For this problem, assume that the earth is a perfect sphere. Also, assume that if your mass is m, then the earth exerts a gravitational force on you of magnitude mg, where g = 9.8 m/s2 at all points of the earth's surface. a) Your mass is m = will the scale read? (Thanks to the Third Law, this is the same as asking for the normal force exerted on you by the scale.) b) Next you go to the Equator and stand on a scale. What does it read? The radius of the earth is 6.4 × 106 m. c) Suppose the earth were rotating so quickly that objects became “weightless" at the equator. How long would the day be? 50 kg. If you are standing on a scale at the North Pole, what
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- (a) Find the magnitude of the gravitational force (in N) between a planet with mass 7.25 ✕ 1024 kg and its moon, with mass 2.25 ✕ 1022 kg, if the average distance between their centers is 2.20 ✕ 108 m. N (b) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) m/s2 (c) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.) m/s2(a) (i) Define gravitational field strength and state whether it is a scalar or vector quantity. A mass m is at a height h above the surface of a planet (ii) of mass M and radius R. The gravitational field strength at height h is g. By considering the gravitational force acting on massm, derive an equation from Newton's law of gravitation to express g in terms of M, R, h and the gravitational conșțant G.A solar sailplane is going from Earth to Mars. Its sail is oriented to give a solar radiation force of FRad = 7.90 × 102 N. The gravitational force due to the Sun is 173 N and the gravitational force due to Earth is 1.00 × 102 N. All forces are in the plane formed by Earth, Sun, and sailplane. The mass of the sailplane is 14,000 kg. A) What is the magnitude of the net force acting on the sailplane? B) What is the direction of the net force acting on the sailplane?
- An exoplanet (JB-2285), located in the galaxy closest to ours, uses a system where the units of mass and force are phljmth and xwyflr. respectively. Xwyflr is defined as the unit of force required to accelerate a unit mass, phljmth, with the gravitational acceleration (in m/s2) on the surface of the exoplanet which is seven tenths of the gravitational acceleration on earth’s surface (9.8066 m/s2). a. What is the conversion factor to convert a force in xwyflr to force in phljmth●m/s2? b. Calculate the weight in xwyflr of a 14.28 phljmth object on the surface of the exoplanet JB-2285. c. Determine the weight of the object in (b) in Newtons (N) in Mintal, Davao City if 137.224 N = 1.00 xwyflr? d. What is the mass in grams of a 796.2-phljmth object?Europa orbits Jupiter at a distance of 6.7 x 108 m from Jupiter's cloudtops (the surface of the planet). If Jupiter's mass is 1.9 x 1027 kg and radius is 6.8 x 107 m, what is the speed of Europa as it orbits in m/s? Round to the nearest hundredth. Don't worry about putting units, just put the number.The drawing shows three particles far away from any other objects and located on a straight line. The masses of these particles are mA = 323 kg, mB = 572 kg, and mc = 199 kg. Take the positive direction to be to the right. Find the net gravitational force, including sign, acting on (a) particle A, (b) particle B, and (c) particle C. B 0.500 m 0.250 m (a) Number Units (b) Number Units (c) Number Units Click if you would like to Show Work for this question: Open Show Work
- A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.1 × 104 m/s. The mass of the planet is M = 6.04 × 1024 kg. The mass of the satellite is m = 1.2 × 103 kg. a)Enter an expression for the radius R in terms of G, M and v. b)Calculate the value of R in meters. c)Enter an expression for the gravitational potential energy PE in terms of G, M, m, and R.Every few months, memes circulate claiming that certain alignments of the planets with the Earth will result in a change in the gravitational force you feel. Usually, these memes state that the alignment will counteract Earth's gravity slightly so you will feel less of a gravitational pull towards the Earth. Can this ever happen? Let's look at the numbers. What is the gravitational force (in N) of the Earth on you (ME = 5.97 ✕ 1024 kg, RE = 6380 km)? Say your mass is 68 kg. (Enter the magnitude.) What is the gravitational force (in N) of Jupiter on you when it is closest to Earth (MJ = 1.90 ✕ 1027 kg, RJE = 5.88 ✕ 108 km)? (Enter the magnitude.) By what factor would the mass of Jupiter need to increase to be equal to the gravitational force you feel from the Earth? Part 1 of 5 The gravitational force between two masses is given by Fg = −GMm r2 where G = 6.67 ✕ 10−11 m3/s2/kg. We can use this expression to determine the magnitude of the gravitational force you feel…The gravitational constant g is 9.807 m/s² at sea level, but it decreases as you go up in elevation. A useful equation for this decrease in g is g = a - bz, where z is the elevation above sea level, a = 9.807 m/s², and b = 3.32 × 10−6 1/s². An astronaut "weighs” 80.0 kg at sea level. [Technically this means that his/her mass is 80.0 kg.] Calculate this person's weight in N while floating around in the International Space Station (z = 355 km). If the Space Station were to suddenly stop in its orbit, what gravitational acceleration would the astronaut feel immediately after the satellite stopped moving? The person's weight in N while floating around in the International Space Station is The astronaut feels a gravitational acceleration of 692.928 m/s² 8.6616 N.