POGIL:
Conceptual Physics POGIL: Universal GravitationalWe have learned about weight as the gravitational force exerted on you by the planet you’re standing on, usually the Earth. But gravity is a force exerted by all masses on each other, not just you and the Earth. In this sense, we say that the gravitational force is universal. In this POGIL we will learn about what influences the magnitude of the gravitational force.Newton’s Law of Universal GravitationAll masses in the universe are attracted to each other by a gravitational force: planets, stars, people, doughnuts…everything that has mass. In the diagram below, we see two masses, labeled m1 and m2, separated by a distance d. 194754522860m2dm100m2dm1The gravitational force between the two masses is always attractive…just like love.The magnitude of the gravitational force F between two masses is directly proportional to the product of the masses m1 and m2 and inversely proportional to the square of the distance d between the masses. This relationship is summed up by the equationF=Gm1m2d2.G is a constant of proportionality, called the Universal Gravitational Constant, equal to 6.67×10?11 N-m2/kg2. This equation is known as Newton’s Law of Universal Gravitation. It was discovered by the same Newton who gave us our trusty three laws of motion.The diagram below shows a 10 kg mass and a 70 kg mass separated by a distance of 1 m.center215901 m10 kg70 kg001 m10 kg70 kgOn each mass above, draw arrows indicating the direction of the force on each mass.Arrows should be drawn towards the other mass equal in lengthDetermine the magnitude of the gravitational force on the 10 kg mass.F = 4.7 x 10-7 NDetermine the magnitude of the gravitational force on the 70 kg mass.F = 4.7 x 10-7 NWhich mass exerts the greater gravitational force on the other? Why is this so?According to Newton’s 3rd Law, they exert the same force on each other.The diagram below shows a 10 kg mass and a 70 kg mass separated by a distance of 10 m.center2159010 m10 kg70 kg0010 m10 kg70 kgOn each mass above, draw arrows indicating the direction of the force on each mass.Arrows should be drawn towards the other mass equal in lengthDetermine the magnitude of the gravitational force on the 10 kg mass.F = 4.7 x 10-10 NDetermine the magnitude of the gravitational force on the 70 kg mass.F = 4.7 x 10-10 NHow do your answers to (b) and (c) compare to your answers to (b) and (c) in question 1?The answers are the same because of Newton’s 3rd Law.The mass of the Sun is approximately 2×1030 kg, while the mass of the planet Mars is approximately 6.4×1023 kg. The average distance between Mars and the Sun is 2.28×1011 m.Determine the magnitude of the gravitational force that the Sun exerts on Mars.F = 2.5 x 1031 NDetermine the magnitude of the gravitational force that Mars exerts on the Sun.F = 2.5 x 1031 NIn the diagram below, we see two masses, labeled m1 and m2, separated by a distance d. The two masses are attracted to each other with 36 N of force.center22860dm1m200dm1m2If we double the mass m1, what is the magnitude of the gravitational force between the masses?72 NIf we double the mass m2, what is the magnitude of the gravitational force between the masses?72 NIf we triple the mass m1, what is the magnitude of the gravitational force between the masses?108 NIf we double the distance between the masses, what is the magnitude of the gravitational force between the masses?9 NIf we triple the distance between the masses, what is the magnitude of the gravitational force between the masses?4 NIf we halve the distance between the masses, what is the magnitude of the gravitational force between the masses?144 NIf gravitation is universal, why do you only observe its effects between you and the Earth?A system must always be defined for purpose of study. You cannot study the whole universe all at once. Therefore, when speaking of gravity, we simply look at gravity’s effect on one object at a time, including a person. Still, gravitation is universal at all times.Problem SolvingThe mass of the Earth is approximately 5.98×1024 kg. The average distance between Earth and the Sun is 1.5×1011 m.Determine the magnitude of the gravitational force that the Sun exerts on Earth.F = 3.5 x 1022 NDetermine the magnitude of the gravitational force that Earth exerts on the Sun.F = 3.5 x 1022 NWhat is the acceleration of the Earth in its orbit?a = 5.9 x 10-3 m/s2What causes the Earth to follow a curved path around the Sun instead of a straight path?The gravitational pull the Sun exerts on the Earth causes the Earth to travel in a circular pattern much like tying a string to a ball and swinging it above your head. ................
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