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Physics Force and motion Image thanks to www.wolvertonmountain.com Objectives • By the end of this lesson, you should be able to • Explain how forces and motion are related • Explain the differences between scalar and vector quantitites • Explain the differences between distance and displacement • Explain the differences between speed and velocity • Explain acceleration • Explain the difference between average velocity and instantaneous velocity • Using data, construct a distance-time graph • Using data, construct a velocity-time graph Objectives, continued • Calculate distance or displacement when no acceleration is taking place • Calculate velocity or speed when no acceleration is taking place • Calculate distance or displacement when acceleration is taking place • Calculate velocity or speed when acceleration is taking place • Use acceleration of gravity in 1-dimensional vertical movement calculations • Describe free fall • Determine the resultant velocity of an object • Calculate the instantaneous velocity from a distance-time graph • Calculate the instantaneous acceleration from a velocity-time graph Standards • SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. What is fast? • How do you know if something is moving? • You must compare its position to something else • Frame of reference: the "something else " that you are comparing So, how fast ARE you moving? • A conceptual version • https://www.youtube.com/watch?v=wIzvfki5ozU • A more mathematical version • https://www.youtube.com/watch?v=F77MBqpkul8 Types of motion • There are three primary types of motion • One-dimensional • When an object only moves horizontally or only vertically through space • Also known as 1D motion, straight line motion, or rectilinear motion • Two dimensional motion • When an object moves both vertically and horizontally through space • Also called 2D motion • Three dimensional motion • We won’t cover this one….for that, we’d need calculus Some more types of motion • Rotational motion: when an object does not move through space. Instead, it turns around a fixed point • Periodic motion: when an object moves through space but returns to its starting point over regular intervals • Vibratory motion: when the interior components of an object move back and forth within the object at regular intervals Introductory vocabulary words • Kinematics is the study of motion • Motion is directly tied to forces • Mechanics is the study of how forces affect objects “An apple a day..” • When Newton was 24, he was walking through a garden and noticed an apple fall to the ground • Newton realized that the apple falling was really caused by the Earth pulling on the apple • Most of the first half of the course is based on the mechanics and dynamics partially developed by Newton Forces • A force is a push or pull on an object • There are two main types of forces • Contact forces • Forces between two or more objects in direct contact • Examples include: friction, tension, and applied forces • Field forces • Forces that act on an object from a distance • Examples include: gravity, electrical and magnetic fields Unbalancing the apple cart • So, the apple fell. Why did it fall just then? • Before then, something (say, the branch) was counteracting the pull of gravity. • This is an example of balanced forces • Newton realized that nothing would change unless forces were unbalanced • Newton's 1st Law of Motion • An object at rest stays at rest and an object in motion maintains its velocity unless acted upon by an unbalanced force Some vocabulary terms • Distance: how far through space an object has moved • Displacement: how far an object ends up from its starting point • Speed: how much distance an object moves over time • Velocity: how much displacement an object moves over time • Acceleration: how rapidly velocity is changing Scalars and vectors • If a quantity has no direction, it is called a scalar quantity • Examples of scalar quantities • Distance • Speed • Examples of vector quantities • Displacement • Velocity • Acceleration Positive Attitude • When giving directions , you could use • Cardinal directions (north, south, northeast, etc) • Angular direction (in degrees or radians") • With positive meaning one direction and negative meaning the opposite direction • Commonly, up is positive and down is negative • Commonly, to the right is positive and to the left is negative • Technically, you can make any direction you want as positive (as long as you are consistent) Who's on first? • A baseball player is on first base and plans to steal second base, which is 90 feet away • The player runs quickly, making it to second • Distance ran is 90 feet • Displacement is 90 feet Who's on