Chapter 2:Motion along a straight line Translational Motion and Rotational Motion Today Later

Current information 1. Please read carefully all the instructions on the coursewebsite http://sibor.physics.tamu.edu/teaching/phys201/ 2. The problems in the syllabus are the same as in Mastering Physics on the web. 3. Have a notebook, solve the problems first and then submit them on Mastering Physics site. 4. There are due dates for the problems on Mastering Physics, so don’t procrastinate. 5. Enroll in WebAssign, since all tasks for the labs are given and submitted through this system. Prelab part is due 15 min before the start of the recitation.

Modified Mastering Physics Course: schuessler29324 Settings in Mastering Physics: 4 attempts are given (no subtractions within this attempts), after 4 attempts – no credit. Sometimes need use reset button. Graded tutorials are due soon after the lecture. Other problems are due on the date of the respective exam. Practical hint: perform calculations to 4 sign. figures and round as needed.

Describing Motion … Coordinates  Position (displacement)  Velocity  Acceleration a) Motion with zero acceleration b) Motion with non-zero acceleration

Kinematics in One Dimension: Displacement

Average speed and velocity Average velocity = total displacement covered per total elapsed time, Speed is just the magnitude of velocity! The “how fast” without accounting for the direction. Average speed = total distance covered per total elapsed time, Instantaneous velocity, velocity at a given instant

Average velocity

Instantaneous velocity

Graphic representation: Velocity Slope is average velocity during t=t2-t1 Slope is instantaneous velocity at t1

The figure shows x versus t graphs for four cars (A–D) moving on a straight road. The x axis is aligned with the road. Decide which car, if any, satisfies each of the following questions. Choose E if none of the cars satisfies the question. Which car reverses direction? Which car is slowing down? Which car reverses direction? Which car is speeding up? Which car is not moving? Which car moves in the -x direction? Answer: e) © 2016 Pearson Education, Inc.

Engine traveling on rail

Acceleration We say that things which have changing velocity are “accelerating” Acceleration is the “Rate of change of velocity” You hit the accelerator in your car to speed up (Ok…It’s true you also hit it to stay at constant velocity, but that’s because friction is slowing you down…we’ll get to that later…)

Average acceleration Unit of acceleration: (m/s)/s=m/s2 Meters per second squared

Average Velocity For constant acceleration The area under the graph v(t) is the total distance travelled v vav v0 t Dt

Kinematics in one dimension Motion with constant acceleration. From the formula for average acceleration We find On the other hand Then we can find

Recap So for constant acceleration we find: x t v t a t

Examples Can a car have uniform speed and non-constant velocity? Can an object have a positive average velocity over the last hour, and a negative instantaneous velocity?

Conceptual Example If the velocity of an object is zero, does it mean that the acceleration is zero? Example? If the acceleration is zero, does that mean that the velocity is zero?

Constant acceleration         (b) What is the officer’s speed when he catches up?     (c) What is the total distance the police has traveled at that time?  

Motion with constant acceleration    

Kinematics equations for constant acceleration

All objects fall with the same constant acceleration!!

Apollo 15 Launch date: July 26, 1971 © 2016 Pearson Education, Inc.

Testing Kinetics for a=9.80m/s2 Experiments on the motion of objects falling from leaning tower of Pisa under the action of the force of gravity

Acceleration of gravity on different planets, =9.81m/s2

A brick is dropped from the roof of a building The brick strikes the ground after 5s. (Sign convention does not matter!) How tall? Velocity of brick just before it strikes the ground? Choose + upward:       Choose + downward:   Important to have the correct interpretation of the results! The optimal selection of the reference frame helps.  

Problem: Vertical motion Stone is thrown vertically upward

Ball thrown upward How high? How long in the air?   How high? at point A: How long in the air? How long for highest point?       height of the cliff h=50m        

Ball thrown upward (cont.) Velocity when ball reaches the thrower’s hand?   At what time does the ball pass a point 8m above the throwers hand       = How long does it take to reach the base of the cliff and what is the velocity there? (h = 50m)   t1 = (15 + (15^2 + 4*4.9*50)^0.5)/(2*4.95) = 5.0727 = 5.07 s t2 = (15 - (15^2 + 4*4.9*50)^0.5)/(2*4.95) = -1.9912 = -1.99 s      

1-D motions in the gravitational field

Clicker problem When you brake on dry pavement, your maximum acceleration is about three times greater than when you brake on wet pavement. For a given initial speed, how does your stopping distance xdry on dry pavement compare with your stopping distance xwet on wet pavement? a) xdry = 1/3xwet b) xdry = 3xwet c) xdry = 1/9xwet d) xdry = 9xwet Answer: a) xdry = 1/3xwet © 2016 Pearson Education, Inc.

Average Velocity (example) x (meters) 6 4 2 t (seconds) -2 1 2 3 4 What is the average velocity over the first 4 seconds ? A) -2 m/s B) 4 m/s C) 1 m/s D) not enough information to decide.

Instantaneous Velocity x (meters) 6 4 2 -2 t (seconds) 1 2 3 4 What is the instantaneous velocity at the fourth second ? A) 4 m/s B) 0 m/s C) 1 m/s D) not enough information to decide.