Physics Pre-AP
Universal Gravitation
Earth’s mass = 5.98 x 1024 kg, planetary radius of earth = 6.38 x 106 m, G = 6.67 x 10-11 N*m2/kg2
Mathematical Conceptions:
1.)
The gravitational force of attraction between earth and the sun is 1.6 x 1023 N. What would this force have been
if the earth had been three times as massive? Show or explain why. (4.8 x 1023 N) The gravitational force of attraction
between the earth and the sun is 1.6 x 1023 N. What would this gravitational force have been if the earth had formed
three times as far away from the sun? Show or explain why. (1.8 x 1022 N)
2.) Oscar, whose mass is 65 Kg, and Olivia, whose mass is 45 Kg, sit 2.0 m apart in the physics classroom. Olivia sees
Oscar and feels an attraction.
a) If the attraction is gravitation between them, find its magnitude. (4.9 x 10-8 N)
b) Does the force of gravitation between them cause them to drift toward each other? Explain.
3.) Our galaxy, the Milky Way contains approximately 4.0 x 1011 stars with an average mass of 2.0 x 1030 kg each. How
far away is the Milky Way from our nearest neighbor, the Andromeda Galaxy, if Andromeda contains roughly the same
number of stars and attracts the Milky Way with a gravitational force of 2.4 x 1030 N? (4.2 x 1021 m)
4.) The gravitational force between two electrons 1.0 m apart is 5.42 x 10-71 N. Find the mass of an electron. (9.11 x 1031
kg)
5.) The planet Mercury has a radius of 2400 km and a mass of 3.3 x1023 kg. What is the acceleration due to gravity on a
person at the surface of Mercury? How much would an 85 kg astronaut weigh on Mercury? (3.8 m/s2, 324 N)
6.) Satellites often orbit at 640 km above Earth's surface, which is 1/10 of Earth's radius.
a) What is the approximate gravitational acceleration, g, in satellite territory? (8.05 m/s2)
b) What is the tangential velocity of the satellite? (7527 m/s or 7.5 km/s!) Solve this later!
Kepler’s 3rd Law – These (7-10) are only for PHUN! However, Kepler’s Laws will be studied conceptually!!!
7.) Pluto is 40 times farther than Earth is from the sun. Find Pluto's orbital period in earth years. (253 years)
8.)
Uranus requires 84 years to orbit the sun. Find Uranus' orbital radius. (19 Earth radii …Wow, Uranus sure does
cover a lot of space!)
9.)
Galileo discovered four moons of Jupiter. Io, which is 4.2 arbitrary units from the center of Jupiter, has a period
of 1.8 days. He measured the radius of Ganymede orbit as 10.7 arbitrary units. Use Kepler's 3rd law to find the orbital
period of Ganymede in days. (7.3 days)
10.) Use the information given in problem 7 and your answer to calculate the mass of the sun. (2.0 x 10 30 kg)
Recommended reading Essential Physics by Hsu:
 Chapter Seven: Gravitation & Orbits
 Reading p. 215-223
 Review p. 233 # 62,63,66
Also Recommended:

www.physicsclassroom.com Newton’s Law of UG
 www.khanacademy.org/#physics
Uniform Circular Motion: (First, Know the difference between Period and Frequency really well)
1) It takes a 615-kg race car 14.3 s to travel at a uniform speed around a circular racetrack of 50.0 m radius. What is the
centripetal acceleration of the car? What average force must the track exert on the tires to produce this acceleration?
(9.65 m/s2, 5.94 x 103 N)
2) Sven whirls a 7.00-kg hammer tied to the end of a 1.3-m chain in a horizontal circle. The hammer moves at the rate of
1.0 rev/s. What is the centripetal acceleration of the hammer? What is the tension in the chain?
(51
m/s2, 359 N)
3) Whirly Steve whirls a yo-yo in a horizontal circle. The yo-yo has a mass of 0.20-kg and is attached to a string 0.80 m
long. If the yo-yo makes 1.0 complete revolution each second, what force does the string exert on it? If Whirly Steve
increases the speed of the yo-yo to 2.0 revolutions per second, what force does the string now exert? (6.3 N, 25 N)
4) A jet plane traveling 1800 km/h (500 m/s) pulls out of a dive by moving in an arc of radius 6.00 km. What is the
plane’s acceleration in g’s? (4.25g’s – as in 4.25 times the acceleration due to gravity)
FBD’s & ΣF Statements are required from here on out!!!
5) A ball on the end of a string is cleverly revolved at a uniform rate in a vertical circle of radius 85.0 cm. If its speed is
4.15 m/s and its mass is 0.300 kg, calculate the tension in the string when the ball is (a) at the top of its path, and (b) at
the bottom of its path. (3.14 N, 9.02N)
6) What is the maximum speed with which a 1050-kg car can round a turn of radius 70 m on a flat road if the coefficient
of friction between tires and road is 0.80? Does this result depend on the mass of the car?
(23 m/s)
7) While upside down and traveling 14m/s at the top a vertical loop on The Spine Buster Rollercoaster, how large of a
normal force acts on an 800 kg car of passengers? Assume a radius of 8.6 m. At what minimum speed must the
passenger car be traveling when upside down through the loop if the passengers are not to fall out? Assume the same
radius of 8.6 m. If there are more passengers, would the car have to travel faster or slower? Explain. (1.04 x 104 N, 9.2
m/s)
8) A coin is placed on your parents’ old K.C. and the Sunshine Band record, revolving at 33 1/3 revolutions per minute.
In what direction is the acceleration of the coin, if any? Find the acceleration of the coin when it is placed 5.0, 10.0, and
15 cm from the center of the record. (0.61 m/s2, 1.2 m/s2, 1.8 m/s2)
What provides the force to accelerate the coin? At which of the three radii listed would the coin be most likely to fly
off? Why?
9) In the NAUSTEATOR! (didn’t have enough after The Spine Buster, huh?), people pay money to be rotated in a vertical
cylindrically walled “room.” If the room radius is 5.0 m, and the rotation frequency is 0.50 revolutions per second when
the floor drops out, what is the minimum coefficient of static friction so that the people will not slip down? People
describe this ride by saying they were being “pressed against the wall.” Is this true? Is there really an outward force
pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides
nauseated)? [Hint: First draw the free-body diagram for a person.] (0.20)
**10) A curve of radius 30 m is “**banked” so that a car may make the turn at a speed of 13 m/s without depending on
friction. What must be the slope of the curve (the banking angle)? (30°)
Recommended reading Essential Physics by Hsu:
 Chapter Seven: Circular Motion
 Read p. 206-214
Also Recommended:

www.physicsclassroom.com Circular Motion
 www.khanacademy.org/#physics