Download AP physics final AP test review Mechanics

Physics B
AP Review Packet: Mechanics
Name:________________
Position (x) (unit: m)
Location of a particle in space.
Uniformly Accelerated Motion
aave = ∆v/∆t
Distance (unit: m)
The total length of the path traveled by an object.
Does not depend upon direction.
3. Acceleration (A-182 #1)
In which of the following situations would an object be
accelerated?
I. It moves in a straight line at constant speed.
II. It moves with uniform circular motion.
III. It travels as a projectile in a gravitational field with
negligible air resistance.
(A) I only (B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III
Explain your answer:
Displacement (x) (unit: m)
Change in position. Depends only on the initial and final
positions, not on path.
Includes direction.
1.
Distance vs Displacement (PAB)
A hiker hikes 25 miles due north and then all the way back to
the starting point.
a) How far does the hiker hike? Show your work:
b) What is the hiker’s displacement? Show your work:
Average Velocity (unit: m/s)
vave = ∆x/∆t
Average speed (unit: m/s)
save = d /∆t
For motion in a straight line, average speed is the magnitude
(abs. value) of the average velocity.
2.
Kinematic Equations
v = vo + at
x = xo + vot + 1/2 at2
v2 = vo2 + 2a(∆x)
4. Kinematic Equations (A-195 #65)
A body moving in the positive x direction passes the origin at
time t = 0. Between t = 0 and t = 1 second, the body has a
constant speed of 24 meters per second. At t = 1 second, the
body is given a constant acceleration of 6 meters per second
squared in the negative x direction. The position x of the body
at t = 11 seconds is
(A) +99 m
(B) +36 m
(C) -36 m
(D) -75 m
(E) -99 m
Show your work:
Average Speed/Velocity (S-113 #11)
5.
Kinematic Graphs for 1-D motion
Stationary particle - draw
The graph above represents position x versus time t for an
object being acted on by a constant force. The average speed
during the interval between 1 s and 2 s is most nearly
a. 2 m/s
b. 4 m/s
c. 5 m/s
d. 6 m/s
e. 8 m/s
Show your work:
x vs t
x vs t
Acceleration (a) (unit: m/s2)
Any change in velocity, including speeding up, slowing down,
or turning.
If the sign of the velocity and the sign of the acceleration is the
same, the object speeds up.
If the sign of the velocity and the sign of the acceleration are
different, the object slows down.
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v vs t
a vs t
Particle moving with constant non-zero velocity - draw
v vs t
a vs t
Particle moving with constant non-zero acceleration - draw
x vs t
v vs t
Bertrand
a vs t
Physics B
6.
AP Review Packet: Mechanics
Projectile Motion
Something is fired, thrown, shot, or hurled near the earth’s
surface.
Horizontal velocity is constant.
Vertical velocity is accelerated.
Air resistance is ignored.
Kinematic Graphs (S-199 #1)
The displacement x of an object moving along the x-axis is
shown above as a function of time t. The acceleration of this
object must be
(A) zero
(B) constant but not zero
(C) increasing
(D) decreasing
(E) equal to g
Explain your answer:
Trajectory of Projectile
Parabolic path of a projectile
RANGE is how far it travels horizontally.
MAXIMUM HEIGHT occurs halfway through range, if fired
over level ground.
Acceleration is DOWN at 9.8 m/s2 everywhere.
Instantaneous velocity is tangent to the path.
The vertical velocity changes while the horizontal velocity
remains constant.
9.
Kinematic Graphs for 2D Projectiles
x-component of motion – draw for a projectile
x vs t
7. Kinematic Graphs (S-195 #3)
The graph shows the velocity versus time for an object
moving in a straight line. At what time after time = 0 does the
abject again pass through its initial position?
