International University, Vietnam National University, HCMC Physics 1: Mechanics Tran Nguyen Lan, Ph.D Department of Physics, HCMIU-VNU Phone: 0905 623 462, email: lantrann@gmail.503 Week 01 https://drive.com/file/d/1aSR7PEIH6kfWQApoPtP8k4xLH_i6A8VA/view?usp=sharing • No of credits: 02 (30 teaching hours) • Textbook: Halliday/Resnick/Walker (2011) entitled Fundamentals of Physics, 9th edition, John Willey & Sons, Inc. Course Requirements • Attendance + Discussion + Homework: 15% • Assignment: 15% • Mid-term exam: 30% • Final: 40% Preparation for each class • Read text ahead of time • Finish homework Content Part A Dynamics of Mass Point - Chapter 1 Bases of Kinematics - Chapter 2 Force and Motion (Newton’s Laws) Midterm exam Part B Laws of Conservation - Chapter 3 Work and Mechanical Energy - Chapter 4 Linear Momentum and Collisions Part C Dynamics and Statics of Rigid Body - Chapter 5 Rotation of a Rigid Body About a Fixed Axis - Chapter 6 Equilibrium and Elasticity - Chapter 7 Gravitation Final exam Chapter 1 Bases of Kinematics 1. Motion in One Dimension 1. Position, Velocity, and Acceleration 1.
One-Dimensional Motion with Constant Acceleration 1. Freely Falling Objects 1. Motion in Two Dimensions 1. The Position, Velocity, and Acceleration Vectors 1.
Two-Dimensional Motion with Constant Acceleration. Tangential and Radial Acceleration 1. Relative Velocity and Relative Acceleration Measurement • Why do we need physics? – Explain the nature (develop modern technologies!) • How to know the laws of physics are correct? – Do experiment • Physical quantities have their own units Quantities SI system CGS system length meter (m) centimeter (cm) mass kilogram (kg) gram (g) time second (s) second (s) 1. Motion in one dimension • Dynamics and kinematics: Động học – Kinematics: describing motion (how objects move) Động lực học – Dynamics: concerning causes of motion (why objects move) Xf • Two basis quantities of motion: (t = tf) – Displacement: Δx = xf – xi Xi – Time interval: Δt = tf – ti (t = ti) • Restriction for this chapter: – Along the straight line only (vertical, horizontal, slanted) – Will not discuss the cause of motion (force) – Consider particles or particle-like objects only A.
Position, velocity, and acceleration Position defined in terms of a frame of reference. Scalar number: a val Two features of displacement: - its direction (a vector) - its magnitude For positive direction: Δx > 0 For opposite direction: Δx < 0 Question t0 = 0 t1 = 1 h x0 = 0 t2 = 1.5 h x1 = 40 km x (origin) x2 = 20 km x (a) What is the displacement of the car after 1.5 h? 20km (b) What is the distance the car travelled after 1.5 h? 60km Position-time graph Note: position-time graph is not necessarily a straight line, even though the motion is along one dimension! A. Position, velocity, and acceleration Average velocity - Unit: m/s, km/h, or cm/s - Magnitude: the slope of the straight Δx x 2 - x1 line that connects two particular vavg = = Δt t 2 - t1 points on the x(t) curve. - Sign: the sign of Δx Average speed total distance s avg = Δt Note: average speed does not include direction Question t0 = 0 t1 = 1 h x0 = 0 t2 = 1.5 h x1 = 40 km x (origin) x2 = 20 km x What is (a) the average velocity 40/3 40 over 3 (b) the average speed 40 of the car during the total trip of 60 km? Instantaneous velocity when delta t approach 0 (t2-t1 approx The instantaneous velocity corresponds to the velocity of a particle at a particular time.
