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The Big G In 1665, Isaac Newton saw that all matter was attracted by all other matter. He tested this theory he had made with objects that were huge like the earth, moon and sun. Henry Cavendish then measured tiny gravitational pools using two small spheres on a wire, then bringing in a larger one to watch the wire move. For the dependence on mass and separation, Newton found that if you double the space on something, there force is divided by four. This equation can be made: F is proportional to (M1M2)/R2. The big “G” is important because by knowing “G,” we can find the mass of the earth by measuring the radius of the moon’s orbit and the length of one of the months, or by finding the acceleration of gravity on earth. We can also find the suns mass by finding the earths orbit around the sun and the year. Science is marching ahead because scientists are expecting to get even more accurate as time passes, and we use new technology. Accuracy of the “Big G” has gotten ten times more accurate already since 1987, from .013% error to .0015% error. Fluids In Space Micro gravity allows people to feel weightless, like inside an orbiting space station, it is called microgravity because “due to small residual accelerations of the spacecraft, including aerodynamic drag, vehicle rotation, and venting of gases.”We study fluids in space because understanding how fluids act without gravity may help scientists and engineers to better apply fluid on earth, which will change applications like engines, powerplants etc. Vomit Comet The aircraft that simulates microgravity by flying in a parabolic arc for around 25 seconds. What Happens to a Candle in Space? It goes out because there is no oxygen. What happens when water boils in space? The bubles start to rise, but continuosly rise until they are stopped by an outside force. What are gravity Waves? Stars that spin around each other release waves that travel the speed of light and are called gravity waves. The Velocity Addition Problem It asks “Given U and V', what is V?” It uses the distance from the moving thing to the non moving, and another moving object to the non-moving one. Why was the special Theory of Relativity Needed? When scientists found out that the speed of light was constant in every direction, it brought up problems with the Newtonian model from measuring time. Time is relative. Each person sees time as slightly different, which opened up the possibility of time travel through wormholes and blackholes. What is the Relativistic velocity addition formula? V = U + V' Space must be relative too. If we want to make a math model for spacetime that is consistent to the observed speed of light, “the measurement of space and time is not the same for all observers.” What is Gravity? Objects fall because of the gravity on earth. Constant G is called Newton’s gravitational constant. Fmoon/Fearth = (Mmoon/Mearth) (Rearth2/Rmoon2) is the formula for the gravity on the earth vs the moon. Oscillation and Gravity: Intro 1. The amplitude of the movind spot is 5.0 meters. The peg is moving around the center at a constant 1.5 rad/s Where is the spot 2.5 seconds after starting from positive x axis? A: -4.1 2. How long would it take for the spot to travel all the way from the far right side to the far left side? A: 2.09 Sec 3. Do you suppose the spot in the first question was moving to the left or to the right after 2.5 seconds? A: Right 4. What is the velocity of the spot 1.0 seconds after it has started at its maximum amplitude on the right if the amplitude is 4.8 meters and the wheel rotates at 2.0 rad/s? A: -8.7 m/s, position is -2.0m 5. What is the acceleration of the spot on the x axis at t=1.2 seconds? The amplitude is 3.0 meters and the angular velocity, w, is 0.75 rad/s? A: -1.0 m/s2 Gravitational Law 1. What is the attractive force between two students of masses 50kg and 75 kg sitting one meter apart from each other? A: 2.5x10-7 kg m/s2 2. Find the value of g that the moon experiences due to the earth. A: 2.7 x 10-21 kg m/s2 3. After reordering a set of 4 balls with the same diameter but slightly different but slightly different densities, a scientist has mixed them up again. She now wished to reorder these balls according to their densities by using gravitational forces to compare their masses to a reference ball B0, of mass m0. The only specific information she remembers regarding the balls is that at least one is identical to B0. A: Blue < Green < Grey = Red > 4. Find the magnitude of the force on a particle of mass 20 g located at a point A, 5m away from the center of the sphere, and a particle of the same mass at point B on the surface of the sphere. A: FA=0.053 x 10-11N FB=1.33 x 10-11N 5. What is the force on a particle of mass 20 g, inside the sphere 0.4m radially onward from the surface? A: 8.0 x 10-12N

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