(A) Between O and 1 s
(B) at 1 s
(C) Between 1 and 2 s
(D) at 2 s
(E) Between 2 and 3 s
Show your work:
v vs t
a vs t
y-component of motion – draw for a projectile
x vs t
v vs t
a vs t
10. Projectile Motion (A-182 #64, #65)
Free Fall
An object falls accelerated by gravity
g = 9.8 m/s2 downward.
a = -g if up is positive.
acceleration is down when ball is thrown up EVERYWHERE
in the balls flight.
8. Free Fall (A-182 #5)
An object is released from rest on a planet that has no
atmosphere. The object falls freely for 3.0 meters in the first
second. What is the magnitude of the acceleration due to
gravity on the planet?
(A) l .5 m/s2 (B) 3.0 m/s2 (C) 6.0 m/s2
(D) 10.0 m/s2 (E) 12.0 m/s2
Show your work:
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a) How do the speeds of the ball at the three points compare?
(A) vP < vQ< vR
(B) vR < vQ < vP
(C) vQ < vR < vP
(D) vQ < vP = vR
(E) vP = vR < vQ
Explain your choice:
b) Which of the following diagrams best
shows the direction of the acceleration of
the ball at point P ?
Explain your choice:
Bertrand
Physics B
AP Review Packet: Mechanics
Vertical Component of Velocity
Accelerated by gravity (9.8 m/s2 down)
Use kinematic equations for accelerated motion.
11. Graphs of Projectiles (A-177 #63)
A projectile is fired with initial velocity v0 at an angle 
with the horizontal and follows the trajectory shown above.
Which of the following pairs of graphs best represents the
vertical components of the velocity and acceleration, v and a,
respectively, of the projectile as functions of time t ?
Explain your reasoning:
13. Vertical Component (S-199 #5)
A 2-kilogram block rests at the edge of a platform that is 10
meters above level ground. The block is launched horizontally
from the edge of the platform with an initial speed of 3 meters
per second. Air resistance is negligible. The time it will take
for the block to reach the ground is
(A) 0.3 s
(B) 1.0 s
(C) 1.4 s
(D) 2.0 s
(E) 3.0 s
Show your work:
14. Vertical Component (A-187 #59)
A rock of mass m is thrown horizontally off a building from a
height h, as shown above. The speed of the rock as it leaves
the thrower's hand at the edge of the building is  0 . How
much time does it take the rock to travel from the edge of the
building to the ground?
(A)
h 0
Working 2-D Motion Problems
Resolve vectors into components.
Work as one-dimensional problems.
(B) h  0
(C) h 0 g
(D) 2h g
(E)
2h g
Show your work:
Force (F) (unit: N)
A force is a push or pull on an object.
Forces cause an objects to accelerate.
Horizontal Component of Velocity
Not accelerated by gravity (or anything)
Follows equation x = Vo,xt
12. Horizontal Component (A-177 #9)
A diver initially moving horizontally with speed v dives off
the edge of a vertical cliff and lands in the water a distance d
from the base of the cliff. How far from the base of the cliff
would the diver have landed if the diver initially had been
moving horizontally with speed 2v ?
(A) d
(B) 2d
(C) 2d (D) 4d
(E) It cannot be determined unless the height of the cliff is
known.
Show your work or explain your reasoning:
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Newton’s First Law (Law of Inertia)
A body in motion stays in motion at constant velocity and a
body at rest stays at rest unless acted upon by an external
force.
Equilibrium
A body with no net force on it is in equilibrium. Bodies in
static equilibrium are stationary; bodies in translational
equilibrium are moving.
Bertrand
Physics B
AP Review Packet: Mechanics
15. Newton’s 1st Law (A-187 #7 - mod)
Three forces act on an object. If the object is in translational
equilibrium, which of the following must be true?
