1 Honors Physics 1 Class 03 Fall 2013 Force Newton’s Laws Everyday Forces

2 Newton’s Laws Mechanics laws are hard to observe because there are confounding forces, such as friction and drag. 1rst Law – A body will continue to move with constant velocity unless a net force acts on it. 2 nd Law – F=ma (We need to define inertial mass and force. We should write acceleration as second derivative of position.) 3 rd Law – Force is necessarily the result of interaction between two systems.

3 Questions What is a force? What is mass? What is an isolated body? How do we measure acceleration? –Inertial reference frame. When are Newton’s Laws true? Are there any special conditions? Note: Newton’s Laws are easy to apply when dealing with “point” masses, but not for fluids.

4 Simplifications We will start by treating physical objects as particles. Particle: an object for which internal structures and motions can be ignored or all of whose parts move in the same way. Force: the interaction of an object with its environment in ways that can influence the motion of the object.

5 Inertial systems If the net force on an object is zero, then it is possible to find a set of coordinate systems, or reference frames, in which that body has no acceleration. Inertial frames are defined by the sentence above. The laws of Physics are the same in all inertial frames. Inertial frames are related by x’=x+vt+d

6 Forces and accelerations are related in the same way in different inertial reference frames

7 Mass The mass of an object is a quantitative measure of the resistance of an isolated body to acceleration for a given net applied force.

8 Types of Forces There are four (maybe five) “fundamental” forces -strong nuclear, -weak nuclear, -electromagnetic, -gravity -+ maybe “dark”.

9 Everyday forces in mechanics Contact (Normal and/or Tension) Gravity Electromagnetic Friction Drag Spring

10 Using Newton’s Laws 1)Mentally divide the system of objects into smaller systems, until the forces and motion of each can be analyzed. 2)Draw a force diagram for each mass. A.represent each object as a point mass or simple symbol. B.Draw a force vector on each mass for each force acting on the mass. –Convention: Label forces with subscripts indicating which body the force is acting on and which one the force is exerted by: –F AB is the force on A due to B »Draw only forces acting on the object. 3.Choose a coordinate system 4.Take care to address interactions 5.Carefully consider and include constraints on the motion. (Sometimes constraints are trivially included, sometimes not.) 6.Keep track of which variables are known, which are unknown, and what is the goal of your calculation.

Free-Body Diagrams

12 PHYS 1100 Summer Normal force The normal force F N acts perpendicular to the point of contact between two objects. When two objects are in contact and remain in contact, the normal force is equal to the force that the object exerts on the surface. mg FNFN

13 PHYS 1100 Summer Tension When a cord (or spring, cable, wire, chain, band…) is attached to a body and pulled taut, the cord pulls on the body with a force T that is directed away from the body. This is called the tension force. mg

14 PHYS 1100 Summer Friction If we attempt to slide a body over a surface, the motion is resisted by bonding between the two surfaces. This friction force is directed along the surface and is opposite to the intended motion. The magnitude of the friction force depends on the normal force between two surfaces and on the nature of the surfaces. mg FNFN F AppliedF

15 PHYS 1100 Summer Friction vs Applied Force Frictional Force Applied Force Static Friction Kinetic Friction Starting Friction Motion begins (usually less than starting friction)

16 PHYS 1100 Summer Coefficient of Friction

17 Illustration of Newton’s 3 rd Law Reaction force of table on book Force of book on table Reaction forces of floor on table Forces of table on floor

18 Example 1: Two astronauts – tug of war Unequal strengths (A>B), unequal masses (A>B). Mass of rope can be neglected. Find their motion if each pulls on the rope as hard as he can. Make a sketch. Draw forces on each object. Things to note: –Each astronaut can only apply force to the rope. –Make a sketch and force diagram –Newton’s third law applies between rope and each astro. –If rope mass is negligible then F AB =F BA –Forces must be equal and opposite. B must let rope slip and A can’t exert max force.

19 Activity The motion of an asteroid is measured by the crew of two space ships. Crew 1 observes that the asteroid moves with v=1000m/s. Crew 2 observes that the asteroid moves with v=2000 m/s. Can they both be making their measurement from an inertial frame?

20 Activity The motion of an asteroid is measured by the crew of two space ships. Crew 1 observes that the asteroid moves with v=1000m/s+10m/s 2. Crew 2 observes that the asteroid moves with v=2000 m/s+20m/s 2. The asteroid has a mass of 10 6 kg. Do both crews measure the same force on the object. Can both crews be in a inertial frame?

21 Activity – Motion with constraints Frictionless pulley and table. Only net external force=gravity on mass 2. Rope massless and fixed length. Find acceleration of mass 1.