Download Unit 8 Review Answer Key

Uniform Circular Motion Review
Use the following equations to answer the next 6 questions.
𝑣2 =
𝐹𝑐 (𝑟)
𝐹𝑐 =
𝑚
𝑚𝑣 2
𝑟
𝑣=
2𝜋𝑟
𝑇
NOTE: Questions 1 -3 do NOT say that the centripetal force remains constant!!!!!
1. How does the velocity of an object change if the radius is doubled but the mass, and period remain the
same? Focusing on the 3rd equation, the velocity would be twice as great.
2. How does the velocity of an object change if the mass is tripled but the radius, and period remain the
same? Focusing on the 3rd equation, the velocity would be the same.
3. How does the velocity of an object change if the period is ½ the time and the mass and radius remain
the same? Focusing on the 3rd equation, the velocity would be 2 times greater.
4. How would the centripetal force change in the situation in question number 1? Focusing on the 2nd
equation and the fact that the velocity is twice as great and the radius is twice as great. . . Fc would be
22 / 2 = 2 times greater.
5. How would the centripetal force change in the situation in question number 2? Focusing on the 2nd
equation and the fact that the velocity is the same . . . Fc would be 3 times as great.
6. How would the centripetal force change in the situation in question number 3? Focusing on the 2nd
equation and the fact that the velocity is 2 times greater . . . Fc would be 22 or 4 times greater.
7. Draw in velocity vectors for each labeled point if the object is rotating in a horizontal circle.
A
8. Show the direction of the acceleration at point
B
Top view
C with vectors.
C
∆V
Vf
D
-Vo
9. Draw in velocity vectors for each labeled point if the object is rotating in a vertical circle.
10. Also put a dashed line from point A and point D to
A
B
to show the path the object would take if the
centripetal force disappeared.
Side view
C
D
Uniform Circular Motion Review
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11. Explain what a centripetal force is and what is a centrifugal force? Centripetal is a label put on the net
force on an object that causes it to move in a circle. Centrifugal is an imaginary force that makes you feel like
you are being pulled out of the circle but it is a result of your inertia resisting the turn (NOT a force).
12. Make a general statement about each of the following for the listed situation. Describe how each changes
(or doesn’t change) and if it changes how and why. A car coasts around a corner. Assume that all types of
friction are negligible except the friction that allows the car to turn.
a. Speed – remains constant
b. Velocity – is changing because your direction is changing toward the center of the turn.
c. Acceleration- is towards the center because your velocity is changing towards the center.
d. Centripetal force – There must be a net force toward the center for an object to accelerate toward
the center.
13. What is the difference between period and frequency? What are the units for each? Period is the time to
complete one revolution and measured in time (seconds). Frequency is the number of rotations in a
certain amount of time. The time is usually 1 second (units are Hertz) or 1 minute (units are rpm).
14. If you can stand anywhere on earth, where would you velocity be the slowest? Fastest? Explain why.
Your velocity would be the slowest at the poles because you have no radius to move around. With no
radius you have no velocity. Fastest would be at the equator because you have the largest radius. The
mass, centripetal force, and period remain constant no matter where you are on Earth.
15. A rollercoaster is making a loop that has a diameter of 10m. What would the speed of the coaster be at
the top of the loop if a 60kg passenger feels 1/3 his normal weight?
𝑚𝑣 2
r = 5m
Fg
Σ𝐹 = 𝐹𝑐 = 𝐹𝐺 + 𝐹𝑁
𝐹𝑐 =
m= 60kg
Fg= 600N
FN= 200N
FN
Σ𝐹 = 𝐹𝑐 = −600 − 200
Σ𝐹 = 𝐹𝑐 = −800𝑁
800 = 5
𝑣 = 8.16 𝑚⁄𝑠
16. What is the acceleration of the coaster? 𝑎𝑐 =
17. What is the period of the coaster?
𝑣=
𝑣2
𝑟
2𝜋𝑟
𝑇
𝑎𝑐 =
8.162
5
8.16 =
2𝜋(5)
𝑇
𝑟
60𝑣 2
𝑎𝑐 = 13.32 𝑚⁄𝑠 2
𝑇 = 3.85𝑠
18. A 1000kg car drives through circular ditch with a radius of 18m. What is the centripetal force if the car is
going 20 m/s?
19. What is the acceleration of the car?
Uniform Circular Motion Review
𝐹𝑐 =
𝑎𝑐 =
𝑚𝑣 2
𝑟
𝑣2
𝐹𝑐 =
𝑎𝑐 =
𝑟
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1000(20)2
18
202
18
𝐹𝑐 = 22,222.22 𝑁
𝑎𝑐 = 22.22 𝑚⁄𝑠 2
Devenney 09
20. What is the normal force on 55 kg driver? 𝐹𝑐 =
𝑚𝑣 2
𝐹𝑐 =
𝑟
Σ𝐹 = 𝐹𝑐 = 𝐹𝑔 + 𝐹𝑁
55(20)2
𝐹𝑐 = 1222.22 𝑁
18
Σ𝐹 = 1222.22 = −550 + 𝐹𝑁
𝐹𝑁 = 1772.22 𝑁
21. Betty Joe decides to make a sweet pea shake. What is the frictional force on a 5g pea that is suspended on
the side wall of a blender that has a radius of 25 cm?
Σ𝐹𝑦 = 0 = 𝐹𝑔 + 𝐹𝑓
Σ𝐹𝑦 = 0 = −.05 + 𝐹𝑓
1
𝑇=𝑓
22. What is the speed of the pea if the frequency is 2 Hz?
𝑣=
2𝜋𝑟
𝐹𝑓 = .05 𝑁
1
𝑇=2
𝑣=
𝑇
2𝜋(.25)
.5
𝑇 = .5𝑠
𝑣 = 3.14 𝑚⁄𝑠
23. What is the coefficient of friction between the pea and the blender?
𝐹𝑐 =
𝑚𝑣 2
𝑟
𝐹𝑐 =
.005(3.14)2
𝐹𝑐 = .197 𝑁
.25
Ff
Fg
FN
𝐹𝑓 = 𝜇𝐹𝑁
So FN = Fc
.05 = 𝜇(. 197)
𝜇 = .25
*** Review ALL problems on All Worksheets and the Lab***
Uniform Circular Motion Review
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