I. The vector sum of the three forces must equal zero.
II. The magnitudes of the three forces must be equal.
III. One force must be the equilibrant of the other two.
(A) I only
(C) I and III only
(E) I, II, and III
Explain your reasoning
(B) II only
(D) II and III only
Newton’s 1st Law (A-177 #58)
When an object of weight W is
suspended from the center of a
massless string as shown above, the
tension at any point in the string is
(A) 2W cos
(B) W cos
Show your work:
2
(C) W cos
(D) W
2 cos
(E) W
cos
16. Newton’s 1st Law (A-187 #44 - mod)
Newton’s Second Law
F = ma
The sum of the forces on the object is zero in which of the
cases?
(A) II only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
Explain your reasoning
17. Newton’s 1st Law (S-195 #5)
A hall of mass m is suspended from two strings of unequal
length as shown above. The tensions T1 and T2 in the strings
must satisfy which of the following relations?
(A) T1= T2
(B) T1>T2
(C) T1<T2
(D) T1+T2=mg
(E) T1-T2 = mg
Show your work or explain your reasoning:
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Procedure for Second Law Problems
Step 1: Draw the problem
Step 2: Free Body Diagram
Step 3: Set up equations
F = ma Fx = max Fy = may
Step 4: Substitute known values
Step 5: Solve
18. Second Law (A-173 #11)
When the frictionless system shown above is accelerated by an
applied force of magnitude F, the tension in the string between
the blocks is
(A) 2F
(B) F
Show your work:
2
F
(C)
3
1
F
(D)
2
1
F
(E)
3
Bertrand
Physics B
AP Review Packet: Mechanics
19. Second Law (A-182 #2)
A ball falls straight down through the air under the influence
of gravity. There is a retarding force F on the ball with
magnitude given by F = bv, where t is the speed of the ball and
b is a positive constant. The magnitude of the acceleration a of
the ball at any time is equal to which of the following?
(A) g  b
Show your work:
bv
(B) g 
m
(C) W
(E) W + Fcos 
Show your work
(D) W + Fsin 
22. Normal Force Ramp (A-271 #62)
(C) g  bv
m
(D) g
b
bv
(E)
m
20. Second Law (A-182 #45)
A block of mass 3m can move without friction on a horizontal
table. This block is attached to another block of mass m by a
cord that passes over a frictionless pulley, as shown above. If
the masses of the cord and the pulley are negligible, what is
the magnitude of the acceleration of the descending block?
(A) Zero
(B) g/4 (C) g/3
(D) 2g/3
(E) g
Show your work:
Newton’s Third Law
For every action there exists an equal and opposite reaction.
If A exerts a force F on B, then B exerts a force of -F on A.
A plane 5 meters in length is inclined at an angle of 37, as
shown above. A block of weight 20 newtons is placed at the
top of the plane and allowed to slide down. The magnitude of
the normal force exerted on the block by the plane is most
nearly
(A) l0 N
(B) 12N
(C) l6 N (D) 20 N
(E) 33 N
Show your work
23. Elevators and Normal Force (PAB)
A 50-kg middle school student stands on a scale in an elevator
that is moving downward, but slowing with an acceleration of
magnitude 2.0 m/s2. What does the scale read (in N)?
(A) 300
(B) 400
(C) 500 (D) 600
(E) 700
Show your work
Weight (W) (N)
W = mg (near the surface of the earth)
Normal Force
Force that prevents objects from penetrating each other
Reaction to other forces
Commonly a reaction to gravity
21. Normal Force Flat (A-177 #4)
Friction (f) (unit: N)
The force that opposes a sliding motion.
Static friction exists before sliding occurs.
Kinetic friction exists after sliding occurs.
In general Kinetic friction <= Static friction
fs  sN (for static friction)
Static friction increases as the force trying to push an object
increases, until it reaches its maximum value.
A block of weight W is pulled along a horizontal surface at
constant speed v by a force F. which acts at an angle of  with
the horizontal, as shown above. The normal force exerted on
the block by the surface has magnitude
(A) W - Fcos 
(B) W - Fsin 
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fk = kN
(for kinetic friction)
Bertrand
Physics B
AP Review Packet: Mechanics
24. Friction on Flat Surface (S-195 #61)
Uniform Circular Motion
An object moves at uniform speed in a circle of constant
radius.
