Your Weight on Other Worlds
(Interactive)
National K -12 Subject:
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In normal conversation, when we use the word “massive” we’re usually referring to how big something is. Scientifically speaking, though, “mass” isn’t related to size (or volume). Mass is related to how much an object resists changes to its state of motion. Though it’s true that, for a given density, more volume will mean more mass, some objects can be “small” - in the sense that they don’t take up a lot of volume - yet still have a lot of mass. (One example would be the dense material that makes up a neutron star.) Conversely, large objects can have low mass. Think about a mountain of granite versus a mountain of cotton candy. Both might have the same volume, but they have different masses. (And one tastes better, too.) An object with more mass requires more effort – more force - to get moving from a state of rest, or to stop once it’s in motion. That quality of being easy or hard to set in motion or bring to a stop is “inertia.” An object’s “inertial mass” is its resistance to being accelerated (or decelerated) by a force.
Gravitational Force
All masses near Planet Earth feel a gravitational force proportional to their mass: the bigger the mass, the bigger the gravitational force. The equation for gravitational force is: FG = Mass x Gravity = mg. The value of “g” (the strength of the gravitational field) is unique to each planet. While g here on Earth may be ~10 m/s2, on Jupiter, g ~25 m/s2 and on the Moon, g is only ~ 1.6 m/s2. And since the value of g changes based on the gravitational field strength, the gravitational force also changes. Neither an object’s state of motion nor its specific location impacts gravitational force. What matters is the value of g.
Weight
Gravitational force is associated with acceleration in the direction of that force. Simply put, an object subject to a gravitation force will “fall” in the same direction in which the force is acting. The force it takes to counteract and balance out that falling is the object’s “weight.” Unlike mass and unlike gravitational force, weight will change based on whether there are forces acting that increase or reduce the “upward” force necessary to balance out the “downward” gravitational force; for instance the buoyant force that helps an object float in water, making it weightless.
Another example of an object’s weight changing is due to it’s acceleration relative to the gravitational field. If an object is pushed upwards so that it accelerates up, it’s weight on the surface pushing it up will increase. Alternatively, if the object is allowed to fall, it’s weight will be reduced. For example, when you’re in an elevator, going over the top of a steep bump in your car or riding a roller coaster, your weight changes because you are experiencing an upward or downward acceleration, so your weight does not completely offset the gravitational force. In each scenario, your weight is the net force required to counteract the downward force such that you experience a certain acceleration, and that value can change even though the gravitational force remains the same.
Weightlessness
When astronauts are in the space station, their mass is the same as it is on Earth. The gravitational force on the space station - contrary to what many people think – is only slightly less than the gravitational force on Earth. The space station, and everything in it, is subject to Earth’s gravity. Indeed, that’s what keeps it in orbit. However, since the station and everything on it moves together around Earth, the space station and its contents are constantly falling towards Earth; they are in free fall. They never fall to Earth, since the curvature of Earth exactly matches the shape of the orbit, but they are constantly falling, nonetheless. The station and its contents are weightless since no force is exerted to counterbalance the gravitational force. Based on what it means for something to have weight, this explains why – despite having mass and despite being subject to a gravitational force – the astronauts are weightless. The condition of weightlessness on board the space station allows astronauts to conduct experiments and demonstrations that would be impossible to do on Earth.
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Classroom Activity: Car Design Lab
Students work in small groups to explore the relationship between mass and acceleration for different car designs. Student groups research actual technical data for specific cars to find respective masses, or that information is provided for them. (Note: Chart can be developed and provided.)
Students work through several scenarios for different cars (different masses) to explore the relationship between mass and acceleration for a given force (example: 3500 N) and then graph their results to quantify the relationship.
Discussion Questions
Bob: I mentioned earlier one of the properties of mass is that bodies with greater mass are accelerated less by the same force. We’re going to use a force that is provided by a tape measure. There’s a spring inside a tape measure and we will use that as a force to act on an empty bag of water, a full bag of water, and then we have a surprise guest that we’ll try to accelerate as well. And Koichi now will release the spring on the tape measure. Let’s see what happens to an empty bag of water. It accelerates very quickly so we see a body with a very low mass accelerates very rapidly. Let’s do the same thing now with a full bag of water. We’ll stretch the tape measure out to one meter. And now we’re ready to test the mass. So a full drink bag accelerates but at a lower rate than an empty bag. Let’s try one more object a little heavier, a lot heavier, than drink bag of water. I’m gonna ask Koichi to see if I can accelerate so I’ll be on one end of the tape measure and we’ll see if the spring will accelerate me. So I’m holding on to the end of the tape measure I’m gonna lift my feet off of the floor. I’m now free floating within the Japanese lab and very lowly the spring tape measure is pulling me toward Koichi. Much, much slower than the drink bag. But even large masses can be accelerated. So the principle there we wanted to show is bodies with a greater mass are accelerated less by the same force. The same force being the spring and the tape measure.
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