Conceptual Physics POGIL: Universal Gravitational
We 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 Gravitation
All 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.
The 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 m2and inversely proportional to the square of the distance d between the masses. This relationship is summed up by the equation
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.
(a)On each mass above, draw arrows indicating the direction of the force on each mass.
(b)Determine the magnitude of the gravitational force on the 10 kg mass.
(c)Determine the magnitude of the gravitational force on the 70 kg mass.
(d)Which mass exerts the greater gravitational force on the other? Why is this so?
- The diagram below shows a 10 kg mass and a 70 kg mass separated by a distance of 10 m.
(a)On each mass above, draw arrows indicating the direction of the force on each mass.
(b)Determine the magnitude of the gravitational force on the 10 kg mass.
(c)Determine the magnitude of the gravitational force on the 70 kg mass.
(d)How do your answers to (b) and (c) compare to your answers to (b) and (c) in question 1?
- 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.
(a)Determine the magnitude of the gravitational force that the Sun exerts on Mars.
(b)Determine the magnitude of the gravitational force that Mars exerts on the Sun.
- In 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.
(a)If we double the mass m1, what is the magnitude of the gravitational force between the masses?
(b)If we double the mass m2, what is the magnitude of the gravitational force between the masses?
(c)If we triple the mass m1, what is the magnitude of the gravitational force between the masses?
(d)If we double the distance between the masses, what is the magnitude of the gravitational force between the masses?
(e)If we triple the distance between the masses, what is the magnitude of the gravitational force between the masses?
(f)If we halve the distance between the masses, what is the magnitude of the gravitational force between the masses?
- If gravitation is universal, why do you only observe its effects between you and the Earth?
Problem Solving
- The mass of the Earth is approximately 5.98×1024 kg. The average distance between Earth and the Sun is 1.5×1011 m.
(a)Determine the magnitude of the gravitational force that the Sun exerts on Earth.
(b)Determine the magnitude of the gravitational force that Earth exerts on the Sun.
(c)What is the acceleration of the Earth in its orbit?
(d)What causes the Earth to follow a curved path around the Sun instead of a straight path?