A push broom of mass m is pushed across a rough horizontal
floor by a force of magnitude T directed at angle  as shown
above. The coefficient of friction between the broom and the
floor is . The frictional force on the broom has magnitude
(A) (mg +Tsin)
(B) (mg -Tsin)
(C) (mg +Tcos)
(D) (mg -Tcos)
(E) mg
Show your work
25. Friction on Ramp(S-195 #6-#7)
Questions 6-7
A 2-kilogram block slides
30 incline as shown above
acceleration of 2 meters per
squared.
down a
with an
second
(a) Which of the following diagrams best represents the
gravitational force W, the frictional force f, and the normal
force N that act on the block?
Acceleration in Uniform Circular Motion
Turns object; doesn’t speed it up or slow it down.
Acceleration points toward center of the circle.
Called centripetal acceleration.
Centripetal Acceleration
ac = v2/r
Force in Uniform Circular Motion
Any force responsible for uniform circular motion is called a
centripetal force. Centripetal force can arise from one force,
or a combination of sources.
F = mac = m v2 / r
Since speed of object remains constant, kinetic energy remains
constant, and work is zero.
Friction, tension, normal force, gravity and the magnetic force
are common forces that can act centripetally to cause uniform
circular motion.
26. Centripetal Force (A-184 #46)
A car initially travels north and then turns to the left along a
circular curve. This causes a package on the seat of the car to
slide toward the right side of the car. Which of the following is
true of the net force on the package while it is sliding?
(A) The force is directed away from the center of the circle.
(B) The force is directed north.
(C) There is not enough force directed north to keep the package from
sliding.
(D) There is not enough force tangential to the car's path to keep the
package from sliding.
(E) There is not enough force directed toward the center of the circle to
keep the package from sliding.
Explain your reasoning:
27. Centripetal Force (A-355 #2)
The horizontal turntable shown below rotates at a constant
rate. As viewed from above, a coin on the turntable moves
counterclockwise in a circle as shown. Which of the following
vectors best represents the direction of the frictional force
exerted on the coin by the turntable when the coin is in the
position shown?
Explain your Reasoning:
(b) The magnitude of the frictional force along the plane is
most nearly
(A) 2.5 N (B) 5N (C) 6 N (D) 10 N (E) 16 N
Show your work:
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Explain your reasoning:
Bertrand
Physics B
AP Review Packet: Mechanics
Universal Law of Gravity
Fg = Gm1m2/r2
Most orbit problems can be solved by setting the gravitational
force equal to the centripetal force.
Gm1m2 / r2 = m1v2 / r
28. Orbit (A-266 #61)
A satellite of mass M moves in a circular orbit of radius R at a
constant speed v. Which of the following must be true?
I. The net force on the satellite is equal to mv2/R and is directed
toward the center of the orbit.
II. The net work done on the satellite by gravity in one revolution is
zero.
III. The angular momentum of the satellite is a constant.
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III
Explain your reasoning:
Restoring Force (Hooke’s Law)
F = -kx (negative sign indicates force is restoring)
Restoring force is greatest at maximum displacement and zero
at equilibrium
Equilibrium
The midpoint of the oscillation of a simple harmonic
oscillator.
Position of minimum potential energy and maximum kinetic
energy.
Amplitude (A) (unit: m)
How far the oscillating mass is from equilibrium at its
maximum displacement.
Period (T) (unit: s)
The length of time it takes for one cycle of periodic motion to
complete itself.
Frequency (f) (unit: Hz or s-1)
How fast the oscillation is occurring.
f = 1/T
29. Orbit (S-226 #67)
A satellite of mass m and speed v moves in a stable, circular
orbit around a planet of mass M. What is the radius of the
satellite's orbit?
a.
e.