đường tiếp tuyến Average velocity Instantaneous velocity g y y Speed (not average speed) is the magnitude of velocity: |v| - When move from 0 to t1, (1) the slope=tang = velocity increases Constant velocity From t1 to t2, the graph is approx. a line -> the velocity does not c From t2 to t3, the slope = tang.= velocity decreases position - The instantaneous velocities are always the same - All the instantaneous velocities will also equal the average velocity tang. increas (1) v velocity v = const Sample Problem : The position of an object described by: x = 4-12t+3t2 (x: meters; t: seconds) (1) What is its velocity at t =1 s? v=dx/dt=-12+6t=-6 (m/s) (2) Is it moving in the positive or negative direction of x just then? negative (3) What is its speed just then? S=6 (m/s) (4) Is the speed increasing or decreasing just then? Consider the equation o 0<t<2: decreasing; 2<t: increasing (5) Is there ever an instant when the velocity is zero? If so, give the time t; if not answer no. t=2 s (6) Is there a time after t= 3 s when the object is moving in the negative direction of x? if so, give t; if not, answer no no Sample Problem : The position of an object described by: x = 4-12t+3t2 (x: meters; t: seconds) (1) What is its velocity at t =1 s? v=dx/dt=-12+6t=-6 (m/s) (2) Is it moving in the positive or negative direction of x just then? negative (3) What is its speed just then? S=6 (m/s) (4) Is the speed increasing or decreasing just then? 0<t<2: decreasing; 2<t: increasing (5) Is there ever an instant when the velocity is zero? If so, give the time t; if not answer no.
t=2 s (6) Is there a time after t= 3 s when the object is moving in the negative direction of x? if so, give t; if not, answer no no A. Position, velocity, and acceleration Acceleration When a particle’s velocity changes, the particle is said to undergo acceleration Average acceleration Unit: m/s2 meter per second squ derive: khai triển Instantaneous acceleration 1st derivative 2nd derivative • Example v1=0 v2=-40 (moving the opposite of positive directio t = 10 s speed = 40 m/s (1) speed = 0 m/s t = 0 s x v1=0 v2=40 (2) t = 40 s t=0s speed = 40 m/s speed = 0 m/s x What is the average acceleration in each case? • Example -4m/s^2 t = 10 s speed = 40 m/s (1) speed = 0 m/s t = 0 s -4m/s^2 x (2) t = 40 s t=0s speed = 40 m/s speed = 0 m/s x What is the average acceleration in each case? Note on the sign of acceleration: If the signs of the velocity and acceleration of a particle are the same, the speed of the particle increases. If the signs are opposite, the speed decreases. Chapter 1 Bases of Kinematics 1.
Motion in One Dimension 1. Position, Velocity, and Acceleration 1. One-Dimensional Motion with Constant Acceleration 1. Freely Falling Objects 1.
Motion in Two Dimensions 1. The Position, Velocity, and Acceleration Vectors 1. Two-Dimensional Motion with Constant Acceleration. Tangential and Radial Acceleration 1.
Relative Velocity and Relative Acceleration 1. Constant acceleration position t1 t2 t3 velocity t1 t2 t3 acceleration From Eqs (1) and (2) one can derive three specialized equations for the constant acceleration Checkpoint The following equations give the position x(t) of a particle in four situations: (1) x = 3t - 4; (2) x = -5t3 + 4t2 + 6; (3) x= 2/t2 +4/t; (4) x= 5t2 - 3. To which of these situations do the equations of the above Table apply? Chapter 1 Bases of Kinematics 1. Motion in One Dimension 1.
Position, Velocity, and Acceleration 1. One-Dimensional Motion with Constant Acceleration 1. Freely Falling Objects 1. Motion in Two Dimensions 1.
The Position, Velocity, and Acceleration Vectors 1. Two-Dimensional Motion with Constant Acceleration. Tangential and Radial Acceleration 1. Relative Velocity and Relative Acceleration In ideal 1.
Free falling objects conditions (no air resistance, no wind, .) Galileo Galilei (1563-1642) sciencephoto.com In ideal 1. Free falling objects conditions (no air resistance, no wind, .) Galileo Galilei (1563-1642) sciencephoto.com In ideal 1. Free falling objects conditions (no air resistance, no wind, .) Galileo Galilei (1563-1642) sciencephoto.com - “Free-fall” is the state of an object moving solely under the influence of gravity. - Free-fall acceleration is the same for all objects.
- The acceleration of gravity near the Earth’s surface is a constant, g = 9.8 m/s2 toward the center of the Earth. Free-falling experiment at NASA (https://www.com/watch?v=E 43-CfukEgs) Free-falling motion is a special case of the constant acceleration! Free-falling motion is a special case of the constant acceleration! Sample problem: A ball is thrown directly upwards with an initial velocity of 15 m/s. On its way down, it was caught at a distance of 1 m below the point from where it was thrown. Determine: (a) the maximum height reached by the ball; (b) the time it takes the ball to reach that height; (c) the velocity of the ball when it is caught; (d) the total time elapsed from where the ball was thrown to where it was caught.