Tuesday, 26 AGUSTUS 2014 Untuk mahasiswa Teknologi Pertanian Universitas Gadjah Mada YOGYAKARTA

20% : HOMEWORK / QUIZ 10% : CLASS ACTIVITY 35% : MIDTERM 35% : FINAL EXAM

How we measure things! fundamental units:All things in classical mechanics can be expressed in terms of the fundamental units: –Length L –Mass M –Time T For example: –Speed has units of L / T (i.e. miles per hour). –Force has units of ML / T 2 etc... (as you will learn). Fundamental Units

Units... SI (Système International) Units:SI (Système International) Units: –mks: L = meters (m), M = kilograms (kg), T = seconds (s) –cgs: L = centimeters (cm), M = grams (gm), T = seconds (s) British Units:British Units: –Inches, feet, miles, pounds, slugs... We will use mostly SI units, but you may run across some problems using British units. You should know how to convert back & forth.

Converting between different systems of units Useful Conversion factors: –1 inch= 2.54 cm –1 m = 3.28 ft –1 mile= 5280 ft –1 mile = 1.61 km Example: convert miles per hour to meters per second:

This is a very important tool to check your work –It’s also very easy! Example:Example: Doing a problem you get the answer distance d = vt 2 (velocity x time 2 ) Units on left side = L Units on right side = L / T x T 2 = L x T Left units and right units don’t match, so answer must be wrong!!Left units and right units don’t match, so answer must be wrong!! Dimensional Analysis

Lecture 1, Act 1 Dimensional Analysis The period P of a swinging pendulum depends only on the length of the pendulum d and the acceleration of gravity g.The period P of a swinging pendulum depends only on the length of the pendulum d and the acceleration of gravity g. –Which of the following formulas for P could be correct ? (b) (c) Given: d has units of length (L) and g has units of (L / T 2 ). (a) P = 2  (dg) 2

Lecture 1, Act 1 Solution TRealize that the left hand side P has units of time (T ) Try the first equation (a)(b)(c) (a) Not Right !!

(a)(b)(c) (b) Try the second equation Lecture 1, Act 1 Solution

(a)(b)(c) (c) This has the correct units!! This must be the answer!! l Try the third equation Lecture 1, Act 1 Solution

The SI unit of time: second, s 1Unit of time No. of... Definition: 1 second is a certain number of vibrations of ‘light wave’ emitted by a cesium atom.

2Measuring time intervals Here are some time intervals.

2Measuring time intervals Stop-watch is a common instrument for measuring time intervals. Some stop-watches are accurate to 0.02 s. Stop-watch and reaction time

average ~ 0.2 s short eventlarge % error This time is called reaction time. Seeing an event Starting/stopping stop- watch by hand time

Liu Xiang in the 2004 Olympic Games Liu Xiang finished 110-m hurdles within s in the 2004 Olympic Games. Discussion: Is it accurate to use the stop-watch to time the race? Why? Find out some other instruments for time measurement.

The National Standard Kilogram No. 20, an accurate copy of the International Standard Kilogram kept at Sèvres, France, is housed under a double bell jar in a vault at the National Institute of Standards and Technology.