Local Gravity, Local F G Any planet’s mass exerts a significant force on

1. Local Gravity, Local FG Any planet’s mass exerts a significant force on any other mass—such as you. If you let that be the net force—the only force acting on you (i.e. you step off a roof and become a projectile)— you know what happens. And here’s the math (and we’re letting downward be the –y-direction): SFyou.y = myouayou.y –FG.earth.you = myouayou.y And we have carefully (and repeatedly) measured the magnitude of freefall acceleration (for any body): It’s g (= 9.80 m/s2 at the earth’s surface. That is, ayou.y above is –g. So: –FG.earth.you = myou (–g) The force by gravity on any mass m is FG = mglocal.* *Of course, glocal varies according to the planet and your location relative to it. (you) FG.earth.you Oregon State University PH 211, Class #15

2. Weight We know what mass is. And we know what gravitational force is. So, what is weight? Weight is a force—a vector quantity—measured in pounds (English), newtons (SI), dynes, ounces, tons, etc… Your weight is the negative of the sum of all contact forcesacting on you (i.e. all forces except gravity). Your weight can be indicated typically by a scale upon which you stand, sit, or hang. So, essentially, your weight magnitude is the measure of how much support you’re receiving to oppose FG. Clearly, then, your weight can change with the circumstances. What factors affect any object’s weight? Its mass, its location, and its acceleration. Try some examples—and be sure to use an FBD and the related equations for each of these.… Oregon State University PH 211, Class #15

3. Your weight in an elevator Suppose you’re an 80-kg person standing on a scale in an elevator. For each of these cases, calculate your weight—that’s the reading on the scale (i.e. it’s the force with which the scale is pushing on you to support you against gravity. For simple numbers, let g ≈ 10 m/s2. — The elevator is stationary. — The elevator is accelerating upward at 2 m/s2. — The elevator is accelerating downward at 2 m/s2. — The elevator is moving upward at a constant 5 m/s. — The elevator has broken cables and brakes and is plummeting downward in freefall. (The solutions are in the After Class 15 materials.) Oregon State University PH 211, Class #15

4. Weightlessness A person can certainly be weightless in a location with no gravity. (Where would that be?) But a person in a state of freefall is also weightless. Even if a scale is present, it won’t push/pull on you if you’re in freefall. But notice: For an object in freefall, gravity is clearly still present! FG is not zero in this case. So how/why are astronauts weightless when in orbit around the earth? Oregon State University PH 211, Class #15

5. A cannon on a mountaintop fires a shell parallel to the ground. The shell leaves the cannon and is thereafter pulled toward the ground by gravity. It is a projectile, essentially. If the shell leaves the cannon with a low velocity, it falls to the ground near the mountain. With a higher velocity, it falls farther from the mountain. Orbital Motion and Gravity:Newton’s Thought Experiment Oregon State University PH 211, Class #15

6. So, what if the shell is traveling so fast, that for every foot it falls, the Earth also curves away from it by one foot? The shell will be forever falling—never landing. It will be in orbit! Being in orbit is being in a state of freefall—being a projectile. The Moon, in orbit, is forever “falling” to the Earth. Likewise, astronauts in orbit are in freefall, and are thus in a state of weightlessness. The same is true for any planet, moon, comet, asteroid, or other satellite in orbit around any other body. Oregon State University PH 211, Class #15

7. Gravity for spacecraft in orbit? YES. There’s still strong gravity for the astronauts in orbit. Otherwise the spacecraft wouldn’t stay in orbit. At the altitude of the space shuttle’s orbit, for example, the strength of gravity is about 90% of that on the earth’s surface: gorbit ≈ 8.7 m/s2 Oregon State University PH 211, Class #15