The Mastering Motion: The Physics Behind It
- 1. Physics Basics, Part I Units Laws of Motion
- 2. Spring 2006 UCSD: Physics 8; 2006 2 Units of Measurement • Physics forms a link between the physical world (concepts) and the mathematical world (quantitative) • This inevitably involves measurements – Measurements inevitably involve units • We’ll stick to MKS (SI) units in this course – MKS: meters; kilograms; seconds – As opposed to cgs: centimeter; gram; seconds • Distance in meters (m) – 1 meter is close to 40 inches • Mass in kilograms (kg) – 1 kg is about 2.2 pounds • Time in seconds (s)
- 3. Spring 2006 UCSD: Physics 8; 2006 3 Secondary Units • Units can be combined in a variety of ways to form complex units, many of which have their own names/symbols quantity formulation Complex unit For short velocity dist/time m/s — acceleration velocity/time m/s2 = m/s/s = m/s per s — force F=ma kg·m/s2 Newton (N) work/energy W=F·d kg·m2/s2 Joule (J = N·m) power energy/time kg·m2/s3 Watt (W = J/s) frequency cycles/second 1/s Hertz (Hz) pressure force/area kg/m·s2 Pascals (Pa = N/m2)
- 4. Spring 2006 UCSD: Physics 8; 2006 4 Electrical Units • We’ll deal a lot with electrical phenomena in this course, with its own (but related) set of units: quantity formulation units for short charge I Coulombs C current charge/time C/s Amps (A) voltage V = IR V Volts (V) resistance R = V/I volts/amp Ohms () power P = VI = I2R = V2/R volt-amps Watts (W = J/s) electric field voltage/distance V/m —
- 5. Spring 2006 UCSD: Physics 8; 2006 5 Mass and Inertia • Mass is how hard it is to get something to move – Intimately related to the idea of inertia – Effectively how many protons and neutrons in the thing – Distinct from weight, which relates to gravity • the same mass weighs different amounts on different planets • Inertia relates to Newton’s first law of motion: an object in motion will remain in that state of motion unless acted on by an outside force • This applies to being at rest as well as being in a state of motion – motion relative to what
- 6. Spring 2006 UCSD: Physics 8; 2006 6 Newton’s Second Law of Motion • Okay, what about when there is an outside force? – outside: not coming from within the body; an external agent – force: something that pushes or pulls • Then we have Newton’s Second Law of Motion: • Great: now we have to talk about acceleration – the rabbit hole gets deeper – but first let’s give some examples of force… F = ma
- 7. Spring 2006 UCSD: Physics 8; 2006 7 Examples of Force • Examples: – gravity exerts a downward force on you – the floor exerts an upward force on a ball during its bounce – a car seat exerts a forward force on your body when you accelerate forward from a stop – the seat you’re sitting in now is exerting an upward force on you (can you feel it?) – you exert a sideways force on a couch that you slide across the floor – a string exerts a centrally-directed (centripetal) force on a rock at the end of a string that you’re twirling over your head – the expanding gas in your car’s cylinder exerts a force against the piston • Note the syntax: Agent exerts directed force on recipient
- 8. Spring 2006 UCSD: Physics 8; 2006 8 Velocity and Acceleration • Velocity is a speed and associated direction – 10 m/s toward the north – 50 m/s straight upward • Acceleration is any change in velocity – either in speed OR direction • Acceleration measured as rate of change of velocity – velocity is expressed in meters per second (m/s) – acceleration is meters per second per second – expressed as m/s2 (meters per second-squared)
- 9. Spring 2006 UCSD: Physics 8; 2006 9 The Force-Acceleration Connection • Whenever there is a net force, there will be an acceleration – A ball thrown into the air has the force of gravity operating on it, so its velocity continuously changes, resulting in a curved path – When you step on the gas, a forward force acts on your car, making it speed up – The force of gravity attracts the earth toward the sun. This has the effect of changing the direction of earth’s velocity, wrapping it into a circle around the sun (centripetal force) – A car, slamming into the side of another car already moving forward, will exert a sideways force, changing the traveling car’s direction of motion – When a bat hits a ball, the large momentary force results in a large acceleration of the ball as long as contact is maintained
- 10. Spring 2006 UCSD: Physics 8; 2006 10 All Forces Great and Small • The relation, F = ma, tells us more than the fact that force and acceleration go together – the relation is quantitative, and depends on mass • For the same applied force: – a small mass will have a greater acceleration – a large mass will have a smaller acceleration • If you want the same acceleration, a smaller mass requires a smaller force, etc. – this then relates mass and inertia in an intimate way: – how hard is it to get an object moving? Force = massacceleration OR Force = massacceleration
