Download Physics Final - Winter 2000

AP Physics 1 Final - Winter 2017
The final will cover the relevant sections of Chapters 1 through 8:
 1-D kinematics - motion in one dimension
 2-D kinematics - motion in two dimensions and projectiles
 Forces - Fundamental forces and Newton's Laws
 Conservation of energy
 Conservation of momentum
 Uniform circular motion and gravitation
 Torque – situations where all torques add to zero – only this in Chap. 8
 Trigonometric components of vectors
 UNIT ANALYSIS – know how every dimension is broken down into M, L, and T.
Make sure you know the physical dimensions and units of all of the variables that we
work with. For example, you should be aware by now that energy is broken down as a
(mass)·(length)2/(time)2. Know how to figure out the breakdown. Never, ever, write
down a dimensionally inconsistent expression.
Use proportional reasoning to solve the practice problems.
You will only be allowed to use a pencil, pen, ruler, and calculator during the exam. An
equation sheet will be provided, and you have been given a sample of that. You may not
bring the sample sheet to the exam.
Do practice problems at home by yourself and limit your response time. When you fail,
during practice, to answer something efficiently, studying is where you change your
concept knowledge to know WHY you had been inefficient.
*Unit Study Guides listed text problem that were and are still essential for practice, even
if they are problems that you never got to or ones that I never mentioned. Study guides
also listed the main concepts of each unit. You can assemble those for content outlines.
The problems of this packet are insufficient for a complete review. Some are not at the
AP level and these are just used to get started and are a reminder of topics. Pay attention
to how to use the College Board site to complete one’s practice. The real final will have
questions based on or stolen from old College Board problems.
More review material is going to be posted, which means that this packet needs to be
absorbed before January 9.
This posting does not have nearly enough Conservation of Energy, which is going to be
heavily represented on the final, so those who failed it the first time are required to learn.
Show all work on the pages provided, so that you can obtain as many points as possible.
Read the questions carefully, and apply what you know, showing equations clearly, and
substitution of numbers clearly.
1. A ball is launched vertically upward from right next to a rooftop. It starts at rooftop
level. The ball’s initial velocity is 15 m/s upward.
15 m/s
A. Define a coordinate system and tell the directions of the ball’s velocity and
acceleration vectors while the ball is ascending, and then while the ball is
descending. (4 answers total). (5 points)
B. How high above the rooftop does the ball come when it reaches the highest point
in its flight? (5 points)
C. If the ball comes back down again, misses the roof and travels down below the
roof level, what will be its velocity at the instant it has fallen 20 meters below the
roof. (Make sure you stick with the coordinate system.) (4)
D. Use the definition g = Fg/m to find the gravitational acceleration g on the surface
of Mars. (4 points)
E. If you solved part B on Mars, what would the maximum height be? (2)
2. A dart is thrown horizontally from a rooftop. The roof is 20 meters above the
ground. The horizontal launch velocity is 15 m/s.
15 m/s
A. Write the equations of motion in two separate columns, the x direction and the y
direction. Write the equations for the quantities x, y, and vy. (5 points)
x direction
x = __________________
y direction
y = ____________________
vy = ____________________
B. Find X, the horizontal distance traveled by the dart before it hits the ground. (5)
C. What are vx and vy of the dart just before the dart hits the ground? (3)
D. Sketch the velocity vector, showing an appropriate right triangle containing the
components vx and vy as they appear just before hitting the ground, and use this
triangle to find the actual magnitude of velocity (the speed) at ground level. (2)
3. The A-Team tries to get its engineless 2000 kg van moving by rigging up a pulley
system as shown. A 400 kg boulder is hung over a cliff. The rope runs from the
boulder, over a pulley and to the van. There is a friction force of 500 N acting on the
van.
A. Draw complete free-body diagrams of horizontal forces acting on the van and
then one of all the forces acting on the boulder, and label all the forces. Do not
draw on the picture above. Make your own free-body diagrams. (5 points)
B. Define coordinate systems for each of your two free-body diagrams. (2)
C. Write the equation for Newton’s Second Law applied to the boulder using the
variables from your diagram to do this. The Newton’s Second Law expression
must be consistent with your diagram and coordinate system. (2)
D. The van and the boulder accelerate in this arrangement. Can you say that the
boulder is in equilibrium? Can you say that there is zero net force on the boulder?