GM
mv
b.
Gv
mM
c.
GM
v
2
d.
GmM
v
GmM
v2
Show your work:
30. Law of Gravity, Weight (S-226 #10)
10. A new planet is discovered that has twice the Earth's mass and
twice the Earth's radius. On the surface of this new planet, a person
who weighs 500 N on Earth would experience a gravitational force
of
a. 125 N
b. 250 N
c. 500 N
d. 1000 N
e. 2000 N
Show your work:
Periodic Motion
Repeats itself over a fixed and reproducible period of time.
Oscillators undergo periodic motion.
Simple Harmonic Motion (SHM)
Periodic motion described by sine or cosine function.
Springs and pendulums are Simple Harmonic Oscillators
(SHOs) that obey Hooke’s Law.
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31. Simple Harmonic Motion (A-271 #43)
A particle oscillates up and down in simple harmonic motion.
Its height y as a function of time t is shown in the diagram
above. At what time t does the particle achieve its maximum
positive acceleration?
(A) 1s (B) 2s (C) 3s (D) 4s
(E) None of the above; the acceleration is constant
Explain your reasoning:
32. Hooke’s Law (A-271 #3)
An ideal spring obeys Hooke's law, F = - kx. A mass of 0.50
kilogram hung vertically from this spring stretches the spring
0.075 meter. The value or the force constant for the spring is
most nearly
(A) 0.33 N/m
(B) 0.66 N/m
(C) 6.6 N/m
(D) 33 N/m
(E) 66 N/m
Show your work:
Period of a spring
T = 2m/k
Potential Energy of a Spring
Us = ½ k x 2
Bertrand
Physics B
AP Review Packet: Mechanics
Pendulum
The pendulum can be thought of as an oscillator.
The displacement needs to be small for it to work properly.
Pendulum Forces: Gravity and tension
(A) 0 J (B) 30 J
Show your work:
(C) 600 J (D) 1,350 J (E) 1,800 J
Period of a pendulum
T = 2l/g
Potential Energy of a Pendulum
Ug = mgh
33. Period of Pendulum (A-177 #8)
8. The length of a simple pendulum with a period on Earth of
one second is most nearly
(A) 0.12 m
(B) 0.25 m
(C) 0.50 m (D) 1.0 m
(E) 10.0 m
Show your work:
34. Period: Spring, Pendulum (A-088 #44)
An object swings on the end of a cord as a simple pendulum
with period T. Another object oscillates up and down on the
end of a vertical spring, also with period T. If the masses of
both objects are doubled, what are the new values for the
periods?
Pendulum
Spring
T
(A)
2T
2
(B) T
(C) 2T
(D) 2T
(E) 2T
Explain your reasoning:
2T
36. Kinetic Energy (A-177 #3)
Which of the following quantities is a scalar that is always
positive or zero?
(A) Power
(B) Work
(C) Kinetic energy
(D) Linear momentum (F) Angular momentum
State your reasoning:
The Work-Energy Theorem
Wnet = K
Net work – work due to ALL forces -- is used in this theorem.
When net work is positive, the kinetic energy of the object
will increase, when negative, the kinetic energy will decrease.
Work and graphs
The area under the curve of a graph of force vs displacement
gives the work done by the force in performing the
displacement.
T
T
T 2
Power (P) (unit: Watt, W which is a J/s)
The rate of which work is done.
When we run upstairs, t is small so P is big.
When we walk upstairs, t is large so P is small.
P = W/t
P=Fv
Work (W) (Unit: Joule, J)
The scalar bridge between force and energy.
W = F x cos 
Power (S-115 #68)
Counterintuitive Results
There is no work if there is no displacement.
Forces perpendicular to displacement don’t work.
By doing positive work on an object, a force or collection of
forces increases its mechanical energy in some way.
The two forms of mechanical energy are called potential and
kinetic energy.
