Essential Question:

• What are gravitational forces and how are they used?

Related Benchmarks:

• SC.912.P.12.4: Describe how the gravitational force between two objects depends on their masses and the distance between them.

Objectives:

• The student will explain and be able to calculate gravitational forces.

Essential Vocabulary:

• Acceleration- the change in velocity divided change in time
• Gravity- The force of attraction between two particles of matter because of their mass. Earth’s gravity is 9.8 m/s2.
• Gravitational Force-all matter must attract each other and this attraction is universal F= Gm1m2/r2 where F is force measured in Newtons (N), G is a constant which is 6.67 X 10-11 Nm2/kg2, m is the mass, and r is the distance between the objects.

Modeled Instruction:

1.What is the gravitational force (F) that the Sun exerts on Jupiter?

• Formula: F=Gm1m2/r2
• The mass of Sun= 1.99 X 1030 kg
• The mass of the Jupiter= 1.90 X 1027 kg
• The distance (r) between the Sun and the Jupiter is 7.78 X 1011m
• The universal constant (G) = 6.67 X 10-11 Nm2/kg2

Answer: F= (6.67X 10-11Nm2/kg2) (1.99 X 1030kg) (1.90 X 1027kg)/ (7.78 X 1011m)2 = 4.17 X 1023 N 

Guided Practice:

Which of the following would double the gravitational force between them? (Two one-kilogram spheres are one meter apart)

A. Doubling the mass of one sphere
B. Doubling the mass of both spheres
C. Halving the distance between both spheres
D.Doubling the distance between both spheres

ANSWER: A

Independent Practice: Students resolve the following questions independtly

1. The formula F=Gm1m2/r2, what happens if the masses are not changed, but the distance of separation is doubled?
2. The formula F=Gm1m2/r2, what happens if the masses are doubled, and the distance of separation is doubled?

ANSWERS

1. F(new)= Gm1m2/(2r)2 = 1/4(Gm1m2/r2) = ¼ as much F
2. F(new)= G2m12m2/(2r)2 = 4/4 (Gm1m2/r2)= NO CHANGE