Projectile+Motion

= Newton's Second Law of Motion and Projectile Motion = Seth McNaughton - __ slm5478@psu.edu __ Clint Mills - __ cbm5073@psu.edu __

__Standards__ o Motions and forces § An object that is not being subjected to a force will continue to move at a constant speed and in a straight line. § If more than one force acts on an object along a straight line, then the forces will reinforce or cancel one another, depending on their direction and magnitude. Unbalanced forces will cause changes in the speed or direction of an object's motion. o Identify and explain the principles of force and motion.
 * Grade 7 - Newton's Second Law of Motion and Projectile Motion**
 * National Science Content Standard D (page 154)
 * Pennsylvania 3.4.7.C

__Objectives__
 * Students will be able to understand the relationship between force, mass, and acceleration
 * Students will be able to explain why things fall at the same rate

__Big Idea__ Isaac Newton made three quite genius laws of motion. The first says that a body at rest stays at rest unless an outside force acts upon it. A force is anything that pushes or pulls on an object. This can be anything from a hand or a table holding your pencil, to the object's weight (the force of Earth pulling on the object) or even wind. The second law says that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the mass of the object. So the more force that acts on an object, the more it accelerates. In the same way, the more massive an object, the less it accelerates. In a mathematical sense, this says that force = mass x acceleration, or F=ma. The force of gravity is Fg=mg, where g is the gravitational constant of acceleration (9.8 m/s2). If objects are in free-fall (gravity is the only force acting upon the object), then mg=ma, and the acceleration of the object is g. Because of this relationship, we can determine the motion of objects. If we drop two objects simultaneously, we know that they fall with the same acceleration - hitting the ground at the same time. Some objects fall noticeably slower than other objects because of air resistance, which is a force. In the case of two balls, the spherical shape helps negate air resistance. The goal of this lesson is not to look into air resistance, but to explore the situations when air resistance is negligible. Displacement (like distance) is which direction and how much different in location an object is from one time to another. Velocity (like speed) is both what direction and how fast an object is traveling at a given time. Acceleration is in what direction and how quickly and object is changing velocities. So an object that starts at rest and constantly accelerates more quickly than another object will have both a higher velocity and a greater displacement at a given time. Using the ball launcher, we can see that a ball that falls straight down hits the ground at the same time as one that was shot directly horizontal. This is because the vertical component of the acceleration is equal. The force that launches the ball in the horizontal direction only creates horizontal acceleration. After showing that the balls fall at the same rate, we can look into how objects of different mass go different distances in this constant time that objects fall when "dropping" from the same vertical height, but are launched horizontally with a force that does not change depending on the mass of the object being launched (some would say a constant force). If we look at Newton's Second Law of Motion again (F = ma), we realize that because force is constant, mass and acceleration are inversely proportional. The greater the mass (m), the smaller the acceleration (a). The smaller the acceleration, the smaller the horizontal displacement. After running a few tests with different masses and measuring the proportional horizontal displacement, we can essentially calculate the force that the ball launcher has. This allows us to estimate the horizontal displacement of an object of known mass before launching the ball.

__Administrative Considerations__ The projectile launcher will be pointed toward a wall in order to not disrupt any other students. Students will not be permitted to lift or transport the ball launcher or point it at any other students. Students will be able to see that the balls fall at the same speed as one that is horizontally launched. This is a concept that can be conveyed and will be a visual explanation for learners. This can help ESL students who do not know much English or visual learners in general.

__Materials__
 * 4 small balls/objects of different masses
 * Balance
 * Projectile Launcher
 * Computer with Microsoft Excel (only used for pre-programed kinematics equations)
 * Table/Desk to launch from
 * Meter stick
 * Masking tape
 * Carbon Paper (1 for each time a lesson is taught)
 * Crayons/Markers

__Set-Up__ For the first experiment in which the one ball is dropped and the other is launched, the launcher should be placed so that nothing interferes with the falling of either ball. It would be a good idea to launch the ball toward a wall or a corner if possible in order to contain the projectiles that like to bounce away. The ball launcher should be placed on the desk so that the projectile end faces off the desk for the mass vs. acceleration experiment. For this experiment, carbon paper will be placed on the ground (and taped down to prevent from sliding) in order to help distinguish the tick marks where the ball lands. This will be used to determine the horizontal distance traveled (measured with the meter stick). The written excel program will calculate the estimated distance for the new mass after the other distances have been recorded.

The students can estimate where they think the ball will land after they know its mass (using their own color if they prefer), and then we can mark down where the equation predicts the mass to land. The meter stick is used to measure the distance each mass travels.

