1.4 The Universal Law of Gravitation (1) (1)

1.4 The Universal Law of Gravitation 1.4 The Universal Law of Gravitation Introduction In this lab, you are going to explore the application of Newton’s Universal Law of Gravitation. This important relationship between masses was the first force law quantified in the history of modern science. The formula provides a means for determining the gravitational pull between two masses, but does not explain how gravity works. F gravity = G m 1 m 2 d 2 G = 6.67 × 10 − 11 N m 2 kg 2 As an example, let’s apply this formula to the screenshot from the simulation below. In this setup, we have mass 1 = 2,000,000,000 kg (2x10 9 kg) and mass 2 = 4,000,000,000 kg (4x10 9 kg). The distance between them is labeled as 4 kilometers, but we must convert this to meters for the calculation so the distance will be 4,000 m. With these parameters set, we see that the gravitational force exerted on mass 1 by mass 2 is 33.4 N and the gravitational force exerted on mass 2 by mass 1 is also 33.4 N (equal and opposite). Now, let’s input these values into the formula to see if we get 33.4 N. F = ( 6.67 × 10 − 11 N ⋅ m 2 k g 2 )( 2 × 10 9 kg )( 4 × 10 9 kg ) ¿¿ You are welcome to use any scientific calculator you chose for the labs in this course. Just make sure that you know how to properly input numbers in scientific notation into your calculator. 1

1.4 The Universal Law of Gravitation It is recommended that you use a free online scientific calculator called Desmos ( https://www.desmos.com/scientific ). Here’s what our sample calculation looks like when you use Desmos: Now, let’s begin the lab. Part 1 - The Effect of Mass on Gravitational Force To complete this lab, you will need to open the following simulation: Gravity Force Lab You have been assigned an initial set of mass values to use in the simulation based upon the first letter of your last name. Consult the table below: First letter of Last Name Mass 1 (billions kg) Mass 2 (billions kg) A-C 1 10 D-F 2 9 G-I 3 8 J-L 4 7 M-O 5 6 P-R 1 5 S-U 2 4 V-Z 3 3 In part 1, we are going to observe the effect that mass has on gravitational force. Setup the simulation with your assigned mass values and set the distance between the masses to 2.5 km. In the table below, record the values for mass, distance, and force you see in the simulation. Be sure to include proper units. Mass 1 1 kg Mass 2 10 kg Distance 4 km 2

1.4 The Universal Law of Gravitation How does the force exerted by the small mass on the large mass compare to the force exerted by the large mass on the small mass? Put an X in the left next to the correct answer. a The small mass exerts less force on the large mass than the large mass exerts on the small. x b The small mass exerts the same force on the large mass as the large mass exerts on the small. c The small mass exerts more force on the large mass than the large mass exerts on the small. This is due to Put an X in the left next to the correct answer. a Newton’s First Law of Motion b Newton’s Second Law of Motion 4

1.4 The Universal Law of Gravitation x c Newton’s Third Law of Motion d Conservation of momentum e Conservation of energy Next, double the value of one of your masses in the simulation and observe the effect on the value for the gravitational force between the masses. Record the new value for the gravitational force: ___83.37N___________________ By what factor has the gravitational force changed from before? _The gravitational force has doubled__________________ Does this observation confirm that gravitational force between masses is directly proportional to the product of the masses? Explain below. __Yes, this is true because when one mass increased the gravitational force also increased ___________________________________________________________________________ _____________________________________________________________________________ Part 2 - The Effect of Distance on Gravitational Force In part 2, we are going to observe the effect that distance has on gravitational force. Let’s begin by recording the mass values, distance, and force values that are currently seen in the simulation since you changed the value of one of your masses in the last part of the lab. Mass 1 2 kg Mass 2 10 kg Distance 4 km Convert distance to meters 4000m 5

1.4 The Universal Law of Gravitation _Yes, as the masses move further away the force between them gets smaller, as they move closer together the force increases. ____________________________________________________________________________ _____________________________________________________________________________ 7