Download Lesson16 Circular Motion Review

Name: «First» «Last»
Physics 20 Circular Motion Review
1. Horizontal Circular Motion – Understand how this motion is achieved, that
centripetal acceleration is directed towards the center of a circle and represents a
change in direction of velocity not magnitude. Understand also that this
acceleration is caused by a force acting towards the center of the circle.
2. Vertical Circular Motion – Remember that the minimum velocity required to
maintain vertical circular motion occurs at the top of the circle
(where Fc = T + Fg). Understand that the tension at the top of a circle is zero,
thus the centripetal force is provided only by gravity. (therefore v = (rg)).
Understand that at the bottom of the circle is where velocity and centripetal force is
greatest because Fc = T – Fg.
3. Banked and Unbanked Curves – Understand that in an unbanked curve the
centripetal force is provided by friction alone. In Banked Curves the centripetal
force is provided by the normal force which is a component of the force of
gravity. Using the formula (Tan=v2 / rg), we can calculate the bank of the curve.
See diagram on p. 145 as the derivation and relationship of Fg, Fc, and FN will be
important.
4. Kepler’s Law – Understand that two bodies orbiting the same central body (i.e
two planets around the same star). Will have a predictable relationship or ratio
between their orbital periods and their orbital radii.
5. Newton’s Law of Universal Gravitation – Understand the gravitational forces are
influenced by the masses of the objects and their separation (radius) by Newton’s
Universal Gravitational Constant. Be able to apply this to satellites in orbit around
the earth as well.
Suggestions:
1. Review all your notes (otherwise what is the point of taking them) – this is
where your multiple choice items come from. Understand the concepts
qualitatively, so that you can relate them to other circumstances or be able to
see their applications.
2. Review all your assignments – These are exactly the type of questions that
will be on the exam. If you don’t understand how a question works ask me in
class or come to a help session. Don’t be shy, you are responsible for your
own success.
3. Read the material (explanations) in the blue book as a supplement to your
notes.
4. Do the Chapter 4 review on p. 231 and the Chapter 5 review on p. 289.
Name: «First» «Last»
Formulae You Will Get On The Test
v = d/t = 2r / T (where T is period)
ac = v2 / r
T12/r13 = T22/r23
Fg = Gm1m2 / r2
Ff = µFN
Fg = mg
Fc = mv2 / r
Fc = 42rm/T2 (where T is period)
Tan = v2/rg
Review Problems
1. A car travels around a curved path that has a radius of 225m at a constant speed of
26.0m/s. What is the centripetal acceleration of the car? (3.00m/s2)
2. How fast can a 1.6x103kg car round an unbanked curve radius 55m if the co-efficient
of friction between the car and the road is 0.60? (18m/s)
3. A 0.150kg mass is twirled in a horizontal circle of radius 0.750m at a rate of 2.50 rps
from the end of the string. Assuming the string is also horizontal, what is the tension
in the string? (27.8N)
4. You are riding your bike (total mass = 95.0kg) over a rise (r = 10.0m) on a bike path.
How fast must you be going so that your bike loses contact with the road? (9.90m/s)
5. A student (m = 50.0kg) is riding through a dip (r = 15.0m) on a roller coaster at a
speed of 10.0m/s. What will be the student’s apparent weight at the bottom of the dip?
(824N)
6. A 1.75kg mass is swung in a vertical circle (r = 1.10m) using a cord that will break if it
is subject to a force greater than 262N. What is the maximum speed that this mass can
travel as it passes the bottom of the circle? (12.4m/s)
7. A car travels around a curve (r = 60.0m) at a speed of 22.0m/s. At what angle must it
be banked so that the car does not have to rely on friction to remain on the road?
(39.4º)
8. An engineer is to design a curved exit ramp from a freeway for traffic with a
maximum speed of 20.0m/s. If she decides to bank the curve at an angle of 20.0º,
what does the radius of the curve have to be? (112m)
9. Calculate Kepler’s constant for objects rotating around the sun given that the earth has
a period of revolution about the sun of 3.16x107s and an orbital radius of 1.49x1011m.
(3.02x10-19s2/m3)
Name: «First» «Last»
10.
If a sun’s planet has a period of revolution of 7.82x109s, how far is it from the
sun? (5.87x1012m)
11.
On the surface of Planet T, which has a mass of 7.90x1025kg, an object has a
weight of 112N and a mass of 75.0kg. What is the radius of the Planet? (5.94x107kg)
12.
An object (mass = 525kg) is 3.0x103km above the earth’s surface. This object is
falling towards the earth because of the earth’s gravitational force on it. What is the
rate of acceleration when it is at this distance? (4.54m/s2)
13.
How far from the surface of the earth is the gravitational field strength 6.13x10-1
N/kg? (1.91x107m)
14.
Calculate the gravitational field strength at a point in space where the weight of an
object is 7.22x102N and its mass is 1.10x102kg. (6.56N/kg)
15.
What is the speed of an artificial satellite (m = 625kg) which is placed in an orbit
1.00x106m above the surface of a planet? (mP = 3.18x1023kg, rP = 2.43x106m)
(2.49x103m/s)
16.
An artificial satellite is put into orbit around the earth. If the radius of this orbit is
1.2x107m, how long will it take to make one revolution? (1.3x104s)
17.
An artificial satellite is put into a circular orbit around Jupiter (m = 1.90x1027kg
and r = 6.99x107m). If this satellite has an orbital velocity of 3.12x104m/s, how far
above the surface of Jupiter is the satellite? (6.03x107m)