Pascal's Law

Topic: Gravity

Objectives & Outcomes

• Understand what gravity is and how it works
• Be able to use the formula for calculating the gravity of the Earth to find the gravitational force between two objects of known masses.

Materials

• Two identical objects (e.g. two balls of equal mass or two identical weights)
• Balance or scale
• Calculator
• Pen and paper for recording calculations

Warm-up

• To begin, ask students if they have ever experienced gravity. Encourage them to think about experiences such as riding in a car, diving into a swimming pool or dropping a toy from their hand. Ask them to share their experiences and explain how they think gravity was responsible for these events.

Direct Instruction

• Next, explain that gravity is a force that attracts any two objects with mass towards each other. Demonstrate this by holding a ball in one hand and another ball in the other hand. Ask students to observe how the balls are attracted to each other and seem to want to come together.
• Ask students if they can think of any reasons why objects with mass might be attracted to each other. Encourage them to make suggestions and write them on the board. Examples might include: "Objects with mass want to be close to each other because they want to be friends." "Objects with mass want to be close to each other because they want to be together." "Objects with mass want to be close to each other because they want to be a family."
• After students have had a chance to make suggestions, explain that scientists have been able to calculate the strength of gravity using a formula called "Newton's law of gravity". This formula allows us to calculate the strength of gravity between any two objects with mass, based on the distance between them and the masses of the objects.
• Explain that Newton's law of gravity can be written using the following formula:

F=G(m1*m2)/r^2

Where:

F = the strength of gravity between the two objects with mass m1 and m2

G = the gravitational constant, which is 6.67 x 10-11 Nm2/kg2

• r = the distance between the two objects with mass m1 and m2
• Ask students to work in groups to calculate the strength of gravity between two different objects with mass using the formula. Have them use a calculator to enter the values for the masses and the distance between the objects.

Guided Practice

• Next, have students use the formula to calculate the strength of gravity between two different objects with mass, and compare their answers to those of their groupmates. Encourage them to check their calculations for accuracy and to reason through any differences in their answers.
• After students have had a chance to practice using the formula to calculate the strength of gravity between two objects with mass, explain that it can also be used to calculate the gravity of the Earth. Ask students to work in groups to calculate the gravity of the Earth based on the following information:
• The average radius of the Earth is approximately 6,400 km
• The mass of the Earth is approximately 5.97 x 10 24 kg
• The gravitational constant, G, is 6.67 x 10-11 Nm2/kg2
• Have students use the formula to calculate the strength of gravity on the surface of the Earth and compare their answers to those of their groupmates. Encourage them to check their calculations for accuracy and to reason through any differences in their answers.
• After students have had a chance to calculate the gravity of the Earth, explain that it actually changes slightly depending on where you are on the Earth's surface. The closer you are to the center of the Earth, the stronger the gravity will be. The farther you are from the center of the Earth, the weaker the gravity will be.
• Have students work in groups to calculate the average value of the gravity on the surface of the Earth and compare their answers to those of their groupmates. Encourage them to check their calculations for accuracy and to reason through any differences in their answers.
• After students have had a chance to calculate the average value of the gravity on the surface of the Earth, explain that this value can be written as:

g = GM/R2

Where:

• g is the average value of the gravity on the surface of the Earth
• M is the mass of the Earth
• R is the average radius of the Earth
• G is the gravitational constant, which is 6.67 x 10-11 Nm2/kg2
• Have students use the formula to calculate the average value of the gravity on the surface of the Earth and write the answer on the board.
• Supplementary Instruction
• Next, explain that the strength of the gravity on the surface of the Earth actually changes slightly depending on where you are on the Earth's surface. The closer you are to the center of the Earth, the stronger the gravity will be. The farther you are from the center of the Earth, the weaker the gravity will be.
• Have students work in groups to calculate the average value of the gravity on the surface of the Earth and compare their answers to those of their groupmates. Encourage them to check their calculations for accuracy and to reason through any differences in their answers.
• After students have had a chance to calculate the

average value of the gravity on the surface of the Earth, explain that this value can be written as:

g = GM/R2

Where:

• g is the average value of the gravity on the surface of the Earth
• M is the mass of the Earth
• R is the average radius of the Earth
• G is the gravitational constant, which is 6.67 x 10-11 Nm2/kg2
• Have students use the formula to calculate the average value of the gravity on the surface of the Earth and write the answer on the board.
• Independent Practice
• Finally, have students work in groups to calculate the average value of the gravity on the surface of the Earth for a specific location on the Earth's surface. For example, have them calculate the average value of the gravity on the surface of the Earth at the equator, at the -10th parallel, at the -50th parallel, and at the -90th parallel.
• Have students share their answers with the class and allow for a discussion of any differences in their answers and the reasons for those differences.

Closure

• Summarize the main points of the lesson, emphasizing the concept of gravity and its definition as the force that acts between two objects that have mass, and explaining how gravity plays a role in the orbital motion of the planets around the Sun and in the formation of star systems.
• Ask students to share their thoughts on the importance of understanding gravity and its role in the Universe.

Assessment

• Formally, assess student understanding through a written or oral quiz that includes multiple-choice, short answer, and equation-solving questions.
• More informally, assess student understanding through observations of their participation in class discussions and their ability to explain the concept of gravity in their presentations.