change velocity) requires a Force An alternative formulation of the 2 nd Newton s law: The net force vector is equal to the mass of the object times the acceleration of the object.

14 Mass Mass characterizes inertial properties of an object and for a given object this quantity is a constant.

15 Newton s Second Law Now need to translate English into Math: Net forces cause the velocity to change This is a VECTOR equation Vector F Equation m a : F x ma x, F y ma y Same equation presented in components

16 Reminder: Pulling a tanker Given: T 1 =T 2, D, R, m a-? 2T 1 cos 30 o +D- R =ma m The Law of Gravity

17 Units Mass: 1 kg F=ma, 1 Newton, 1N=1kg 1m/s 1m/s 2 Force: 1 N is the amount of force that gives the acceleration of one meter per second squared to a body with a mass of 1 kilogram.

18 Example: Force to stop a car What constant net force is required to bring a car of mass m to rest from a speed of V within a distance of D? V 0 = V V = 0 X 0 = 0 X F = D

19 Getting to Newton s Third Law How does one apply a force? Applying a force requires another object! A hammer exerts a force on a nail However, the nail acts on the hammer with a reaction force (this is what stops the hammer)!

20 Newton s Third Law Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force (reaction). OR To every action there is an equal and opposite reaction. (counter action)

21 Example Skater pushes on the wall. The wall pushes back, that s why she moves off with some non- zero speed!

22 Weight and normal force (the force component perpendicular to the surface that the surface exerts on an object) Weight: mg Without reaction from supporting surface the object will fall with Acceleration of gravity. Difference: weight and mass weight is a vector, directed toward the center of the Earth, measured in N. Mass is a scalar quantity measured in kg of mass. (weight)

She pushes on the ground and the ground PUSHES her forward (especially when the

23 Examples F Ground on the Person - F Person on the Ground Force exerted by the person on the ground is equal and opposite to the force exerted by the ground on the person. She pushes on the ground and the ground PUSHES her forward (especially when the motion starts!!!). t Also vertical forces: weight reaction from the ground upward. F N W=mg

24 Newton s 3d law is very general: action and reaction via field (gravitational, electric, etc.) also is valid, not only contact forces! The Law of Gravity

25 Analysis of forces: free body diagram Problem: pulling a box mg=100 N Forces Free body diagram: Action of surrounding objects is replaced with the forces they exert. Note: F N is less than mg The Law of Gravity

26 Problem: weight, normal force and a box mg=98.0 N a-? F N -? The Law of Gravity

27 Free body diagram Free body diagram is the main approach to solve dynamics problems, when different objects interact with each other. Action of surrounding objects is replaced with the forces they exert. If there are several interacting objects such a diagram should be drawn for each of them.

28 Free body diagram for a block on a surface with friction F.B.D. Dynamic equations: The Law of Gravity

29 Motion of 2 blocks No friction, force F F.B.D.-? F F The Law of Gravity

30 Problem: Apparent Weight (F N ) F.B.D.? y F net = F N mg =ma The Law of Gravity

31 Weightlessness F.B.D.? The Law of Gravity

32 Thanks for your attention!

Dynamics: Newton s Laws of Motion

Lecture 6 Chapter 4 Physics I 02.10.2013 Dynamics: Newton s Laws of Motion Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov2013/physics1spring.html