__Body of the Lesson__ a) **Engagement**: (7 min) o If the force is constant, and we used a bigger mass, would acceleration increase or decrease. (Decrease - think about if you're throwing something really heavy, like a huge rock. Can you throw that as far as a baseball?) o So what's a force again? Exactly, something that pushes or pulls an object o What's acceleration? - The change in velocity (or speed) of an object o Take this block for example that is at rest on the table. What are the forces acting on that object? (The table PUSHING the block up and gravity PULLING the block down. These forces balance causing zero acceleration. o Let's find out! o What did you notice? (Should be that they hit the ground at the same time, this could be a misconception) o Explain that although there is a force that launched the one ball, it did not launch it up or down, so the ball only received acceleration in the horizontal direction. Because there was no other force, the ball fell vertically like it was in free fall.
 * What is a force? (Not the Force, that's something different from Star Wars...): Whichever student answers something along the lines of a push or a pull, go along with that and explain that a force is anything that pushes or pulls something. This can be your hand, an object's weight (because it's pulled by the Earth's mass), the table pushing back on your pencil so it doesn't fall down, or even the wind.
 * Have you ever heard of Isaac Newton? Well he was a very smart man that came up with 3 famous laws of motion. The first is that a body at rest stays at rest unless an outside force acts upon it. Let's test that now. (Put a dice on the desk and closely inspect it). I didn't see it move, did you? Nope. What if we apply a force like our hand to it. Did that move? Yup. So that we can agree with that law.
 * Do you know what acceleration is? (Reinforce that acceleration is the change in velocity (or speed)). An analogy can be made to a car's 'accelerator' which makes the car go faster. The faster something goes, the further it goes in a certain time. So you and I are racing, and you're faster than I am, then you'll have run further if we both run for 20 seconds.
 * Newton's Second Law of Motion says that when a force acts on an object, it accelerates. In the same way, the more massive an object, the less it accelerates. In a mathematical sense, this says that force = mass x acceleration, or F=ma.
 * Check understanding
 * What happens if we move the block off the table and if we were to drop it, what are the forces then? - Just gravity PULLING down (though air resistance would be acceptable too).
 * A neat thing about gravity - all things fall with the same acceleration here at Earth's surface. So if we drop two things, they will hit the ground at the same time pretty much regardless of their weight. (Drop two balls, a ball and a dice, different weights, let them feel the weights).
 * What do you think will happen if we shoot one horizontally and let the other drop?

b) **Exploration**: (8 min) o First we need to use the balance to get the mass of the 3 objects. § Which object do you think will launch the furthest? Why? (Newton's second law, F=ma, constant F, so the larger mass must mean a smaller acceleration) o Second, we'll measure the height of the ball launcher (and make a mark on the carbon paper vertically below) o Third we'll launch each object and measure the horizontal distance traveled for each. (We'll put these values into the excel program as we go) o The fourth object: we can get the mass of it, and the students can take a guess where it might land and mark it with their own color. In another color we'll mark where the equations say it should land. o We can compare the actual result with the estimation.
 * We've seen that the projectile launcher shoots the object horizontally. Let's say we want to calculate where an object will land depending on its mass. Each time the spring is compressed the same amount and therefore shoots with the same force. So if we use the balance to get the mass of these three objects, and launch them and measure that distance, we can find the horizontal distance any object would travel before it flies.

c) **Explanation**: (3 min)
 * Why might it not be exactly right? (Perhaps need more test objects, more trials of the test objects, air resistance, etc)
 * If we wanted the heavier mass to reach where the lighter mass landed, what could we change? (More force, higher)
 * Say we were to have 4 ball launchers and we could launch all four objects at the same time. Would all four go the same distance? Would all four land at the same time? Why? (Gravitational acceleration is the same for all objects at Earth's surface)

d) **Evaluation**: (2 min).
 * We've seen that it's possible to determine where something will land if we know the force and the object's mass. How might this be helpful in real life? Expected answers: Sports (baseball, football, basketball, etc), weapons (missiles, cannonballs, etc.)
 * If you were able to shoot a basketball straight, with the same force every time, would it be possible to make a certain shot every time? (yes)

e) **Elaboration**: (2 min). o 1 pound = 0.454 kilograms o How many of the steel balls does it take to weigh the same as you? § If the ball launcher were to shoot an object with your mass, would you go very far? § Why?
 * If you drop paper and one of these objects, why do they not hit the ground at the same time? (Air resistance - which is a force) - In fact, David Scott proved this on the 1971 Apollo 15 mission. He dropped a feather and a hammer, and they both fell at the same speed.
 * __ [] __ (About 35 seconds in)
 * Convert your weight to kg!