E. Can you say that the upward force that acts on the boulder is equal to the
downward force that acts on the boulder? (Remember, your answers must be
consistent with what you have already done in this problem.) (1)
F. Finish setting up the system and solve for the acceleration. (6)
G. Solve for the tension in the system. (2)
4. (Actually includes a bit of torques from Chapter 8, which we haven’t done yet, but
why limit our practice? I don’t want to hear questions about whether Chapter 8 is on
the test. I answered that on Page 1 of this packet. This problem should be interesting
regardless. Do not limit yourself.) The object shown is at rest. It is a beam with two
ropes attached whose directions are given. One tension is 1200 N. The other is
unknown, T. The weight of the beam is 1,400 N, and a person with a weight of 600
N hangs from the beam.
T
1200 N
37˚
53˚
x
Person
A. Find the unknown tension. (Hint: you do not need to consider rotation or torques
to do this part, just forces.) (8 points)
B. Any physical quantity, such as force or Newtons, can be broken down into the
three fundamental dimensions, length (m), time (s), and mass (kg). Show how the
units of torque can be broken down into these three fundamental units of measure.
For example, momentum is (kg)(m)/s. (3 points)
C. What distance, x, from the left end does the 600 N person have to be located so
that the system can be in equilibrium? The beam is 6 m long. (6 points)
5. Two lacrosse players run toward each other. One is moving 5 m/s to the right and has
a mass of 60 kg. The other is moving 2 m/s to the left with a mass of 100 kg. The
two collide and stick together. Solve for the final speed and direction of motion of
the two after the collision. (8 points)
6. Two planets orbit in circles with the same star at the center. The inner planet is 1
Astronomical Unit from the star. The other planet is 2 AUs from the center. The
outer planet’s orbital speed is 10,000 m/s. Answer the following, (realizing that there
are many ways to do this problem, so your method may or may not work better by
doing the problems out of order.) 1 AU = 1.5 x 1011 m.
A. Find the period of orbit of the outer planet. (4)
B. Find the star’s mass. (4)
C. Find the inner planet’s speed. (3)
D. Find the period of the inner planet. (3)
7. A toy marble track consists of a 500 gram marble that gets its energy from a
horizontal spring. First the spring is compressed, then the marble is released and
travels along the track through points A and B before climbing the hill and
momentarily coming to rest at point C. Assume that the marble never loses contact
with the track, and for now assume that friction is to be ignored.
Released
Spring
C
Ball in motion
A
0.5 m
B
A. The graph below shows how much force is required to compress the spring as a
function of distance compressed. Use it to find the potential energy stored in the
spring when the spring is compressed a distance of 8 cm. (4 points)
Force on Spring
(N)
Force Curve for Spring
60
40
20
0
0
2
4
6
8
Distance Compressed (cm)
10
For the rest of the problem, assume that the potential energy stored in the loaded spring
was 10 J.
B. If the spring is completely relaxed by the time the marble leaves it, what is the
kinetic energy of the marble at point A? (2 points)
C. Find the KE of the marble at point B which is 0.5 meters lower than point A. (5)
D. Find the speed of the marble at point B. (3)
E. Find the maximum height above the spring level that the marble will reach when
it momentarily comes to rest at point C. (5 points)
F. Suppose now that friction did 7 Joules of negative work on the marble as it
traveled from point A to the other side. What would be the potential energy of the
marble when it stops on the hill? Would the maximum height reached be
changed? (2)
Show all work on the pages provided, so that you can obtain as many points as possible.
Read the questions carefully, and apply what you know, showing equations clearly, and
substitution of numbers clearly.
8. (10) A rocket starts from rest. It's engine provides a forward thrust and this is the
only force acting. The thrust force is 20,000 N and the rocket's mass is 2,000 kg.
A. (3) What is the rocket's acceleration?
B. (3) How much time does it take the rocket to accelerate to 500 m/s?
C. (2) At the time that the rocket has reached 500 m/s, how far will the rocket have
traveled from its starting resting point?
D. (2) How much work did the thrusting force do in bringing the rocket from 0 m/s
to 500 m/s?
E. Bonus: Show an alternate method for determining the last answer.
9. (8) Suppose a rocket is traveling through space at 500 m/s, and it is moving toward a
region called sector C where the speed limit is 400 m/s. To slow down, the rocket
pilot turns on thrusters that point backwards (to your left in the picture). The slowing
down begins when the rocket is 4,500 meters away from sector C's boundary, as
shown. Right when the rocket has covered those 4,500 meters and its nose enters
Sector C, its speed indeed just reaches 400 m/s.
