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QUESTION #6 Asked by: Terri If no air resistance is present, the rate of descent depends only on how far the object has fallen, no matter how heavy the object is. This means that two objects will reach the ground at the same time if they are dropped simultaneously from the same height. This statement follows from the law of conservation of energy and has been demonstrated experimentally by dropping a feather and a lead ball in an airless tube. When air resistance plays a role, the shape of the object becomes important. In air, a feather and a ball do not fall at the same rate. In the case of a pen and a bowling ball air resistance is small compared to the force a gravity that pulls them to the ground. Therefore, if you drop a pen and a bowling ball you could probably not tell which of the two reached the ground first unless you dropped them from a very very high tower. Answered by: Dr. Michael Ewart, Researcher at the University of Southern California The above answer is perfectly correct, but, this is a question that confuses many people, and they are hardly satisfied by us self-assured physcists' answers. There is one good explanation which makes everybody content -- which does not belong to me, but to some famous scientist but I can't remember whom (Galileo?); and I think it would be good to have it up here. (The argument has nothing to do with air resistance, it is assumed to be absent. The answer by Dr. Michael Ewart answers that part already.) The argument goes as follows: Assume we have a 10kg ball and a 1kg ball. Let us assume the 10kg ball falls faster than the 1kg ball, since it is heavier. Now, lets tie the two balls together. What will happen then? Will the combined object fall slower, since the 1kg ball will hold back the 10kg ball? Or will the combination fall faster, since it is now an 11kg object? Since both can't happen, the only possibility is that they were falling at the same rate in the first place. Sounds extremely convincing. But, I think there is a slight fallacy in the argument. It mentions nothing about the nature of the force involved, so it looks like it should work with any kind of force! However, it is not quite true. If we lived on a world where the 'falling' was due to electrical forces, and objects had masses and permanent charges, things would be different. Things with zero charge would not fall no matter what their mass is. In fact, the falling rate would be proportional to q/m, where q is the charge and m is the mass. When you tie two objects, 1 and 2, with charges q1, q2, and m1, m2, the combined object will fall at a rate (q1+q2)/(m1+m2). Assuming q1/m1 < q2/m2, or object 2 falls faster than object one, the combined object will fall at an intermediate rate (this can be shown easily). But, there is another point. The 'weight' of an object is the force acting on it. That is just proportional to q, the charge. Since what matters for the falling rate is q/m, the weight will have no definite relation to rate of fall. In fact, you could have a zero-mass object with charge q, which will fall infinitely fast, or an infinite-mass object with charge q, which will not fall at all, but they will 'weigh' the same! So, in fact, the original argument should be reduced to the following statement, which is more accurate: If all objects which have equal weight fall at the same rate, then _all_ objects will fall at the same rate, regardless of their weight.In mathematical terms, this is equivalent to saying that if q1=q2 then m1=m2 or, q/m is the same for all objects, they will all fall at the same rate! All in all, this is pretty hollow an argument. Going back to the case of gravity.. The gravitational force is
( G is a constant, called constant of gravitation, M is the mass of the attracting body (here, earth), and m1 is the 'gravitational mass' of the object.) And newton's law of motion is
where m2 is the 'inertial mass' of the object, and a is the acceleration. Now, solving for acceleration, we find:
Which is proportional to m1/m2, i.e. the gravitational mass divided by the inertial mass. This is our old 'q/m' from the electrical case! Now, if and only if m1/m2 is a constant for all objects, (this constant can be absorbed into G, so the question can be reduced to m1=m2 for all objects) they will all fall at the same rate. If this ratio varies, then we will have no definite relation between rate of fall, and weight. So, all in all, we are back to square one. Which is just canceling the masses in the equations, thus showing that they must fall at the same rate. The equality of the two masses is a necessity for general relativity, and enters it naturally. Also, the two masses have been found to be equal to extremely good precision experimentally. The correct answer to the question 'why objects with different masses fall at the same rate?' is, 'beacuse the gravitational and inertial masses are equal for all objects.' Then, why does the argument sound so convincing? Since our daily experience and intuition dictates that things which weigh the same, fall at the same rate. Once we assume that, we have implicitly already assumed that the gravitational mass is equal to the inertial mass. (Wow, what things we do without noticing!). The rest of the argument follows easily and naturally...Answered by: Yasar Safkan, Physics Ph.D. Candidate, M.I.T.