35. Work (A-088 #6)
A horizontal force F is used to pull a 5-kilogran block across a
floor at a constant speed of 3 meters per second. The frictional
force between the block and the floor is 10 newtons. The
work done by the force F in 1 minute is most nearly
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Kinetic Energy (K) (unit: Joule, J)
Energy due to motion
K = ½ m v2
8
A constant force of 900 N pushes a 100 kg mass up the
inclined plane shown above at a uniform speed of 4 m/s. The
power developed by the 900 N force is most nearly
a. 400 W
b. 800 W
c. 900 W
d. 1000 W
e. 3600 W
Show your work:
Bertrand
Physics B
AP Review Packet: Mechanics
How We Buy Energy…
The kilowatt-hour is a commonly used unit by the electrical
power company.
Power companies charge you by the kilowatt-hour (kWh), but
this not power, it is really energy consumed.
1 kW = 1000 W
1 h = 3600 s
1 kWh = 1000J/s • 3600s = 3.6 x 106J
Gravitational potential energy close to earth’s surface.
Wg = -mgh (close to earth’s surface)
U = -Wg = mgh
Note: we calculate changes in potential energy only using this
method. We assign the potential energy to be zero at some
certain point, usually the surface of the earth.
39. Problem: Work, gravity (A-182 #63)
37. Power (A-187 #5)
Units of power include which of the following?
I.
Watt
II. Joule per second
III. Kilowatt-hour
(A) I only
(B) III only (C) I and II only
(D) II and III only
(E) I, II, and III
State your reasoning:
38. Power (A-187 #9)
A child pushes horizontally on a box of mass m which moves
with constant speed  across a horizontal floor. The
coefficient of friction between the box and the floor is . At
what rate does the child do work on the box?
mg
mg
C) mg
(D) mg/
(E) m
Show your work:
Force Types
Conservative forces:
Work is path independent.
Work along a closed path is zero.
Work done against conservative forces increases potential
energy; work done by them decreases it.
Ex: gravity, springs
Non-conservative forces:
Work is path dependent.
Work along a closed path is NOT zero.
Work may be related to a change in total energy
(including thermal energy).
Ex: friction, drag
A plank 5 meters in length is inclined at an angle of 37, as
shown above. A block of weight 20 newtons is placed at the
top of the plane and allowed to slide down. The work done on
the block by the gravitational force during the 5-meter slide
down the plane is most nearly
(A) 20 J
(B) 60 J
(C) 80
(D) 100 J
(E) l30 J
Show your work:
Gravitational potential energy changes far from earth’s
surface.
Ug = -GMem/r (close to earth’s surface)
Ug has been defined to be zero when an object is infinitely far
from the earth, and it gets increasingly negative as an
object approaches the earth.
Note: This literal definition is impractical in most problems,
but this is the equation that must be used to calculate
U when you a very far from the earth’s surface.
40. Escape Velocity (PAB)
Use conservation of energy to derive an expression for the
escape velocity of a rocket of mass m from the surface of a
planet of mass M and radius R. Assume the planet has no
atmosphere.
(A)
(B)
(C)
(D)
(E) None of
Gm
Gm
2GM
2GmM
r
r
r
r
the above
Show your work:
Potential energy
Energy of position or configuration.
Examples:
Gravitational, Spring, Electrical energies
Potential energy is related to work done by CONSERVATIVE
FORCES only.
Ug = -Wg (gravity)
Ug = -Ws (spring)
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Spring potential energy
Us = ½ kx2
Us is zero when a spring is in its equilibrium position (neither
compressed nor extended)
Bertrand
Physics B
AP Review Packet: Mechanics
Law of Conservation of Mechanical Energy
The total mechanical energy of a system remains constant,
provided only conservative forces act upon the system.
