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Introductory Physics 101
Final Exam Review Sheet
DATE AND TIME: The exam will be given at 1:30 PM, Monday Dec. 12, in the South Lobby.
FORMAT: The exam will contain three sections. The first section will be short answer questions
(true/false, multiple choice, multi-select, fill in the blank, conceptual questions, essays, and so on.)
The second section will be standard problems. Lastly, the exam will have some intriguing problems. I
predict, but do not guarantee, that these three sections will be worth 40%, 40%, and 20%, respectively.
WHAT IS COVERED:
 Chapters 1  6, all sections
 Chapter 7, sections 1  8
 Chapter 8
EQUATIONS AND CONSTANTS:
You are allowed to bring one 7.62 cm  12.7 cm note card with any 15 equations you wish hand
written on one side. I strongly advise you only write down the main equations (often blocked off in
tan in the book.) The others are NOT acceptable starting points. No "text", unless it’s an inspirational
poem or quote. I'll give you any constants you need (although I might not tell you the units) except the
value of g, the acceleration due to gravity on the Earth’s surface. You are also responsible for knowing
the common prefixes down to pico and up to tera (they're on the back side of the first page in your
book) and these may not be on your note card. Furthermore, no information may be stored in your
calculators. I’ll examine note cards and calculators at random. If yours violates these guidelines I’ll
take it from you. Make sure the equations are correct; I hate it when they aren’t! Please, I beg and
plead with you to understand the derivation and applications of the equations. Having them written
down on your card won't help you if you don't.
SOME MAJOR CONCEPTS:
 Accuracy and Significant Figures, Unit Conversion
 Position and Displacement
 Speed, Average and Instantaneous Velocity
 Average and Instantaneous Acceleration
 Kinematic Equations, Range
 Vectors and Relative Motion. Vectors. Vectors! Oh, did I mention vectors?
 Newton's Three Laws and Free Body Diagrams
 Static and Kinetic Friction
 Static Equilibrium, including rigid body equilibrium from chapter 9.
 Circular Motion, Centripetal Force, and Centripetal Acceleration
 Universal Gravitational Force
 Kepler's Laws and Other Applications of Gravitational Force
 Work, Kinetic Energy, Potential Energy, Power
 Hooke's Law, Potential Energy of a Spring
 Conservation of Mechanical Energy, and E1 + WNC = E2
 Impulse and Linear Momentum
 Conservation of Linear Momentum (1D and 2D), and pi + Jext = pf
 Elastic, Inelastic, Completely Inelastic Collisions
 Center of Mass and Applications
 Angular Position, Velocity, and Acceleration
 Torque, Moment of Inertia, Rotational Dynamics
 Rotational Kinetic Energy, especially with Conservation of Mechanical Energy
 Angular Momentum, especially conservation thereof. Also Li + ext·t = Lf
 Anything from the laboratory part of our class
Sample Problems:
1. Find algebraically and graphically the a) resultant and b) equilibriant of the following coplanar forces: 300. N at 0.00,
400. N at 30.0, and 400 N at 150.
2. A Segway PT with an initial velocity of 80.0 cm/s moves along a straight line with a constant acceleration and travels
120. m in 60.0 s. For the first 40.0 s interval find (a) the average velocity, (b) the final speed, (c) the acceleration, and (d)
the distance traveled.
3. A New York Yankees batter hits a home run ball with a velocity of 132 ft/s at an angle of 26.0 above the horizontal.
A fielder who has a reach of 7.00 ft above the ground is backed against the bleacher wall, which is 386 ft from home plate.
The ball was 3.00 ft above the ground when hit. How high above the fielder’s glove does the ball pass? For extra fun,
calculate how far the ball travels horizontally assuming a level field! In British units, g is 32.2 ft/s2.
4. A 20.0 kg crate hangs at the end of a long rope held by a person. Find its acceleration when the tension in the rope is
a) 250. N, b) 150. N, c) zero, and d) 196 N.
5. Three blocks are connected such that a 6.00 kg block (m1) hangs off the left side of a table, a 10.0 kg block (m2) sits flat
on the table, and a 9.00 kg block (m3) hangs off the right side of the table. Strings that pass over frictionless pulleys
connect the three blocks. Find the minimum coefficient of static friction (s) between the table and the middle block such
that the system does not move. If the coefficient of friction is negligible find the acceleration (a) of the system and the
tension in the two strings. Repeat the second part for a coefficient of kinetic friction (k) of 0.200. Solve symbolically.
6. In the previous problem, imagine that the 6.00 kg block starts on the ground and the 9.00 kg block starts 50.0 cm (y0) in
the air. Initially the system is at rest. What is the velocity of the three blocks (v) right before the 9.00 kg block hits the
ground if  = 0.00? Repeat for  k = 0.200. Start from scratch and use energy techniques, not kinematics.