500 m/s velocity
4,500 m
Slowing Begins
Sector C's Boundary
A. (1) While slowing down, is the rocket's acceleration pointing to the left, right, or
neither (That is, to your left or right, while looking at the picture?
B. (2) What is the magnitude of the rocket's acceleration? (Hint: you don't know the
time, so how about using the given equation without time in it? That would save
you time.)
C. (2) Those backward thrusters were left on by accident once the rocket had entered
Sector C, so the rocket's acceleration stayed constant, and it eventually slowed to
a stop. How much time did it take to go from 400 m/s to rest?
D. (2) Still assuming the constant thrusters were left on, what would the rocket's
velocity (magnitude and direction!) be 80 seconds after entering Sector C?
E. (1) Assuming the thrusters are never shut off ever again, can you give at least one
other specific fact about the rocket's motion as time increases. (No more than two
sentences, the fact should relate to topics such as velocity, change of speed,
location relative to C's boundary, acceleration, etc.)
10. (20) Some people have objected to the fact that NASA has spent millions of dollars
so that astronauts could stand on the moon and hit golf balls there. But if you can get
there, you might as well test the laws of projectile motion in an air-free environment!
And better yet, g is different, so you can experiment with the effect of a changed g.
A. (3) Given the moon's statistics, prove that g on the moon is about one-sixth of
what it is on earth.
B. (1) Why is it so important to have an air-free environment when assuming freefall for projectile motion? (10 words or less.)
20 m/s
Suppose a person hits a golfball on the moon. The launch velocity is 20 m/s at an
angle of 37 degrees above the horizontal.
C. (5) Write the equations of motion in two separate columns, the x direction and the
y direction. Write the equations for the quantities x, y, and vy.
x direction
x = __________________
y direction
y = ____________________
vy = ____________________
D. (3) Solve: (vx)0 = ?
(vy)0 = ?
E. (1) Which of the following choices is a variable that changes while the ball is in
flight:
vx, vy, (vx)0, (vy)0
F. (5) Find X, the horizontal distance traveled by the ball once it hits the ground.
G. (2) On earth, where g is 9.8 m/s2, the horizontal distance traveled by a ball
launched exactly as above would be 38.5 m. Does this indicate a direct or an
inverse relationship between the value of g and the X value covered in this type of
problem? Explain very briefly.
11. (6) The golf ball shown below is hit ON EARTH. When it is at the highest point in
its trajectory, its speed is 16 m/s. Use conservation of energy to find the height of the
ball above the ground when it is at its highest point moving at 16 m/s. Its launch
speed is 20 m/s. Assume there are no non-conservative forces.
Reminder: The v used to calculate energy refers simply to speed, not the vector v, so
don't make this one unnecessarily difficult.
Bonus: Explain how I know that the speed at the highest point is 16 m/s without doing
any new calculations
12. (17) The system below has the following facts associated with it:
There is no friction of any kind.
String A, which runs over the pulley on the right, has a tension in it of 30 N.
String B, which runneth over the pulley on the left, has unknown tension T.
All three objects share the same unknown acceleration "a".
The masses are given.
2 kg
string B
2 kg
string A
Table
4 kg
A. (4) Below, the free-body diagrams for the problem are incomplete. The tensions
due to the strings are already correctly represented below, so you do not need to put
those in. You only need to complete the diagrams to correctly account for any other
real forces that are directly acting on each object. Put the answers on the diagrams
below, not above.
30 N tension
T
T
30 N tension
B. (3) Define coordinate systems for each of the free-body diagrams.
C. (4) Write four Newton's Second Law equations, one for each hanging mass, and
two for the 2kg mass on the table (Why two?)
D. (2) Find the acceleration.
E. (2) Find the unknown tension.
F. (2) Is the tension you found consistent with the fact that the hanging mass on the
left accelerates upward? Explain in one brief sentence.
13. (11) A person named Galileo Galilei pointed his telescope at the planet Jupiter. What
he saw changed the way people look at the world. Round objects were observed to orbit
Jupiter on circular paths! Galileo saw that one of these (now called Io) would always
take 3.5 days to travel from one side of Jupiter to the exact opposite side of the planet
(i.e.halfway around the circle.) The radius of this orbit is 10.7 x 108 m.
A. (4) Calculate Io's speed in the circular orbit.
Once Newton’s theories were established (after Galileo’s lifetime), Newton’s theories
and Galileo’s observations made the following calculations possible:
B. (4) Calculate the mass of Jupiter itself.
C. (3) Another moon is observed orbiting Jupiter on another circular path, and its
period is double that of Io. Calculate the radius of this other moon’s orbit.