U + K = Constant
U1 + K 1 = U 2 + K 2
U + K = 0
U = -K
41. Springs (A-088 #11,#12)
A block oscillates without friction on the end of a spring as
shown above. The minimum and maximum lengths of the
spring as it oscillates are, respectively, xmin and xmax The
graphs below can represent quantities associated with the
oscillation as functions of the length x of the spring.
42. Conservation of Energy (A-098 #38)
A block of mass 3.0 kg is hung from a spring, causing it to
stretch 12 cm at equilibrium, as shown above. The 3.0 kg
block is then replaced by a 4.0 kg block, and the new block is
released from the position shown above, at which the spring is
unstretched. How far will the 4.0 kg block fall before its
direction is reversed?
(A) 9 cm (B) 18 cm (C) 24 cm (D) 32 cm
(E) 48 cm
Show your work:
43. Cons. of Energy (A-098 #60)
(a) Which graph can represent the total mechanical energy of
the block-spring system as a function of x ?
(A) A (B) B (C) C (D) D
(E) E
Explain your reasoning:
A rock of mass m is thrown horizontally off a building from a
height h, as shown above. The speed of the rock as it leaves
the thrower's hand at the edge of the building is  0 .What is
the kinetic energy of the rock just before it hits the ground?
(A) mgh (B) 1 m 2 (C) 1 m 2  mgh
2
(D) 1 m 2  mgh
2
(b) Which graph can represent the kinetic energy of the block
as a function of x ?
(A) A (B) B (C) C (D) D
(E) E
Explain your reasoning:
0
0
2
0
(E) mgh  1 m 2
0
2
Show your work:
.
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Bertrand
Physics B
AP Review Packet: Mechanics
44. Cons. of Energy (A-182 #47)
A block of mass m slides on a horizontal frictionless table
with an initial speed v 0 . It then compresses a spring of force
constant k and is brought to rest. How much is the spring
compressed from its natural length?
2
(A) v0
2g
Show your work:
mg
(B)
k
m
(C) v0
k
(D) m v
0
k
(E) k v
0
m
46. Cons.of Energy (A-093 #4)
The figure above shows a rough semicircular track whose ends
are at a vertical height h. A block placed at point P at one end
of the track is released from rest and slides past the bottom of
the track. Which of the following is true of the height to which
the block rises on the other side of the track?
(A) It is equal to h/2  . (B) It is equal to h/4.
(C) It is equal to h/2.
(D) It is equal to h.
(E) It is between zero and h; the exact height depends on how
much energy is lost to friction.
Explain your reasoning:
45. Cons. of Energy (A-355 #51,52)
A ball swings freely back and forth in an arc from point I to
point IV, as shown above. Point II is the lowest point in the
path, III is located 0.5 meter above II, and IV is l meter above
II. Air resistance is negligible.
a) If the potential energy is zero at point II, where will the
kinetic and potential energies of the ball be equal?
(A) At point II
(B) At some point between II and III
(C) At point III
(D) At some point between III and IV
(E) At point IV
State your reasoning:
47. Momentum (A-098 #43)
The magnitude of the momentum of the object is increasing in
which of the cases?
(A) II only (B) III only (C) I and II only
(D) I and III only (E) I, II, and III
Explain your reasoning:
b) The speed of the ball at point II is most nearly
(A) 3.0 m/s
(B) 4.5 m/s (C) 9.8 m/s
(D) l4 m/s
(E) 20 m/s
Show your work:
Conservation of Energy and Dissipative Forces.
Dissipative forces cause loss of mechanical energy by
producing heat.
Wnc = U + K
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Momentum (P) (unit: kg m/s or N s)
How hard it is to stop a moving object.
For one particle
p = mv
For a system of multiple particles
P = pi = mivi
Momentum is a vector!
