Prove that Ω=V/A Note that: L=Length M=mass T=Time
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- We will use differential equations to model the orbits and locations of Earth, Mars, and the spacecraft using Newton’s two laws mentioned above. Newton’s second law of motion in vector form is: F^→=ma^→ (1) where F^→ is the force vector in N (Newtons), and a^→ is the acceleration vector in m/s^2,and m is the mass in kg. Newton’s law of gravitation in vector form is: F^→=GMm/lr^→l*r^→/lr^→l where G=6.67x10^-11 m^3/s^2*kg is the universal gravitational constant, M is the mass of the larger object (the Sun), and is 2x10^30 kg, and m is the mass the smaller one (the planets or the spacecraft). The vector r^→ is the vector connecting the Sun to the orbiting objects. Step one ) The motion force in Equation(1), and the gravitational force in Equation(2) are equal. Equate the right hand sides of equations (1) and (2), and cancel the common factor on the left and right sides. Answer: f^→=ma^→ f=Gmm/lr^→l^2 a^→=Gmm/lr^→l^2 x r^→/lr^→l r^→=r^→/lr^→l * Gmm Could you please…A proton is located at (0, 0, -1.0 x 10-9) m, and an alpha particle (consisting of two protons and two neutrons) is located at (1.0 x 10-9, 0, 2.5 x 10-9) m. (Express your answers in vector form.) (a) Calculate the force the proton exerts on the alpha particle. XN (b) Calculate the force the alpha particle exerts on the proton. X NH.W: In the Boher model of the hydrogen atom an electron moves at 2.19*10m/s in an orbit of radius 5.29*10" centered on a proton. (a)what is the centripetal force on the electron? (b)what is the number of revolutions made each second? Ans. (a)9.06*10"m/s (b = 6. 58 + 1015 1/s H.W: A ball is thrown with an initial speed voat an angle 0 below the horizontal from rooftop 44m above the ground. It lands 2sec later at a point 32m from the Vor base of the building. Find vo and 0 Ans. 0 = -37.32vo = 20. 1m/s H.W: A ball thrown up from a rooftop of height 40m lands on ground in 4s. (a)what is its maximum height above the ground? (b)what is its velocity 15m below the rooftop? Ans. (a)44.7m (b) v = -19.65 4 H.W: An object is thrown horizontally at 20m/s from a cliff top 45m above sea level. Find (a)the time to land; (b)the angle at which it hits the water; (c)the speed at which it hits the water. Ans. (a)3.03s (b)Ø = -54.73 (c)35.79m/s
- Tidal forces are gravitational forces exerted on different parts of a body by a second body. Their effects are particularly visible on the earth's surface in the form of tides. To understand the origin of tidal forces, consider the earth-moon system to consist of two spherical bodies, each with a spherical mass distribution. Let r. be the radius of the earth, m be the mass of the moon, and G be the gravitational constant. Part B Since the gravitational force between two bodies decreases with distance, the acceleration anear experienced by a unit mass located at the point on the earth's surface closest to the moon is slightly different from the acceleration afar experienced by a unit mass located at the point on the earth's surface farthest from the moon. Give a general expression for the quantity anear-afar Express your answer in terms of G, m, r, and re. ▸ View Available Hint(s) anear afar = ΜΕ ΑΣΦ ? x Xb √√x √x X [X] X.10" Variables are case sensitive. No credit lost. Try again.Find gravitational force as formulaFor A= î + 2j - 4k, B = -4î + 4j + k, and C = 2j - 3k, find C· (A - B).
- A person riding a Ferris Wheel with a diameter of 102 feet travels once around the wheel in 3.5 minutes. What is the average speed of the rider? a) O183.1 [fpm] b) O29 [fpm] c) 091.5 [fpm] d) O 14.6 [fpm] e) ONone of the above Review LaterThe gravitational force exerted by the earth on a unit massat a distance r from the center of the planet is where M is the mass of the earth,R is its radius, and G isthe gravitational constant. Is F a continuous function of r ?