7. An engine expends 40.0 hp (P) in propelling a 1200. kg (m) car along a level track at 15.0 m/s (v0). How large is the
total retarding force (Ffr) acting on the car? What power is required to drive up a 30.0 slope (), at the same speed, if the
retarding force is the same as before, and parallel to the hill?
8. If the car in the previous problem stalled out at the hill, how far up the hill would the car coast given its initial velocity,
if the retarding force magically disappeared? If the retarding force was still present? If the retarding force was still present
and the engine didn’t stall, but rather continued to provide a constant power of 40.0 hp?
9. Two bodies of 8.00 and 4.00 kg move along the x-axis in opposite directions with velocities of 11.0 and –7.00 m/s,
respectively. They collide and stick together. What type of collision is this? Find their velocity after collision. What is the
kinetic energy of the system before and after the collision? Compute the fraction of the initial kinetic energy that remains.
Calculate the momentum of the center of mass. Does it ever change?
10. a) For the problem above, repeat if the two objects experience an elastic collision. b) Repeat yet again for a 2D elastic
collision knowing that the 8.00-kg object is seen traveling at +30.0 after the collision.
11. The uniform bar shown below weights 40.0 N and is subjected to four additional forces, as shown. The magnitudes of
the forces are 60.0, 50.0, 70.0, and 80.0 N, left to right, and the bar’s length is 2.00 m. Find the net torque and the angular
acceleration of the bar, about an axis perpendicular to the page and through point A. Repeat for point B, located at the bar’s
geometric center.
30
A
40 cm
B
120 cm
40 cm
12. From what minimum height (y) above the ground must a small mass m be released in order to safely navigate a loopthe-loop of radius R such that the normal force on the mass is always greater than or equal to its weight? Repeat for a small
solid sphere of radius r. Repeat both if the kinetic frictional coefficient on the hill is k (but zero on the loop) and the angle
of the hill is a constant .
13. A 14.8-gram DVD rotates from rest to an angular speed of 31.4 rad/s in a time of 0.892 s. What is the angular
acceleration of the DVD? How many revolutions does the DVD make? If the radius is 4.45 cm, find the linear speed,
tangential acceleration and centripetal acceleration of a microbe riding on the rim of the DVD. What is the angular speed
and displacement of the DVD 0.300 s after it begins to rotate? What torque is necessary to accelerate it as described?
14. A frictionless pulley in the shape of a solid cylinder of mass 3.00 kg and radius 40.0 cm is used to draw water from a
well. A bucket of mass 2.00 kg is attached to a cord wrapped around the cylinder. If the bucket starts from rest at the top
of the well and falls for 3.00 seconds before hitting the water, how deep is the well? Solve using torque and kinematics.
15. Repeat problem 13 knowing that right before the bucket hits the water the pulley is rotating at a speed of 42.0 rad/s.
Solve using energy and kinematicsand note you do not know the time.
16. A mass m stretches a spring a distance x1, when hung vertically. The same spring is used to launch the same mass
horizontally towards a loop-the-loop of radius R. How far must the spring be compressed (x2) in order for the mass to
safely traverse the loop-the-loop? Assume friction is negligible.
b) Calculate for m = 500. grams, x1 = 2.50 cm, R =
18.0 cm
Answers:
1.
2.
3.
4.
5.
6.
7.
8.
8.
9.
11.
12.
13.
500. N at 53.1, 500. N at 233.1
1.60 m/s, 2.40 m/s, 4.00 m/s2, 64.0 m
13.8 ft (thus a sure homerun!), 432.47 ft (NOT 426.4 ft!!!)
2.70 m/s2 up, 2.30 m/s2 down, 9.80 m/s2 down, zero.
0.300; 1.176 m/s2, 65.9N, 77.6 N; 0.392 m/s2, 61.2 N, 84.7 N
1.08 m/s up, right, and down, respectively; 0.626 m/s up, right, and down, respectively.
1990 N, 158 hp 8. 23.0m, 17.2m, 34.7 m
Completely inelastic, +5.00 m/s, 582 J and 150 J, 0.258, 60.0 kgm/s, no
a) Elastic, –1.0 and +17.0 m/s, 582 J and 582 J, 1.000; b) Elastic, 9.78 m/s at 30.0, 9.98 m/s at 259, 582 J
a) 52.0 Nm and 9.56 rad/s2, both clockwise, b) 28.0 Nm and 20.6 rad/s2, both counterclockwise
a) y = 3R, b) y = 17R/5, c) y = 3R/[1 – (/tan)]
35.2 rad/s2, 2.23 rev, 1.40 m/s, 1.57 m/s2, 43.9 m/s2, 10.6 rad/s, 1.58 rad, 5.16  10–4 Nm
25.2 m
14. 25.2 m
15. Answer: x2 = sqrt(5x1R), 15.0 cm