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Inertia, Forces, and Acceleration: the Legacy of Sir Isaac Newton

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Inertia, Forces, and Acceleration: the Legacy of Sir Isaac Newton Newton's Laws 4/14/2008 UCSD Physics 10 UCSD Physics 10 Position is a “Vector” • Compare “A ball is 12 meters North of the Sun God” to Inertia, Forces, and Acceleration: “A ball is 10 meters from here” The Legacy of Sir Isaac Newton • A vector has both a direction and a value, or “magnitude” • Which of these descriptive properties are vectors? – Position –Mass – Color – Speed Used interchangeably in casual language, but not in physics – Velocity – Temperature Objects in Motion Spring 2008 2 UCSD Physics 10 UCSD Physics 10 Speed vs. Velocity Discussion Questions Speed is the rate of motion (how fast) See if you can come to a consensus on answers to these questions: Speed = distance / time 1. A yellow car is heading East at 100 km/h and a “The satellite has a speed of 15,000 mi/hr” red car is going North at 100 km/h. Do they “But officer, my speed was only 56 miles per hour!” have the same speed? Do they have the same velocity? Velocity is speed plus directional information: 2. A 16-lb bowling ball in a bowling alley in Del Mar heads due north at 10 m/s. At the same time, “The spacecraft is moving at 18 km/sec towards Jupiter” a purple 8-lb ball heads due north at 10 m/s in an alley in La Jolla. Do they have the same velocity? Spring 2008 3 Spring 2008 4 Lecture 6 1 Newton's Laws 4/14/2008 UCSD Physics 10 UCSD Physics 10 Approaching a Physics Question or Problem Newton Says 1. Extract relevant facts • A ball sitting still will stay that way, unless acted upon by a force. 2. Draw a sketch, if needed 3. Determine applicable reasoning Inertia Mass 4. Draw irrefutable conclusion An object that is not subjected to any outside forces 5. Perform a “sanity check”. Does your answer moves at constant velocity, covering equal make sense? distances in equal times, along a straight path, x(t) = x(0) + vt Newton’s 1st Law • This is not intuitively obvious. Spring 2008 5 Spring 2008 6 UCSD Physics 10 UCSD Physics 10 Sliding Book Demonstration Constant Velocity Motion – No Forces • If no external forces are acting, velocity is constant Why doesn’t it keep on going, like the Energizer Bunny? • Position changes, at a steady (constant) rate When are there forces acting on the book, and what is responsible for them? t=0 sec 1 sec 2 sec 3 sec 4 sec 5 sec 6 sec When is the speed a maximum? x =1 m 2 m 3 m 4 m 5 m 6 m 7 m When is the speed a minimum? v= 1 m/s 1 m/s 1 m/s 1 m/s 1 m/s 1 m/s to right How much force is acting on it after it stops? How does determination of velocity depend on choice x=0 and t=0? Spring 2008 7 Spring 2008 8 Lecture 6 2 Newton's Laws 4/14/2008 UCSD Physics 10 UCSD Physics 10 A Data Table Acceleration constant velocity • If an object’s velocity changes, it’s accelerating. Time Position Velocity • If an object’s velocity changes, it’s accelerating. 0 sec 1 meter = dist/time & direction • The change can be in the speed of motion, in the direction of motion, or both. 1 sec 2 meters 1 m/s to right • Acceleration is a generic term velocity change – includes “deceleration” 2 sec 3 meters 1 m/s to right • Can you feel if you’re moving with a constant velocity? 3 sec 4 meters 1 m/s to right • Can you feel being accelerated? Why? Spring 2008 9 Spring 2008 10 UCSD Physics 10 UCSD Physics 10 Acceleration is the rate of change of velocity Acceleration is a Vector too • A constant acceleration means that the object’s • Direction of acceleration = direction in which velocity velocity is changing at a constant rate changes – Example: if the acceleration is along the direction of motion, the speed grows by the same amount in each – Accel. in same direction as velocity speed increases time interval (e.g., second) – Accel. in direction opposite to velocity speed