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Using Newton’s Formula for Universal Gravitation

Useful Information:

  1. Scientific Notation. First, let’s just check on scientific notation.

Rank the following numbers, from greatest to least:

A. 5103B. 3105C. 210-4D. 710-8E. 1.951030

Greatest 1______2______3______4______5______Least

Convert these numbers to scientific notation:

1000 = ______One million = ______5000000000000 = ______

31600000 = ______0.045 = ______0.00000000000000000000025 = ______

Convert these numbers from scientific notation to “regular notation” (is that “unscientific notation?”):

1102 = ______2.16104 = ______3 =10-5 = ______1.6710-10 = ______

Then try the following multiplication and division problems:

(71022)  10 = ______(3.8108)2 = ______

(71022)  10 = ______(61024)  (21030) = ______

(71022)  1000 = ______(8105)  (4104) = ______

  1. Identifying Kinds of Quantities. For each of the following quantities, identify what kind of quantity it is. If the quantity is an distance, mark it with an “d”, If it is a force, mark it “F.” If it is a mass, mark it “m.” If it is none of these, mark it “X.”

____5.971024 kg____4.184 m____7.63108 m/s2____1.51011 km

____39.4 m/s2____1.6610-26 N____15 g____43,268 N

  1. Getting the Formula Right. Newton figured out how gravitational force strength depends upon the mass of the two objects involved and the distance between their centers. You may need to solve for any of those values, so figure out the formula, and write it here:

To find the gravitational force:To find mass:To find the distance between their centers:

  1. Plugging in Quantities. Each formula has a set of quantities with it. Rewrite the equation, “plugging in” appropriate quantities. Then find the answer to the equation and write it, with units. The first one is done as an example.

Formula:
Quantities:
18 m1000 kg5 m/s23 kg / Quantities “plugged in”:
Fg=(6.67x10-11 N2m2/kg2)(1000 kg)(3kg)
(18 m)2 / Answer, with units:
Fnet = 6.2x10 -12 N
Formula:
Quantities:
6x1024 kg2 m/s16 N6.3x106 m
/ Quantities “plugged in”: / Answer, with units:
Formula:
Quantities:
70 kg13 m/s2 70 kg0.000001 N
/ Quantities “plugged in”: / Answer, with units:
  1. Identifying Known Quantities and Finding Formulas. Read the following problems. In each case, write out the “known quantities.” then write the symbolic formula necessary to solve the problem. That’s it. Don’t solve the problem, at least not at this point… The first one is done as an example.
  2. Calculate the distance between two objects of mass 1000 kg and 200 kg, when their gravitational force is 0.000001 N.

Known Quantities: m = 200 kg, M = 1000 kg
Fg = 0.000001 N / Symbolic Formula:

Question: Why is the formula written instead of ?

  1. A 70.-kg physicist weighs 700. N on the surface of Earth, 6,380,000 m from the center of the planet. What is Earth’s mass?

Known Quantities: / Symbolic Formula:
  1. What is the weight of a 2500 kg spacecraft on the Moon? The Moon’s mass is 7.4x1022 kg, and the surface of the Moon is 1,740,000 m from its center.

Known Quantities: / Symbolic Formula:
  1. A man takes his dog for a walk on a deserted beach. At one time, the 105 kg man and the 11 kg dog are exerting 810-10 N of force on each other. How far apart are they?

Known Quantities: / Symbolic Formula:
  1. Put It All Together. Read the following problems and solve them showing all four steps.
  2. Juliet (m = 50. kg) stands on her balcony, 5 m from her beloved Romeo (M = 70. kg). They are attracted gravitationally as well as romantically. How strong is the gravitational force that Juliet exerts on Romeo?

Known Quantities / Symbolic Formula / Quantities “plugged in” / Answer, with units

Follow-up Question: How much force does Romeo exert on Juliet?

  1. The Sun exerts a force of about 3.5x1022 N on Earth, Earth is about 150,000,000,000 m from the Sun, and has a mass of about 6x1024kg. How much mass does the Sun have?

Known Quantities / Symbolic Formula / Quantities “plugged in” / Answer, with units
  1. Two bowling balls sit on a rack. One has a mass of 6.1 kg, and the other’s mass is 7.2 kg. If the gravitational force of attraction between them is 210-9 N, how far apart are they?

Known Quantities / Symbolic Formula / Quantities “plugged in” / Answer, with units
  1. Write your own problem, then solve it!
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Known Quantities / Symbolic Formula / Quantities “plugged in” / Answer, with units