first, part 2 • Instead of making it, the first baseman throws the ball to second. Being too far to slide, the runner quickly turns and makes it back to first • Distance ran: up to 180 feet ( depending on the place along the base line that the turn was made) • Displacement: 0 feet (ended up at the starting point) • So, distance and displacement CAN be the same quantity but often are not “Feel the need for speed” • Speed and velocity are often used interchangeably • However, they are not necessarily the same quantity • Speed is calculated by distance traveled divided by time • Velocity is calculated by displacement traveled divided by time • • • • Velocity must have a direction v = Δ x /t Δ x means “change in x (horizontal movement)” Δ x = xfinal - xinitial Road Trip! • If you have ever taken a road trip, you know that the same speed is not maintained throughout the entire trip • You will have different legs of your journey that you traveled faster than others or for longer periods of time than others • Average speed is NOT adding up the individual speeds and dividing! • Instead, it is the sum of the distances divided by the sum of the times • Average velocity is similar (just replace the word distance with displacement) Gone in an instant • Instantaneous speed or velocity is how fast something is going at one particular time (in that instant, get it?) • In the road trip example, a 300 mile trip completed in 6 hours would have an average speed of 50 miles per hour • The instantaneous speed might be 60 miles per hour, 25 miles per hour, or even stopped, depending on which instant along the trip you observe Motion related graphs • Several graphs that can be used to illustrate the straight line motion of an object • Distance-time graphs • Displacement-time graphs • Speed-time graphs • Velocity-time graphs Hike! • Imagine a football team is running plays • • • • The first play nets 4 yards The second play nets 3 more The third play nets 4 yards The fourth play nets 5 yards • For this example, we’ll pretend that each play took 10 seconds to execute • Let’s look at the difference between a distance-time graph and a displacement-time graph Distance-time graph Trial 2 18 16 14 12 10 8 6 4 2 0 10s 20s 30s Trial 2 40s Additional notes on graph 1 • Remember, distance doesn’t matter the direction of travel – only the amount of travel • Notice, that the x-component and y-component are directly related • Also notice that the distance increases Displacement-Time graph Trial 1 6 5 4 3 2 1 0 10s 20s 30s Trial 1 40s The other point of view • From the opposing team’s perspective, they are moving backwards with each play • If we created a distance-time graph, it would like identical to that of our home team • If we created a displacement-time graph, you will notice that the line falls under the x-axis Displacement-time graph…from the other team’s point of view Trial 3 0 10s 20s 30s -2 -4 -6 -8 -10 -12 -14 -16 -18 Trial 3 40s Dry your eyes • Think back to Algebra class (it’s ok, it’s over now) • The steepness of a line was called its slope • Recall that m=y/x (sometimes known as “rise over run”) • Wait a minute!.....in a displacement-time graph, displacement is the y-axis and time is the x-axis • Displacement divided by time is……..velocity! • The velocity found by slope is the instantaneous velocity of that time period • So, the slope of the displacement-time graph is the velocity Acceleration • A change in velocity is known as an acceleration • Accelerations can be changes in “speed”, changes in direction, or both • Acceleration is calculated as: a = Δv / t • Sometimes, negative acceleration is thought of as only “slowing down” • In reality, it means accelerating in the opposite direction • Huh? • Imagine a sprinter running attached to a parachute when a strong breeze comes along • It is true that the sprinter will slow down, but eventually, he/she will start picking up speed IN THE OPPOSITE DIRECTION Acceleration on a graph • On a velocity-time graph, • Slope is velocity over time…..the same as acceleration • So, slope of a velocity-time graph is the instantaneous acceleration for that segment of the trip • Note: if slope is zero, then there is no acceleration and the objects maintains the same velocity • Imagine a moving sidewalk at an airport that is moving 2 miles/hour compared to the terminal floor • One person gets on the moving sidewalk and another does not and simply stands still • How fast is the person on the moving sidewalk moving compared to the moving sidewalk itself? • How fast is the person on the moving sidewalk moving compared to the observer? • The answer?....It depends (of course, right?!) 