**163 Your Turn Solutions**

**a. more acceleration to remain in the
curved path.**

**b. less acceleration to remain in the curved path.**

**c. no acceleration since you will be traveling at a constant
speed.**

** **

**2. Let's say you double your speed at which you round the curve
mentioned in question 1. By what factor will your acceleration
change? Will your required force also change? Explain.**

**Both acceleration and force will increase
by a factor of 4.**

**3. Based upon your answer to challenge 2, describe the
relationship between centripetal acceleration and tangential
speed.**

**There is a quadratic
relationship.**

**4. The radius of the path of an object in uniform circular
motion is doubled. **

**The centripetal force needed if its speed remains the same
is:**

**a. half as great.**

**b. one fourth as great.**

**c. the same as before.**

**d. twice as great as before.**

**e. four times as great as before.**

** **

**5. Based upon your answer to challenge 4, describe the
relationship between centripetal force and radius.**

**They have an inverse
relationship.**

**6. Rex Things and Doris Locked are out on a date. Rex makes a
rapid right-hand turn. Doris begins sliding across the vinyl seat
(which Rex had waxed and polished beforehand) and collides with Rex.
To break the awkwardness of the situation, Rex and Doris begin
discussing the physics of the motion which was just experienced. Rex
suggests that the objects which move in a circle experienced an
outward force which pushed her towards Rex. Doris disagrees, arguing
that objects which move in a circle experience an inward force. With
whom do you agree? Explain.**

**Doris is correct, an object moving in a
circle requires an inward force. As Doris continues to move in a
straight line, Rex curves in front of her (gets in her
way).**

**7. The centripetal force on a car rounding a curve on a level
road is provided by:**

**a. the force of gravity.**

**b. the frictional force between the car's
tires and the road.**

**c. the force from the brakes.**

**d. wind resistance.**

**e. an unseen string attached to the car.**

** **

**8. Ben Twirlinit has a 1.2 kg plane attached to a 3.5 meter
string. If Ben holds it and twirls it in a circle with the plane
completing one revolution every 4.0 seconds:**

**a. what is the centripetal acceleration of the plane?**

**b. with what force does Ida pull the plane in toward
herself?**

**9. Ida Goround is a 55.0 kg softball player for the Titans. If
she runs at a velocity of 7.0 m/s around a curve which has a radius
of 5.0 meters, what is the centripetal acceleration and centripetal
force acting upon her? (include the direction of both)**

**Both are directed toward the center of
the circular path.**

**10. What provides the inward centripetal force acting upon Ida
in challenge #9.**

**The inward force is provided by the field
by means of friction between the dirt and Ida's shoes.**

**11. Draw the centripetal force vector on the car shown
above.**

**Your vecto should point toward the center
of the circle.**

**12. Determine the centripetal acceleration and the centripetal
force acting upon the 900 kg car that is traveling at 10 m/s around
the circular track. The track has a radius of 18.0 meters.**

**13. Twila Twirlalot spins a yo-yo in a horizontal circle. The
yo-yo has a mass of 0.15 kg and is attached to a string 0.80 meters
long. **

**a. If Twila's yo-yo makes one complete revolution each second,
what is the inward force the string applies to the yo-yo.**

**b. If Twila increases the speed so that the yo-yo goes around
twice each second, what is the inward force exerted upon the yo-yo
now.**

**c. Determine the ratio of your force in a to your force in b.
Explain this ratio.**

**If the period of circular motion is cut
in half (linear speed is doubled) the required force will be four
times as great.**

**14. A 0.50 kg ball moves in a circle 40.0 cm in radius at a
speed of 4.0 m/s. Its centripetal acceleration is ___ m/s/s.**

**a. 10 b. 20 c. 40 d. 80**

** **

**15. The centripetal force on the ball in challenge #6 is ___
N.**

**a. 10 b. 20 c. 40 d. 80**

** **

**16. A toy cart at the end of a string 0.70 meters long moves in
a circle on a frictionless air table. The cart has a mass of 2.0 kg,
and the string has a breaking strength of 40.0 N. The maximum speed
of the cart is approximately ___ m/s.**

