Universal Gravitation

3.5 Universal Gravitation

Open Ended

What is the difference between weight and mass?

​Mass vs Weight

• ​Mass is an inherent quality of objects.

• It is the amount of matter present in an object.

• Whether on Earth, in space, or on the moon, this amount remains the same.

• Weight, on the other hand, is the force acting on an object that has mass.

• This force is the pull of gravity.

• Weight is not a property of the object; rather, it is the pull exerted by the surface on which the object exists.

• Therefore, objects will have different weights on different planets.

Open Ended

Are mass and weight vector or scalar quantities? Give reasons for your answers.

Calculating Weight

• ​Recall that Newton's Second Law states the sum of the forces acting on an object is equal to the mass of the object times its acceleration.

• Since weight is a force, we can say that: F_g = mg

• Here F_g is the wieght, m is the mass, and g is the acceleration due to gravity.

• On a planet then, the weight vector is pointed towards the center of the planet.

• While there are many units used to measure weight in society, since it is a force, we use the units of newtons (N) in physics.

• So for example, a 2.0 kg bar would be said to weigh 19.6 N on Earth, since g = -9.8 m/s²

Multiple Choice

The value of acceleration due to gravity on the planet Saturn (g_Saturn) is about 11.2 m/s². How much will an object weighing 680 newtons on Earth weigh on Saturn?

• 777 N

• 7616 N

• 61 N

• 595 N

• 560 N

Universal Law of Gravitation

• We know that gravity is a field force, meaning that it doesn't need contact to transmit the force.

• We also know that the acceleration from gravity is different on different planets.

• What we haven't mentioned yet is that the acceleration of gravity is different depending on how far we are from the planet's center of mass.

• The table shows the values for different distances from the Earth's surface.

Inverse Square Law

• Based on the motion of the planets, Newton proposed that the force of gravity (F_g) follows an inverse square law with respect to the distance between two bodies.

• In other words: F_g ∝ 1/r²

• This means that if we double the distance between two objects, then the gravitational force decreases by a factor of four.

• Newton also realized that gravity's pull on an object is not just influenced by its distance from Earth's center, its mass also plays a role.

• The greater the mass of the object, the greater the pull of gravity.

• Gravity is directly proportional to the mass of the object.

Universal Law of Gravitation

• Putting all of this together, we can express gravity as: F_g = G(m_E⋅m_obj)/r².

• Where m_E is the mass of the Earth, m_obj is the mass of the object, and G is the universal gravitational constant.

• The value of G was found by Lord Henry Cavendish almost a century after Newton's death.

• He found that the value of the gravitational force between two objects of 1 kilogram each, kept 1 meter apart, would equal just 0.0000000000667 newtons.

• Thus, the value of G is 6.673 × 10^-11 newtons⋅meters²/kilograms².

• From the value of this constant you can see that the gravitational force is insignificant for most day–to–day objects you encounter.

Multiple Choice

An astronaut is on a spacewalk 300 kilometers above Earth's surface. If the astronaut's mass plus suit is 170 kilograms, what is the force of interaction between Earth and the astronaut? (Earth's radius is 6.38 × 10⁶ meters, Earth's mass = 5.98 × 10²⁴ kg, and G = 6.673 × 10^–11 Nm²/ kg²)

• 6.9 x 10² N

• 1.7 x 10³ N

• 8.6 x 10² N

• 4.9 x 10¹ N

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Multiple Choice

A person on the Earth weighs 180 pounds. How much will they weigh on the moon? ( Note: The moons "g" is1/6 that of Earth)

• 30 lbs
• 360 lbs
• 0- you are weightless in space
• 18 lbs

Multiple Choice

Complete the following statement: The farther away two planets are the _______ the gravitational force between them.

• more
• same
• dosen't matter
• less

Multiple Choice

Find the distance between two objects whose masses are m₁ = 4,500 kg, and m₂ = 8,700 kg; if the gravitational force between them is F = 2.0 x 10^-8 N.

• 130565.25 m

• 361.34 m

• 0.19575 m

• 0.783 m

Multiple Choice

Doubling the mass of an object...

• ...will double the force of gravity.

• ...will half the force of gravity.

• ...will quadruple the force of gravity.

• ...will quarter the force of gravity.

Multiple Choice

Calculate the gravitational force between two objects when they are 0.750m apart. Each object has a mass of 5.00kg.

• 2.96x10^-9N

• 3.00x10^-6N

• 2.22x10^-9N

• 2.23x10^-8N

Multiple Choice

If the sun's mass is 2.0x10³⁰ kg, and its radius is 7.0 x 10⁸ m, what is the strength of its gravitational field, "g"?

• 9.8 m/s²

• 272.2 m/s²

• 27.2 m/s²

• 200 m/s²