2 Miles/Hour overall 0 Miles/Hour 2 Miles/Hour Scenario #1, the person on the moving sidewalk is standing still; the sidewalk is moving 2 Miles/Hour overall 2 Miles/Hour 0 Miles/Hour Scenario #2, the person on the moving sidewalk is walking and the sidewalk stopped moving 4 Miles/Hour overall 2 Miles/Hour 2 Miles/Hour Scenario #3, the person on the moving sidewalk is walking 2mph compared to the sidewalk; the sidewalk is moving 0 Miles/Hour overall 2 Miles/Hour 2 Miles/Hour Scenario #4, the person on the moving sidewalk forgets something and walks the other way at 2 mph; the sidewalk is moving Resultant velocity • In each scenario, there were two objects that had velocities compared to two different things • To get an overall velocity to the same thing, called a resultant velocity, you must combine the velocities Hurray!?! • The velocity formula you have seen so far is when there is no acceleration….the object has been travelling at a constant speed • But what about when the object is accelerating while it is moving? • Answer: Three new formulas! Again, but with acceleration • Position while accelerating • xf = xi + vit + ½ at2 • Velocity while accelerating • vf = vi + at • If you don’t know the time travelled but you do know the distance • vf2 = vi2 + 2ax • Note: the “f” in the subscript means final and the “i” in the subscript means initial Acceleration and velocity; the different effects • Note the difference in acceleration: https://www.youtube.com/watch?v=apoeGMWF17c • Another look; different race: https://www.youtube.com/watch?v=7rVTIpS5zb4 • One car can attain a much higher speed • The other car gets to its maximum speed sooner • If the race would have continued • The winning car would continue travelling at a constant, but fast velocity • The losing car could continue to accelerate until reaching its much higher velocity; Eventually, the losing car would have passed the winning car Hints, tips, and tricks • Physics problems are know for having many different number quantities • It is suggested that you: • Draw or sketch a picture and then label it with the information • You might be surprised how it helps keep the problem organized • Pick a frame of reference that makes it easiest on you • Use the simplest formula that works for the information that you have and need Vertical motion • If we are talking about vertical (ie up and down) motion instead of horizontal motion, we keep the same formulas but make some changes • First, we switch the letter x (for the x-axis) with the letter y (for the yaxis) • Example: v=Δ x/t becomes v=Δ y/t • Next, we’ll look at acceleration “g, I didn’t know that” • Gravity is always “pulling” on objects • The average acceleration of gravity near the Earth’s surface is 9.81m/s2 • One of the most important numbers for you to memorize! • Instead of writing agravity or ag, we just write g = 9.81m/s2 • If there is no air resistance or any other forces acting besides gravity (like on the Moon, for example), an object is said to be in freefall Choices • When dealing with vertical motion, you need to decide which of the following you want to do • Treating the acceleration as positive in the up direction and negative in the down position • This is the traditional approach • Treating the acceleration as positive if it is in the same direction as the movement and negative if it is the opposite direction as the movement • The is the approach that I use Engines OFF • In the following example, a rocket lifts off from the launch pad • After expending its fuel, it continues flying higher but at a slower and slower rate (due to gravity) • Eventually, it gets to its highest point (also known as apogee) • It then falls towards the Earth at a faster and faster rate • In these types of problems, you must break the motion down into three parts: • Engines are firing • Engines are off and rocket keeps rising • Engines are off and rocket is descending UP Direction Velocity is positive; acceleration is negative Velocity is negative; acceleration is negative Velocity is positive; acceleration is negative Velocity is positive; acceleration is positive DOWN Direction Traditional Frame of Reference Pros and Cons • The advantage of the traditional system is consistency • The positive and negative direction stays the same • Zero is at the ground level • The advantage of the frame of reference approach • Easier (I think) to understand and use • CAUTION: You have to make sure that the sign of your distances & displacements match Magic Kingdom • In some ways, working out physics problems are like visiting a magical land • For example, in almost all problems, we pretend as if there is no air resistance (which means no air!) • Remember, that physics formulas describe idealized situations • If you take further physics classes, you will use more detailed calculations to more realistically model the real world