Velocity Velocity Velocity is how fast something is going and in what direction it is going. Direction is what separates the term velocity from speed. If we were talking about a car, we could say that car is traveling with a velocity of 30 miles per hour due East. We will basically just be using the speed aspect of velocity, since for our purposes, the directional aspect confuses things more then necessary. There is another term that is useful here and that is terminal velocity. The term terminal velocity is normally used when something falling cannot gain any more speed because the air resistance pushing against that something is equal to the force of gravity pulling down on that something. When those two forces are equal (air resistance/friction and gravity) and in opposite directions from each other, the falling object stops accelerating and stays at the same velocity. (We will discuss force and acceleration next lesson.) This is why feathers drop so much more slowly than bowling balls. A A. B. C. A. When Phillip jumps out of the plane with no parachute, the force of gravity pulls much stronger then the force of friction so Phillip speeds up. B. When the parachute is opened, gravity is still a bit stronger then friction so Phillip still speeds up but not as much. C. Now the force of gravity and friction are equal. Since there is zero net force, Phillip s speed is now constant. He s not speeding up or slowing down. He s reached terminal velocity. 1
feather has a very large amount of air resistance and gravity pulls very lightly on it (the feather is very light). The amount of friction force quickly equals the amount of gravitational force and so the feather accelerates only a small amount, gains little speed and drops nice and easy. The bowling ball has very little air resistance and gravity pulls pretty hard on it (the bowling ball is heavy). A bowling ball can accelerate quite a bit and gain a lot of speed before the force of air resistance pushing up equals the force of gravity pulling down. Quick quiz, how fast does gravity accelerate things? If you said 32 ft/s2, 9.8 m/s2 or 22m/h2 you win!!! Let s play with velocity a bit and see if this becomes more clear. Experiment 1 Look Out Below!! You need: Stop watch Feathers, small pieces of paper, plastic bag or anything light and fluffy Tape measure Calculator This experiment will help you get the concept of velocity by allowing you to measure the rate of fall of several objects. 1. Get 5 or so different light and fluffy objects. Feathers of different size, small strips of paper, parts of a plastic bag, cotton balls, whatever is handy. 2. Make a hypothesis by writing down the objects you chose in order of how fast you think they will fall. The fastest on top, the slowest on the bottom. Leave space to the right of your hypothesis so that you can write in your conclusions and then compare the two. 3. Make a table with two columns. Use one column to fill in the name of the items. Use the second column to write down the time it took each object to fall. 4. Drop the different items and time them from the moment you let go to the moment they hit the ground. Be sure to drop each item from about the same 2
height. The higher the better. Just be sure not to fall off anything! We don t want to measure your velocity!! You might want to drop them two or three times to get an average time. 5. Now compare the items. Which one fell the least amount of time (dropped the fastest)? Which one fell the most amount of time (dropped the slowest)? Write your results next to your hypothesis. By the way, did you find anything that dropped slower than a feather? I have seen very few things that take longer to fall straight down than a feather. Did you see how your objects stopped accelerating very quickly? In other words, they reached their terminal velocity soon after you let them go and they fell all the way to the ground at that same constant velocity. This is why a parachute is a skydiver s best friend! A human has a decent amount of air resistance but he or she can reach a lethal dose of velocity if dropped from a great height. The parachute increases the air resistance so that the terminal velocity of that sky-diver is quite a bit safer! If you wish, we can do a little math here and figure out the actual velocity of your objects. Measure the height from which you dropped each object. Now take the height of the drop and divide that by the number of seconds it took for it to drop that distance. That s the velocity of that object. For example, My from-under-thecouch-six-month-old-dust-bunny took 3 seconds to fall 6 feet. I take 6 feet and divide it by 3 seconds to get 2 feet/second. The velocity of my dust bunny is 2 feet/ second downward. Remember, that velocity has a directional component as well as a number. Add a little more math, and I can predict how long my dust bunny will take to fall 15 feet. Take the distance (15 feet) and divide it by the velocity (2 feet/ second) and I get 7.5 seconds. It will take my dust bunny 7.5 seconds to fall 15 feet. Hmmm, maybe we should call it a dust snail. Have you noticed something here? In the last lesson, we used a different formula to find out how far something would fall over a given time. What s going on? Well last month we ignored their terminal velocity. Those things were accelerating (gaining velocity) all the way to the ground. They were never going the same velocity for the entire trip. So, we needed to use the gravitational constant 32 ft/s2 in the equation d=1/2 gt2 to determine how far something fell in a given amount of time. This month we are dealing with things that are at an almost constant velocity, (since 3
they reach their terminal velocity quickly) so we can use the much simpler equation d=vt (d is distance, v is velocity and t is time). In the problems we ve done in this lesson plan, we have modified that formula to find how long the fall took so we ve used t=d/v. If you d like to solve for v you would use v=d/t. Isn t algebra fun! In a Nutshell Velocity is the speed and direction of an object. Terminal Velocity is when something cannot gain any more speed because the friction pushing against that something is equal to the force of gravity pulling down on that something. You can find how far something falls by using the formula d=vt or distance = velocity times time. 4
Did You Get It 1. What is velocity? 2. What s the difference between speed and velocity? 3. What is terminal velocity? 4. Why do feathers have a low terminal velocity? 5. Why do bowling balls have a high terminal velocity? 5