Physics 1: University Physics for Scientists & Engineers

1 Page 1 of 59 Physics 1: University Physics for Scientists & Engineers Please note, this is a work in progress, and as such, will undergo lots of modification until the end of the semester. Most notably, the page breaks, which I want to place at strategic places (so as not to cut off something important into 2 pages), but trying to do it now will only fail as I add and remove lines, so I will do that only at the end. In the meantime, keep this in mind. Chapter 1: Physics and Measurement o Chapter 2: Motion in One Dimension o Chapter 3: Vectors o Chapter 4: Motion in Two Dimensions o Chapter 5: The Laws of Motion o Chapter 6: Circular Motion and Other Applications of Newton s Laws o Chapter 7: Energy and Energy Transfer o Chapter 8: Potential Energy o Chapter 9: Linear Momentum and Collisions o Chapter 10: Rotation of a Rigid Object About a Fixed Axis o Chapter.

2 Rolling Motion o Chapter 11: Angular Momentum o Chapter 12: Static Equilibrium and Elasticity o Chapter 15: Oscillatory Motion o Final Exam study guide o o Comment [as1]: Notes for Monday, June 12, 2006 begin here Page 2 of 59 I. Chapter 1: Measurements (return to top)II. Chapter 2: Motion in One Dimension (return to top) A.

3 Purpose: Comment [as2]: Notes for Wednesday, June 14, 2006 begin here. B. Definitions (and symbols): 1. Distance (d) (scalar) is the total length of space that an object travels. 2. Displacement (D) (vector) is the length of space between your origin and your destination. 3. Speed (s) (scalar) the rate of movement of a particle. a. Average Speed = the ratio of the distance covered in a certain time S=dti. b. Instantaneous Speed = how fast you are going at any particular instant. It is also known as the magnitude of the instantaneous velocity. ri. 4. Velocity (v) (vector) the rate of displacement of a particle S(t)=|v|a.

4 Average Velocity = the ratio of displacement covered in a certain time i. vX= x tb. Instantaneous Velocity = the velocity of an object at an instant in time. vx=lim t 0 x t=dxdti. 5. Acceleration (a) (vector) the rate at which velocity changes a. Average Acceleration = the ratio of velocity covered in a certain time r rvirvf= vi. ra t tb. Instantaneous Acceleration = the acceleration of an object at an instant in timed ra(t)=drvdt i. C. Example 1: 1. A particle begins traveling 5 feet to the right and then stops and travels to the left for 2 feet, traveling the entire distance in 3 seconds.

5 Assuming average velocity, analyze the problem. a. What is the distance (d) and displacement (D)? rD=3ft (or 3ft right, 3 ft east, +3 i ft) d=7ft i. b. What is the average speed (s) and instantaneous speed (s)? i. s=|rv|=73= ft/s s= ft/s (if constant) c. What is the average velocity (v) and instantaneous velocity (v)? i. rv=1 i ft/s ft/s ad. What is the average acceleration () and instantaneous acceleration (a)? i. ra=vf vi=( ) ( )= t3ii. draw the path of the particle Chapter 2 (Motion in One Dimension) iii.

6 Regarding average velocity since the displacement is 3 feet in 3 seconds, the average velocity is 1 ft/s. this would mean that a particle traveling at 1ft/s directly towards the goal (as opposed to the other particle which went forward 5ft and then returned 2 feet), will arrive at the same time as the particle traveling the longer route. As for instantaneous velocity, there is not enough information to figure this out (we don t know if velocity is constant or changing). D. Example 2: 1. A car goes west for 40 miles in 2/5 hours and then stops for hour.

7 It then goes east for 70 miles in 7/10 hours. Assume the car is going at constant speed and its initial & final speeds are not zero. a. What is the average speed of the car in the first stage, second stage, & the whole trip? Page 3 of 59 i. s1=402/5=100mph s2=707/10=100mph stot=11012+25+710= b. What is the average velocity of the car in the first stage, second stage, & whole trip? i. rv1= 100mph rv2=100mph rvtot= c. What is the average acceleration of the car in the first stage, second stage, & whole trip?

8 I. ra1=vf(1) vi(1)t1=0 ( 100)2/5=250mph2 ra2=vf(2) vi(2)t=100 07/10= (2) vi(1)ttot=100 ( 100) d. Draw the path of the particle & include all relevant data e. Graph x vs. t, v vs. t, s vs. t, & a vs. t & show the geometrical meanings of the average values. E. Example 3: Chapter 2 (Motion in One Dimension) Page 4 of 59 x(t)=(t2 4)(t+5)0t1. A particle is traveling on a path given by the equation from 6x(t)=t3+5t2 4t 20x(0)= 20 x(6)=352x(t)= t=2x'(t)=v(t)=3t2+10t 4v(0)= 4 v(6)=164v(t)=0 0=3t2+10t 4 t= ( seconds.)

9 Fully analyze the particle s path, its speed, velocity and acceleration. a. Step 1: figure out the significant markers related to the position function (at the beginning, end and when the function equals zero). To figure out how far the particle will travel and when it will cross the origin (t=0). i. ii. (These will be our initial & final positions) iii. (this is the time the particle will be at the origin) 0 0=t3+5t2 4t 20b. Step 2: derive the position function to get the velocity function and its significant markers (again at the beginning, end, and when the function equals zero) to determine its velocity at the beginning and end of its path.

10 Where the function equals zero, the particle has no velocity and could either continue on its path, or change direction. i. ii. (These will be our initial & final velocities) iii. (velocity is zero here) iv. (This means at seconds, the position will be at either a local max or local min, IF the sign changes. )= this case, the sign changes from negative to positive, meaning x( ) is a local minimum. This also tells us our problem will be broken down into two stages, the one with the negative velocity (up to t= ) and the one with the positive velocity (from t= and beyond).