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MASS vs. WEIGHT Weight is a measurement of the force on an object caused by gravity trying to pull the object down. Mars has less gravity than Earth. Therefore if you were on Mars you'd weigh less because the force of gravity wouldn't be as strong as it is here on Earth. Does this mean you would suddenly be thinner on Mars? No. You would have the same amount of mass as you do on Earth. (Mass is the amount of stuff inside an object.) So, on Mars, your mass would be the same as it is here on Earth. But you'd weigh less because Mars has less gravity than Earth. Gravity is an attractive force between all objects. This doesn't mean it's pretty. What "attractive" means is that an object's gravity pulls other objects toward it. The Earth's gravity naturally pulls us, and everything else, toward the center of the planet, which keeps us from drifting off into space. An important aspect of gravity is its relationship to mass and the distance between two objects. A massive object is capable of exerting more gravitational force than a small one, and it is the strongest between closely-placed objects. All objects in the universe (stars, planets and satellites) have gravity, but its value varies from one object to another. The Earth isn't the only thing that has gravity. In fact, every single object in the universe has gravity. The tables you're sitting at have gravity. They are pulling you towards them. You have gravity, and you are pulling the tables towards you. We can't see or feel these things happening because people and tables have such a small mass that the effects of gravity cannot be seen. Mass is the amount of stuff contained inside an object. It takes a lot of mass to make a lot of gravity. The Earth has a lot of mass, so it has a lot of gravity. The moon's gravity is about 1/6 the amount of the Earth's because the moon has less mass than the Earth. So what does all this have to do with weight? Well, weight is the force on an object caused by gravity trying to pull the object down. A scale measures how much gravity your mass has. A person with more mass has more gravity, and therefore weighs more. You've probably seen video footage of astronauts walking on the moon. They seem to float between each step. Remember that the moon has about 1/6 the amount of gravity that the Earth has? Well, if you went to the moon, you'd weigh less than you do here on Earth. Does this mean you would suddenly be thinner on the moon? Absolutely not. Your mass would be the same -- there is no less of you on the moon. But your weight is different because the moon's gravity is different. Mass and Weight Learning physics is learning the connections among the concepts in nature, and also learning to distinguish between closely related concepts. Velocity and acceleration are often confused. Similarly, we find that mass and weight are often confused. They aren’t the same! Please review the distinction between mass and weight discussed in class. To reinforce your understanding of this distinction, circle the correct answers below. 1. Comparing the concepts of mass and weight, one is basic - fundamental – depending only on the internal makeup of an object and the number and king of atoms that compose it. The concept that is fundamental is [mass] [weight]. 2. The concept that additionally depends on the amount of matter in an object and only depends on the location in a gravitational field is [mass] [weight]. 3. [Mass] [Weight] is a measure of the amount of matter in an object and only depends on the number and kind of atoms that compose it. 4. We can correctly say that [mass] [weight] is a measure of an object’s “laziness.” 5. [Mass] [Weight] is related to the gravitational force acting on the object. 6. [Mass] [Weight] depends on an object’s location, whereas [mass] [weight] does not. 7. In other words, a stone would have the same [mass] [weight] whether it is on the surface of the Earth or on the surface of the moon. However, its [mass] [weight] depends on its location. 8. On the Moon’s surface, where gravity is only about 1/6 of Earth’s gravity, [mass] [weight] [both the mass and the weight] of the stone would be the same as on Earth. 9. While mass and weight are not the same, they are [directly proportional] [inversely proportional] to each other. In the same location, twice the mass has [twice] [half] the weight. 10. The Standard International (SI) unit of mass is the [kilogram] [newton], and the SI unit of force is the [kilogram] [newton]. 11. In the United States, it is common to measure the mass of something by measuring its gravitational pull on Earth, its weight. The common unit of weight in the U.S. is the [pound] [kilogram] [newton]. When I step on a scale, two forces act on it; a downward pull of gravity, and an upward support force. These equal and opposite forces effectively compress a spring inside the scale that is calibrated to show weight. When in equilibrium, my weight = mg. Converting Mass and Weight Objects with mass also have weight (although they can be weightless under special conditions). If you know the mass of something in kilograms and want its weight in newtons, at Earth’s surface, you can take advantage of the formula that relates weight and mass: Weight = mass X acceleration due to gravity W = mg This in accord with Newton’s Second Law, written as F = ma. When the force of gravity is the only force, the acceleration of any object of mass m will be g, the acceleration of free fall. Importantly, g acts as a proportionality constant, 9.8N/kg, which is equivalent to 9.8 m/s2. Sample Questions: How much does a 1-kg bag of nails weigh on earth? W = mg = (1 kg) (9.8 m/s2) = 9.8 N Answer the following questions: Felicia the ballet dancer has a mass of 45.0 kg. 1. What is Felicia’s weight in newtons at Earth’s surface? __________ 2. Given that 1 kilogram of mass corresponds to 2.2 pounds at Earth’s surface, what is Felicia’s weight in pounds on Earth? __________ 3. What would be Felicia’s mass on the surface of Jupiter? __________ 4. What would be Felicia’s weight on Jupiter’s surface, where the acceleration due to gravity is 25.0 m/s2? __________ Different masses are hung on a spring scale calibrated in newtons. The force exerted by gravity on 1 kg = 9.8 N. 5. The force exerted by gravity on 5 kg = __________ N. 6. The force exerted by gravity on __________ kg = 98 N. 7. Make up your own mass and show the corresponding weight: The force exerted by gravity on __________ kg = __________ N. Gravity?…Depends on Where You Are! Gravity is the attraction between all objects, but it is most significant in the case of massive bodies. Sir Isaac Newton first developed the concept of gravity. He understood that gravity varies based on both mass and the distances between the attracting objects. That means that a MASSive object is capable of exerting more gravitational force than a smaller one, and the closer that two objects are to one another, the stronger the gravitational pull is. Gravity is not a peculiar property of the Earth. All objects in the Universe (stars, planets and satellites) have gravity. However, an important aspect of gravity is its relationship to mass and weight. An object’s mass is the amount of matter that it’s made up of and it’s the same everywhere — e.g., on the Earth, on our, Moon on the ISS, etc. On the other hand, the weight of an object varies with the value of gravity — it is heavier in places where gravity is higher (stronger) and lighter in places where gravity is lower. Today you will explore gravity only on our planet, Earth. Class, meet our good friend gravity, whom we will call “g.” Activity Part A: How much would you weigh on other planets and the moon? Location Weight on Earth Gravity Calculated Weight Moon x 0.17 Mercury x 0.38 Venus x 0.86 Mars x 0.38 Jupiter x 2.87 Saturn x 1.32 Uranus x 0.93 Neptune x 1.23 Gravity?…Depends on Where You Are! [ 7 ] Part B: How far could you jump on other planets and the moon? • Determine how far you can jump on the Earth. To do this, place a piece of tape on the floor as a starting line. • Jump as far as you can off of both feet. Have your partner mark where you land not where you end up! • Measure the distance and record in the table. Do this five times then find the average. Jump 1 Jump 2 Jump 3 Jump 4 Jump 5 Average • Use the table below to figure out how long you would have jumped on other planets. Location Length on Earth Gravity Calculated Length Moon ÷ 0.17 Mercury ÷ 0.38 Venus ÷ 0.86 Mars ÷ 0.38 Jupiter ÷ 2.87 Saturn ÷ 1.32 Uranus ÷ 0.93 Neptune ÷ 1.23 Gravity?…Depends on Where You Are! [ 8 ] 1.
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