If someone drops two objects from the same height, one heavy, one light, which one will hit the ground first? If you are like most people, you may instinctively pick the heavier object. And why wouldn’t you? After all, rocks fall faster than feathers. There are other factors besides weight that affect the speed of an object as it falls. This experiment will help students explore those factors, such as gravity and air. Students will use both their eyes and their ears to figure out how mass affects the speed at which something falls. For more information and ideas on how to implement the activity in your classroom check out the video. Key TermsMass: A measure of the amount of stuff (or matter) an object has. Not to be confused with weight or volume. Mass only says how much actual stuff there is, not how big an object is or how hard something is pulling on it. Weight: Mass (amount of stuff) times how hard the planet is pulling on it (gravity). This means that your weight on the moon will be 1/6 of that on Earth (gravity on the moon is 0.166 times of that on Earth). However, your mass will still be the same. Force: The push or pull an object feels because of interactions with other objects. If the interaction stops, then there is no force. It is formally defined as mass times acceleration. For example, gravity is a force that represents the pull the Earth has on all objects. Velocity: A measure of how fast something is going in some specific direction. Not to be confused with speed, which is only how fast something is moving. “The car was going 65 mph south on I-95” is a measure of velocity. “The rollercoaster was moving at 65 mph when Billy got sick” is a measure of speed. Acceleration: How fast the velocity is changing. When something accelerates it changes how fast it is going or the direction in which it is moving. For a positive change in acceleration means that the object is moving faster, a car going from 30 mph to 40 mph. A negative change means the object is moving slower, the car is going from 40mph to 30 mph. Finally, a change in the direction of the object’s velocity without changing speed, such as if a car is moving North and turns East still moving, then the car accelerated because the direction of the car’s velocity changed. Remember that velocity is a vector with direction and magnitude, therefore changes in any (or both) of those factors will produce an acceleration. Air resistance: The force air exerts on something moving through it. When an object with a bigger surface falls through air, it feels more air resistance. Air resistance does not depend on the mass of the object. KEY QUESTION:How does mass affect how fast an object falls?Before the activity students should know: Gravity from the Earth makes things fall by pulling objects toward the ground
AFTER the activity students should know:
The Science Behind Falling ObjectsIf someone showed you two spheres of the same size but with different masses, say 1g and 10kg, and asked which would hit the ground first after being dropped from the Leaning Tower of Pisa, what would you say? If you’re like most people, you would say the 10kg sphere would hit the ground first. Aristotle said so too, and for 1,000 years everyone believed him. But doing the experiment would show you, besides a great view of Pisa, that in fact, both spheres hit the ground at the same time. This is exactly what Galileo did, showing the world that objects of different masses fall at the same rate. (This is also a good example of why it is important to do experiments yourself and not to just take someone else’s word for it.) To start understanding why Galileo was right, we need to understand the difference between several physics words that are often jumbled together and confused: mass, weight, speed, velocity, acceleration, and force. Let’s start with mass and weight. Mass is the amount of stuff an object has. Mass and weight are not the same thing: the mass of an object will stay the same no matter where it is in the Universe, but weight will not. If I had some amount of stuff, say an apple, and took it from the Earth to the Moon, I would still have the same amount of stuff: one apple (assuming I didn’t get hungry on the trip). No matter where I put that one apple, I will always have the same amount of apple, unless I eat it. This means that here or on the Moon, my apple has the same mass. Mass has the unit of kilograms. Now, weight is the amount of mass times the force of gravity, or how hard a planet is pulling an object towards itself. Going back to our apple, that apple would be a lot easier to lift and put in my mouth on the Moon than on Earth, right? The Earth pulls on the apple harder than the moon would, because the pull of the Earth (gravity) is stronger than that of the Moon. Even though I have the same amount of stuff, the same mass, the weight of my apple is greater on Earth than it is on the Moon. Weight is mass times acceleration, this acceleration is from the gravity force that pulls the objects toward the ground. Weight has the unit of Newtons, which is the units of mass (kilograms) times the units of acceleration. But how do we sometimes get units of mass when we ask for the weight of things? That is because the scales we use to measure weight factor in the acceleration of the pull of the Earth on the object. This factor is a constant on the Earth, meaning that it is always the same if you are on Earth. If I were on the moon and my apple weighs .25 Newtons, I will need to know the value of the acceleration of gravity on the moon to find its mass. Now on to velocity, speed, acceleration and force. Velocity and speed are two different things, but the difference is very small. Velocity gives more information than speed does, because it tells us how fast something is moving in a specific direction. Speed is how fast something is going, but says nothing about the direction of that motion.. Acceleration says how much the velocity is changing in a specific direction. If something has a constant velocity, say moving south at 65 mph, there is no acceleration. Now how can you make something accelerate? To accelerate, an object needs to feel a force, that means a pull or a push. If you kick a football with some amount of force, the football is going to change its velocity, which means it’s accelerating. Force is mass times acceleration. This means that force is the amount of stuff times how hard it is being