- 11. Spring 2006 UCSD: Physics 8; 2006 11 Hold On a Second… • I’ve got forces acting on me right now, but I’m not accelerating anywhere – very perceptive, and this is where the concept of net force comes in Force #1 Force #2 Total Force Force #1 Force #2 Total Force = 0
- 12. Spring 2006 UCSD: Physics 8; 2006 12 Examples of Zero Net Force • Sitting in your seat, gravity is pulling down on you, but the seat reacts by pushing up on you. The forces cancel, so there is no net acceleration • Pushing against a huge crate, the force of friction from the floor opposes this push, resulting in no net force and thus no acceleration
- 13. Spring 2006 UCSD: Physics 8; 2006 13 Newton’s Third Law • For every force, there is an equal and opposite force – every “action” has a “back-reaction” – these are precisely equal and precisely opposite • You can’t push without being pushed back just as hard – in tug-of-war, each side experiences the same force (opposite direction) – when you push on a brick wall, it pushes back on you! Force on box by floor (normal force) Force on box by gravity box floor
- 14. Spring 2006 UCSD: Physics 8; 2006 14 Force Pairs Illustrated Force on person by box Force on floor by box Force on box by floor Force on box by person Force on person by floor Force on floor by person Not shown are the forces of gravity and the associated floor forces
- 15. Spring 2006 UCSD: Physics 8; 2006 15 Wait: We cheated two slides back… • When we drew the box and floor, with the “normal” force from the floor canceling the force of gravity, these weren’t strictly force pairs – but these are the two canceling forces on the box that result in zero acceleration of the box • The real pairs have to involve the earth: box floor earth satellite • Force Pairs: • earth-box (grav) • box-floor (contact) • earth-satellite (grav)
- 16. Spring 2006 UCSD: Physics 8; 2006 16 Don’t all forces then cancel? • How does anything ever move (accelerate) if every force has an opposing pair? • The important thing is the net force on the object of interest Force on box by floor Force on box by person Net Force on box
- 17. Spring 2006 UCSD: Physics 8; 2006 17 Gravity • One of the most apparent forces in our daily experience is gravity • Gravity is the mutual attraction of mass – it’s always attractive, never repulsive – all particles in the earth attract all particles in your body – net effect (force) is effectively toward the center of the earth • Follows force law elucidated by Newton: Fgrav = GMm/r2 – where M is mass of earth, m is mass of you (or object of interest), and r is distance (separation) between object and earth’s center. G is just a constant: 6.6710-11 in MKS units – Note that since F = ma, we can say agrav = GM/r2 is the acceleration due to gravity
- 18. Spring 2006 UCSD: Physics 8; 2006 18 Gravity on earth’s surface • The product, GM, for earth, is 3.9861014 m3/s2 – so agrav evaluates to 9.8 m/s2 on earth’s surface (r = radius of earth = 6,378 km) • Bottom line: falling objects accelerate at 9.8 m/s2 on the surface of the earth – downward velocity changes by about 10 m/s with each passing second • This also means that to support a 1 kg book against the pull of gravity, one must exert F = ma = (1kg)·(10m/s2) = 10 Newtons of force – this is the object’s weight: mg • Support for the book is just the “normal” force required to keep the book from accelerating – in other words: to make the net force on the book zero
- 19. Spring 2006 UCSD: Physics 8; 2006 19 Pressure, Density • Pressure is force per unit area – measured in N/m2, or Pascals (Pa) – the pressure of the atmosphere at sea level is about 105 = 100,000 Pa (about 14.6 pounds per square inch—psi) • pounds are also a unit of force, like the Newton • Density is mass per volume – measured in kg/m3 – water is 1000 kg/m3 (same as 1 g/cm3 in cgs units) – air is about 1.3 kg/m3 – rock is 3300 kg/m3 – gold is about 19,300 kg/m3
- 20. Spring 2006 UCSD: Physics 8; 2006 20 Announcements/Assignments • Next up: – energy in its myriad forms – a simple model for molecules/lattices – electrons, charge, current, electric fields • Assignments: – Read Chapter 1 of book • You can skip sections on velocity, position of falling balls, as well as section on projectile motion (pp. 15–21) – Read Chapter 2: pp. 54–59, 61–62, 71–72 – Transmitters will start counting for credit Tuesday 4/11 – First HW will be due Thursday 4/13 – First Q/O due Friday, 4/14 by 6PM via WebCT