**a. 1.9 b. 3.7 c. 12 d. 17**

**17. Determine the centripetal force needed to keep a 3.0 kg
mass moving in a circle of radius of 0.50 meters at a speed of 8.0
m/s.**

**18. Our sun is located at a point in our galaxy about 3.00 X
104 light years (2.8 X 1020 meters) from the galactic center. It is
thought to be revolving around the center at a linear speed of
approximately 250,000 m/s.**

** **

**a. What is the sun's centripetal acceleration with respect to
the center of the galaxy?**

**b. The sun's mass can be taken to be 1.98 X 1030 kg. What
centripetal force is required to keep the sun moving in a circular
orbit about the galactic center?**

**c. Compare the centripetal force in (b) with that necessary to
keep the earth in orbit about the sun. (The earth's mass is 5.98 X
1024 kg, and its average distance from the sun is 1.495 X 1011 m and
the period is the time it takes the earth to travel around the sun
one time.)**

** **

**19. A fan blade takes 0.110 seconds to go around. What is the
acceleration of a point 0.510 meters from the center of the fan?**

**20. A string 1.0 meters long is used to whirl a 0.50 kg stone
in a vertical circle. **

**a. What is the tension in the string when the stone is at the
top of the circle moving at 5.0 m/s?**

**Fc = Tension + Fgrav ----> Tension= Fc
-- Fgrav = 12.5 N -- 4.9 N = 7.6 N**

**b. What is the tension in the string when the stone is at the
bottom of the circle moving at 11 m/s?**

**Fc = Tension -- Fgrav ----> Tension=
Fc + Fgrav = 60.5 N + 4.9 N = 65.4 N**

**21. A 200 gram mass is placed on a rubber band and the ball is
swung in a circle with a relatively constant speed. Will the tension
on the rubber band be largest at the top or bottom of the swing?
Explain.**

**The tension in the rubber band will be
largest at the bottom since it must provide enough force to balance
the force of gravity and cause an upward acceleration. At the top the
force of gravity is in the same direction as the tensional force on
the mass.**

**22. In Great America's ride "The Orbit," you are like the 200
gram mass and the normal force of the seat upon which you sit
provides the inward force. Where would you experience the largest
normal force at the top or bottom of the ride? Explain .**

**The normal force on the Orbit is largest
at the bottom for the same reason as in # 21.**

**23. Bob, has a 750 N weight and sits on a swing that swings
through a radius of 2.5 meters. If the tension in the string is twice
Bob's weight, what is his speed at the bottom of the swing?**

**24. A 55 kg GBS student rides on the Iron Wolf at Great America
and enters a loop-the-loop portion of the ride. The bottom of the
loop-the-loop has a radius of 15 meters and the speed of the coaster
is 25 m/s.**

**a. Determine the centripetal force required to move the student
upwards and keep her traveling in a circular path.**

**b. Considering that the force of gravity pulls the student
down, what normal force is required to keep her traveling upwards in
a circular path?**

**F=2290N+(9.8)(55)=2829N**

**25. You are probably sitting in a chair as you read this. You
and the chair are sitting on the earth which spins you with a speed
of 465 m/s (1040 mi/hr). If you didn't know any better, and believed
in Newton's 1st law, you would expect to continue moving in a
straight line with a velocity of 465 m/s and fly off the earth
tangent to its rotation. The fact that you remain on the earth is
because some force pulls you in toward the center of the earth. That
force is:**