decreases • if the speed changes by 1 meter per second each second, the – Accel. at right angles to velocity direction changes acceleration is (1 meter per second) per second, or 1 m/s2. • Example: An unexpected shove from the side as you run straight down a if v = 15 m/s at time t = 0, and a = 1 m/s2, then hallway might send you careening into the wall. Lesson: you shouldn’t v = 16 m/s at t = 1 sec be running indoors. v = 17 m/s at t = 2 sec • Circular motion is produced by acceleration of v2/r (r is radius of curve) v = 20 m/s at t = 5 sec Spring 2008 11 Spring 2008 12 Lecture 6 3 Newton's Laws 4/14/2008 UCSD Physics 10 UCSD Physics 10 Discussion Questions, cont. Forces Cause Acceleration • Acceleration is proportional to the applied force: The 3. A sprinter who is running a 200 meter race covers the larger the force, the more an object will accelerate, in the second 100 meters in less time than it takes to cover the direction of the applied force. first 100 meters. Why? • Mass is inertia, i.e., reluctance to accelerate, so for the same force, more massive objects experience smaller 4. When you let go of a superball, does it accelerate? In acceleration than less massive ones. which direction? What about when it hits the floor? If you throw it upwards, does it accelerate then? Which Shorthand: direction? Force = mass acceleration, or 5. If you are driving East and apply the brakes to stop your F = ma car, in what direction are you accelerating? Newton’s 2nd Law Spring 2008 13 Spring 2008 14 UCSD Physics 10 UCSD Physics 10 0.4 sec -1.0 m 0.5 sec A Ball in Free Fall Questions on Newton’s Second Law 0.6 sec -2.0 m 6. If identical forces act on two objects, where object 0.7 sec • Is the ball’s direction of velocity constant? A is twice as massive as object B, how do their accelerations compare? -3.0 m 0.8 sec • Does it travel equal distances in equal times? 7. If I double the mass of an object, by what factor -4.0 m 0.9 sec • Is the ball accelerating? must I change the applied force to maintain a certain acceleration? -5.0 m 1.0 sec • What is the direction of the acceleration vector? 8. If one force pulls an object to the East, while a second force of equal magnitude pulls it to the • What is the direction of the force (F = ma)? -6.0 m 1.1 sec West, what is the object’s acceleration? • What’s responsible for the force on the ball? -7.0 m 1.2 sec Spring 2008 15 Spring 2008 16 Lecture 6 4 Newton's Laws 4/14/2008 UCSD Physics 10 UCSD Physics 10 Quantitative exercises, real numbers Another numerical example If you see an object with a mass of 1 kg increase its speed by On planet Splat, the acceleration due to gravity is 1m/s in each second, what force is acting on it? 40.0 m/s2. What would a rock’s velocity be 3 sec after you dropped it on Splat? (Initially at rest.) Is it accelerating? Yes! Velocity increases by 40 m/s in each second. How much is it accelerating? Starts from rest, i.e. v = 0 at t = 0 Velocity changing by 1m/s per sec is acceleration of 1 m/s/s =1 m/s2 So, v(0 s) = 0 m/s, v(1 s) = 40 m/s, What force is acting on it? 2 2 v(2 s) = 80 m/s, F = mass acceleration = 1 kg 1 m/s2 = 1 kg m/s2 = 1 Newton v(2 s) = 80 m/s, v(3 s) = 120 m/s. Spring 2008 17 Spring 2008 18 UCSD Physics 10 UCSD Physics 10 Summary Assignments • Mass is a property of objects, producing a reluctance to accelerate, called inertia – HW 2: due Friday (4/18): • Velocity refers to both speed and direction • Hewitt 11.E.16, 11.E.20, 11.E.32, 11.P.5, 2.E.6, 2.E.11, 2.E.14, 2.E.36, 2.E.38, 3.E.4, 3.E.5, 3.E.6, 3.E.19 • Acceleration means a change in velocity (either • turn in at lecture, or in box outside SERF 336 by 3PM magnitude, or direction or both) – Read Hewitt Chapters 2, 3, 4 • If an object is accelerating, it is being acted upon • suggested order/skipping detailed on website by a force, and F = ma. No exceptions. Spring 2008 19 Spring 2008 20 Lecture 6 5.
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