pushed or pulled. The bigger the force (the stronger the kick), the bigger change in the football’s acceleration, since its mass doesn’t change. When something falls, it falls because of gravity. Because that object feels a force, it accelerates, which means its velocity gets bigger and bigger as it falls. The strength with which the Earth pulls on something in the form of gravity is a type of acceleration. Earth pulls on everything the exact same amount. Everything gets accelerated towards the Earth exactly the same way. The force that objects feel may be different because they have different masses, but the acceleration on Earth they experience is exactly the same. Weight is the force that acts on the mass due to gravity, because it is how much stuff there is times the acceleration at which is pulled towards the Earth, or any planet or moons. Because Earth gives everything the exact same acceleration, objects with different masses will still hit the ground at the same time if they are dropped from the same height. The first time you say that, no one will believe you because everyone has dropped a marble and a feather at the same time and they hit the floor at different times. That is not because of differences in the acceleration - which is constant on Earth, it is because air is pushing against the object in the opposite direction the Earth is pulling. This force is caused by air resistance. Astronaut Neil Armstrong did an experiment on the moon to convince everyone that Galileo was right, that two objects of different mass and shape -in this case a feather and a hammer - in the absence of air resistance will hit the ground at the same time. Experiment 2 that you will be performing, two objects of different masses that roughly experience the same air resistance will be dropped and hopefully convince your kids that mass has nothing to do with how things fall. Experiment 1Materials
In the student’s guide we have asked the students to design their own experiment to test if two objects of the same mass but different shape hit the ground at the same time. The idea is to encourage them to be creative, to understand how to design experiments, and to think like scientists and engineers. They are given a set of materials that they can use to do their experiments. This is to prompt them, but they should be allowed to use other materials in their design. As the teacher, you can ask prompting questions to get them to think about the different aspects of the experiments. Below are the full instructions for one possible design. The goal of the experiment is for students to understand that mass is not a factor that affects how objects fall, that they notice the shape matters and why it matters. Crumpling the paper or changing the direction in which the paper is dropped can support those ideas. They need to figure out which variables they should control for, for example dropping the papers at the same time or the presence of a strong air current, and consistency of the repeated experiments. We ask the students to follow the scientific method to design the experiment. The scientific method has five basic steps, plus one feedback step:
Setting up
Students should reflect on how the masses of the two pieces of paper were the same, yet the crumpled piece hit the ground first. Why? Experiment 2For this experiment students are asked to design a way to test if two objects of different mass but similar shapes hit the ground at the same time. They have been given a different set of materials from Experiment 1. In this case there are other variables to control for, such as how similar or different shapes affect the result and the difference in mass between the two objects.If the mass is double but the shape is the same, will the objects hit the floor at the same time? As with Experiment 1, we have given you a possible set up for the experiment. But again, students should have freedom to create their own designs. Materials
In the kit there are different sets of balls, repeat the experiment with all the possible wooden and rubber balls combinations. Make sure to label the balls and measure them to make good comparisons. If you are working at home and do not have the exact materials, you can always substitute the balls with clay or playdough (see suggested resources for a recipe of homemade playdough). If you do not have either clay or playdough, then find two objects around the house that have the same shape but different weights. For example, two identical water bottles, one full and the other one with less water or no water. The purpose of this experiment is to test if objects with different masses but the same shape fall at the same time. Instead of aluminium tart pans you can use aluminum foil or any other type of paper/foil that will produce a sound when the dropped objects hit them. As with activity 1, we ask the students to follow the scientific method to design the experiment. Setting up
Students should pay attention to how many bangs they heard each time they dropped the balls. Did it depend on how different the masses of the balls were? Which ball hit the floor faster? Next Generation of science standards: 5-PS2-1. Support an argument that the gravitational force exerted by Earth on objects is directed down. MS-ESS1-2. Develop and use a model to describe the role of gravity in the motions within galaxies and the solar system. Corresponding Extension Activitieshttps://colab.research.google.com/drive/1zTsyJ5SZ8bFXugZMmCT0pUtRWgf0pXcg?usp=sharing https://colab.research.google.com/drive/1rliGPMBM7Ixy97Z0xpzADKcq4_aRzqIS?usp=sharing Suggested Resources Videos for younger children Gravity & Free Fall Danger! Falling Objects Simulations & Videos: Was Galileo Right?: Investigate the effect of gravity on objects of various masses during free fall. Predict what the position-time and velocity-time graphs will look like. Compare graphs for light and heavy objects. Free Fall Model: This simulation allows students to examine the motion of an object in free fall. Free Fall Fall Air Resistance: This simulation allows students to compare the motion of free falling objects with and without the influence of air resistance. Veritasium: Misconceptions About Falling Objects 3.5-minute video |
What would happen to two falling bodies of different masses when they are released from the same height near the surface of Earth and why?
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