14.(14) Barney Gumble, a drunken engineer, who works for Six Flags Over Springfield,
is told to design a loop roller coaster whose cars must travel at least as fast as 10 m/s
when they are passing the highest point in the loop. The engineer assumes that the track
will be frictionless and designs a coaster assuming the values shown in the diagram
below. The top of the hill (point A) and the top of the loop are at the same height.
A
10 m/s speed
30 meters
30 meters high
A. (3) Label the top of the roller coaster as point B. Assume that the roller coaster
car starts AT REST at point A, and use calculations or concepts to prove that the
roller coaster, as Barney has designed it, will not be going fast enough when it
gets to point B. If you like, you can make up any car mass you want.
Mass = __________
When the roller coaster is actually constructed, it actually works and looks as shown
below. The mass of the car is 2,000 kg. The car still starts at point A at rest.
A
C
30 meters
B. (3) Assuming it had no friction, how fast would the car be going at the top of the
loop in this roller coaster. The loop is now 20 meters high and the car starts from
rest at the top of the big hill to the left.
C. (2) Still assuming it had no friction, how much kinetic energy would the car have
at the instant it first reaches point C? Point C is 20 m high, just like the loop.
D. (2) If there really were friction, and friction did a total of 50,000 J of work on the
roller coaster between points A and C, what would the last answer be?
E. (2) For simplicity, go back to ignoring friction. After passing point C, the roller
coaster runs into a big spring and compresses it and then springs backward. At
the instant that the spring is compressed fully and the roller coaster car comes to
rest for an instant, how much potential energy is stored in this big spring?
F. (2) Now suppose that the spring were not there and instead, the car travels up
another hill after passing point C. The car travels up the hill, stops momentarily,
and then rolls down backwards. Again, assuming no friction, calculate the car’s
maximum height on the hill. (Solve for the height relative to C’s height.)
Stopping point
C
h=?
15. An explosion can be seen as the interaction of more than one members of a system
who violently decide to divorce or disband.
Suppose you have a stationary watermelon whose mass is 6 kg. It is sitting at rest when
it explodes into two pieces. One piece is 5 kg and moves to right at 5 m/s. Find the
speed and direction of motion of the other part of the watermelon.
16. The circular room below spins at 20 m/s. The person sticks to the wall without
moving up or down. The room's radius is 10 meters. Find the coefficient of friction
between the person and the wall.
Answers:
1.
Ball Launch
A. Ascending: up, down
Descending: down, down
B. 11.25 m
C. 25 m/s
D. 3.71 m/s2
E. 11.25 meters times (9.8/3.71)
2.
Sideways Dart
A. x = 15t
y = - ½ gt2 vy = -gt
B. 30 m
C. vx = 15 m/s vy = -20 m/s
D. Speed = 25 m/s
Angle is 53 degrees below horizon
3.
A-Team
4000 – T = 400a
Nothing is in equilibrium
a = 1.46 m/s2
T = 3417 N
4.
On the beam
A. 1600 N
B. kgm2/s2
C. 0.2 m
7.
Toy marble track
A. 1.6 J
B. 10 J
C. 12.5 J
D. 7 m/s
E. 2 m
F. 3 J, 0.6 m
8.
Rocket
a.
b.
c.
d.
10 m/s2
50 s
12,500 m
250,000,000 J
Rocket
a.
b.
c.
d.
e.
left
-10 m/s2
40 s
400 m/s, left
Speed continues to increase. Motion will always be leftward.
9.
10.
B.
C.
D.
E.
F.
G.
During free-fall, no forces besides gravity are allowed to act.
x = (16 m/s)t
y = (12 m/s)t – ½ gt2 vy = (12 m/s) – gt
(vx)0 = 16 m/s
(vy)0 = 12 m/s
vy is the only thing that changes mid-flight. All those other v symbols are constants.
233 m
Inverse. One 6th the g causes 6 times the X. That’s what inverse means.
11. 7.2 m. Different problem: Given a launch speed of 20 m/s, and a maximum height of 8 meters,
solve for the launch angle. Use conservation of energy to do it. The answer will be given. You
have to show how to prove it. Answer: 39°
14. Barney coaster
a. v = 0
b. 14 m/s
c. 200,000 J
d. 150,000 J
e. 200,000 J
f. 10 m
15. 25 m/s to the left
16. 0.25