Terminology and Gravity Physics 109 Class Period 4 11 September 2007 Outline Solving Problems Summary of terminology that we will use in Physics Review of Vectors Gravity Problem Solving Strategy Interpret Identify concepts and principles Develop Draw a diagram, determine formulas Evaluate Execute your plan (dimensional analysis, then numbers Assess Does the answer make sense? Are the numbers reasonable? Terminology we will use in Physics SI Unit Prefixes Giga 10 9 G Nano 10-9 n Mega 10 6 M Micro 10-6 Kilo 10 3 k Milli 10-3 m Hecto 10 2 h Centi 10-2 c Deca 10 1 da Deci 10-1 d Examples a Gigabyte is 10 9 bytes or 1000 Megabytes. A millimeter is 10-3 meter. 1
More Terminology x, y, z Usually used to indicate distances or displacements in the cartesian coordinate system. v, Velocity, usually a vector quantity. a, Acceleration, also a vector quantity. t, Time r, A radius, usually a vector. Any of these with the subscript zero means the starting value of that quantity. A letter without a subscript usually means the final value. g, The acceleration due to gravity. = 9.8 m/s 2 m, Usually designates mass, in kilograms N, Newton the unit of force, Designates density, usually given in g/cc Important Equations v = v 0 + at Final velocity is equal to the initial velocity plus the acceleration times the time. x = x 0 + v 0 t + 1/2at 2 Displacement is equal to the initial displacement, plus the initial velocity times the time, plus ½ the acceleration times the time squared. Important Equations, cont. x - x 0 = ½(v 0 + v)t The displacement at time t, minus the initial displacement, is equal to ½ the sum of the initial velocity and the final velocity times the time. v 2 = v 02 + 2a(x x 0 ) The final velocity squared is equal to the initial velocity squared plus 2 times the acceleration times the final displacement minus the initial displacement. Vector Review Which of the following is the sum of two vectors? A. B. DIFF. C. SUM D Which is the difference? 2
What do these diagrams illustrate? C B B C A A You travel north for four km, then east for 3 km, and then southwest for 5 km. Which vector diagram illustrates this trip? Correct A. B. A. Vectors can be added in any order B. A + B +C = A + C + B C. That Vector addition is commutative D. All of the above Correct answer C. D. None of them. Gravity The force of gravity between two objects of mass M and mass m, as a function of the distance between them is: F = GMm/r 2 The value of G is 6.67 x 10-11 Nm 2 /kg 2 The force on a mass m by the Earth is given by: F = mg = GMm/r 2 where M is the mass of the earth, and r is the radius of the earth. Note that the small m s cancel, and so g does not depend on the mass m. Galileo showed that objects fall with the same acceleration, independent of their mass. An Interesting Gravity Problem Given that Superman can leap tall buildings at a single bound, what can this tell us about the gravity of Krypton, his home planet? Assume that the tall building is 200m high. His initial velocity must be v 2 = 2gh so v = 62.61 m/s If he achieves this velocity in 0.25s then his acceleration is 250 m/s 2. 3
Superman (continued) Assume Superman has a mass of 100kg, then the force, F = ma = 25,000 N! Assume that 0.7 of this force is required just to stand up on Krypton, that force is 17,500N If 17,500 = mg Krypton, then g Krypton =175m/s 2. This is 17.8 times Earth gravity! (The book works it out to be 15 times.) Krypton Properties (r K K )/(r E E ) = 17.8 If the densities are the same, the radius of Krypton is 17.8 x Earth radius. (Jupiter is only 11 x Earth radius.) If the radii are the same, then the density of Krypton would be 17.8 x 5 = 89 g/cc. No normal material has this density. However, dead neutron star material is about 10 11 g/cc, so a small sphere of about 600m radius at the center of earth would make g about 150 m/s 2. No wonder Krypton exploded! Which of the equations below did we use to calculate Superman s velocity? A. V = V 0 + at B. x = x 0 + ½(V 0 + V)t C. x = x 0 + V 0 t + ½ at 2 D. V 2 = V 0 2 + 2a(x-x 0 ) This equation How did we determine Superman s Acceleration? A. We knew that his mass was 100 kg B. We knew that the time to reach his velocity was ¼ second. Correct answer C. We knew that the building was 200m high. D. We guessed. 4
How did we determine that the acceleration of gravity on Krypton was 17.8 times that of Earth? A. We knew Superman s Krypton weight B. We knew that the density of Krypton was 17.8 times the density of Earth C.. We assumed his Krypton weight and divided that by his mass. Correct answer D. We guessed. What did we conclude about the nature of Krypton? A. It had a radius 17.8 times that of Earth B. It had a density 17.8 times that of Earth C. It must have had a dead neutron star as a core. Correct answer D. There was no possible way that it could have existed and obeyed the laws of Physics. Assignment for next time Do the problems for Chapter 3 Read Chapter 4 Read Experiment 3 Finish the Force Table part of Experiment 2 There will still be a Recitation starting at 2PM on Wednesday in Room 104 Jones Annex. 5