11
Impulse (I) (units: N s or kg m/s)
The product of an external force and time, which results in a
change in momentum
I=Ft
I = p
Bertrand
Physics B
AP Review Packet: Mechanics
48. Impulse (A-187 #57)
A ball of mass 0.4 kg is initially at rest on the ground. It is
kicked and leaves the kicker's foot with a speed of 5.0 m/s in a
direction 60° above the horizontal. The magnitude of the
impulse imparted by the ball to the foot is most nearly
(A) 1 N  s
(B)
3 Ns
Show your work:
(A) Momentum was not conserved, therefore the report is false.
(B) If potential energy was released to the objects during the
collision, the report could be true.
(C) If the objects had different masses, the report could be true.
(D) If the surface was inclined, the report could be true.
(E) If there was no friction between the objects and the surface, the
report could be true.
Explain your reasoning:
(C) 2 N  s
(D)
meters per second relative to the surface. Which of the
following assessments of this report is most accurate?
2
N s
3
(E) 4 N  s
51. Collision (A-004 #63)
Law of Conservation of Momentum
If the resultant external force on a system is zero, then the
momentum of the system will remain constant.
The sum of the momentums before a collision is equal to the
sum of the momentums after a collision.
Pb = Pa
Collisions
Follow Newton’s Third Law (forces exerted on colliding
bodies are equal magnitude)
During a collision, external forces are ignored.
The time frame of the collision is very short.
The forces are impulsive forces (high force, short duration).
The two blocks of masses M and 2M shown above initially
travel at the same speed v but in opposite directions. They
collide and stick together. How much mechanical energy is
lost to other forms of energy during the collision?
4
3
a. Zero
b. 1 Mv 2
c. Mv 2
d.
Mv 2
3
4
2
3
e.
Mv 2
2
Show your work:
Collision Types
Elastic: P is conserved, K is conserved
Inelastic: P is conserved, K is NOT conserved
Perfectly Inelastic means the bodies stick together
49. Collisions (A-093 #10)
Which of the following is true when an object of mass m
moving on a horizontal frictionless surface hits and sticks to
an object of mass M > m, which is initially at rest on the
surface?
(A) The collision is elastic.
(B) All of the initial kinetic energy of the less-massive object is lost.
(C) The momentum of the objects that are stuck together has a
smaller magnitude than the initial momentum of the less-massive
object.
(D) The speed of the objects that are stuck together will be less than
the initial speed of the less-massive object.
(E) The direction of motion of the objects that are stuck together
depends on whether the hit is a head-on collision.
Explain your reasoning:
52. Momentum Change (S-199 #7)
A tennis ball of mass m rebounds from a racquet with the
same speed v as it had initially, as shown above. The
magnitude of the momentum change of the ball is
(A) 0
(B) mv
(C) 2mv
(D) 2mv sin 
(E) 2mv cos 
Show your work:
50. Collisions (A-093 #11)
Two objects having the same mass travel toward each other on
a flat surface, each with a speed of 10 meter per second
relative to the surface. The objects collide head-on and are
reported to rebound after the collision, each with a speed of 20
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Bertrand
Physics B
AP Review Packet: Mechanics
53. Collision (A-276 #41)
Two objects of mass 0.2 kg and 0.1 kg, respectively, move
parallel to the x-axis, as shown above. The 0.2 kg object
overtakes and collides with the 0. 1 kg object. Immediately
after the collision, the y-component of the velocity of the 0.2
kg object is 1 m/s upward. What is the y-component of the
velocity of the 0.1 kg object immediately after the collision?
(A) 2 m/s downward
(B) 0.5 m/s downward
(C) 0 m/s
(D) 0.5 m/s upward
(E) 2 m/s upward
Show your work:
Explosion
Mathematically, handled just like an ordinary perfectly
inelastic collision.
Momentum is conserved, kinetic energy is not.
54. Explosion (A-098 #67)
A stationary object explodes, breaking into three pieces of
masses m, m, and 3m. The two pieces of mass m move off at
right angles to each other with the same magnitude of
momentum mV, as shown in the diagram above. What are
the magnitude and direction of the velocity of the piece
having mass 3m ?
Show your work:
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Bertrand