**a. friction.**

**b. your inertia.**

**c. the gravitational attraction between you and the moon.**

**d. the gravitational attraction between
you and the earth.**

** **

**26. The centripetal force required to keep the space shuttle
orbiting the earth is provided by:**

**a. the inertia of the space shuttle.**

**b. the rotation of the earth on its axis.**

**c. the gravitational attraction between
the shuttle and earth.**

**d. the force of the shuttle's engines.**

** **

**27. Describe the centripetal force needed to keep the moon in
its orbit around the earth.**

**The centripetal force is provided by the
gravitational attraction between the earth and the moon.**

**28. Describe the centripetal force needed to keep the earth in
its orbit around the sun.**

**The centripetal force is provided by the
gravitational attraction between the sun and the earth.**

**29. A hole is drilled to the center of the earth and a stone is
dropped into it. When the stone is at the earth's center, compared
with the values at the earth's surface:**

**a. its mass and weight are both unchanged.**

**b. its mass and weight are both zero.**

**c. its mass is unchanged and its weight
is zero.**

**d. its mass is zero and its weight is unchanged.**

** **

**30. If the earth were three times farther from the sun than it
is now, the gravitational force exerted on it by the sun would
be:**

**a. three times as large as it is now.**

**b. nine times as large as it is now.**

**c. one-third as large as it is now.**

**d. one-ninth as large as it is
now.**

** **

**31. Determine the force of gravity between a 68 kg person and a
75 kg person 2 meters apart., Answer: 8.5 X 10 -8 N**

**32. Which person in challenge #31, the 68 kg or the 75 kg
person, experienced the largest force of gravity? Explain.**

**They both experience the same force
according to newtons third law and also the fact that both masses are
weighted equally in the gravity equation.**

**33. The force of attraction between two masses separated by 1.0
cm is 1.5 X 10-18 N. If one of the masses is 55 kg, determine the
second mass.**

**34. If you wanted to make a profit by buying gold by weight at
one altitude and selling it at another altitude for the same price
per pound, should you buy or sell it at the higher altitude?
Explain.**

**You should buy it at a higher altitude.
This is because the radius is getting bigger as you go further away
from the earth and gravitational force is inversely related to the
square of the radius. So as you get further from the earth, the
gravitational force decreases and therefore an object will weigh
less.**

**35. Using the equation for universal gravitation and the fact
that a 1.0 kg object has a weight (Fg) of 10 N, determine the mass of
the earth. The radius of the earth is 6,380,000 m.**

**36. Using the mass of the earth you determined in challenge 35
and the universal gravitation equation to determine the force of
attraction between the earth and a 75 kg person who stands on the
surface of the earth. Remember the radius of the earth is 6,380,000
m.**

**37. Using the mass of the earth you determined in challenge 35
and the universal gravitation equation to determine the force of
attraction between the earth and a 600 N woman who stands on a planet
with the same mass of the earth, but half its radius. Remember the
radius of the earth is 6,380,000 m.**

**38. Although you calculated a mass of the earth in #35 to be
6.1 X 10 24 kg, the mass of the earth is really closer to 6.0 X 10 24
kg. If a satellite is put into an orbit 400,000 m above the surface
of the Earth. Remember that the Earth has a radius of 6,380,000 m and
using the mass you found in challenge 16, determine the acceleration
of gravity at the height of the satellite.**

** **

**39. The speed needed to put a satellite in a circular orbit
does not depend upon:**

**a. the radius of the orbit.**

**b. the value of the acceleration of gravity.**

**c. the mass of the satellite.**

** **

**40. A 210 kg satellite circles the earth in an orbit 7.0 X
10 ^{6} meters in radius. At this altitude, g = 8.2 m/s/s. The
speed of the satellite is___ m/s.**

**41. According to Kepler's third law, the time needed for a
planet to go around the sun:**

**a. depends on its mass.**

**b. depends on the average radius of its
orbit.**

**c. depends on its speed of rotation.**

**d. is the same for all the planets.**

** **

**42. The speed of a planet in its elliptical orbit around the
sun: **

**a. is constant.**

**b. is highest when it is closest to the
sun.**

**c. is lowest when it is closest to the sun.**

**d. varies, but not with respect to its distance from the
sun.**

**Last Updated: October 8, 1997**