Transcript Document

Problem Solving
Read.
Visualize and translate.
Simplify.
Represent physically.
Represent mathematically.
Solve.
Evaluate the result.
The solid line has length A and makes
an angle  with the negative y-axis.
What is the length of the dotted line?
y
A.
B.
C.
D.
E.
A cos
A sin
A tan
sin/A
cos/A
A
x


 
Three vectors A , B, and C
are as shown. Which vector is
   
S  A  BC ?
B
A
C
Black: None of these!
Red
Blue
Green
Purple
An object goes from one point in space to
another. After it arrives at its destination, the
size of its displacement is:
A: could be smaller or larger
B: always equal to
C: either greater than or equal to
D: either smaller than or equal to
than the distance it traveled.
R
R
The distance traveled,
and the displacement of the ant,
are respectively:
A: p R and p R
B: 2 R and p R
C: p R and 2 R
D: p R and zero
E: none of these
5 m/s
0
7 m/s
640m
X
Find the position and time when the two bikes meet
a)Algebraically: Find the position and time using
mathematical expressions.
b)Graphically: Construct a position-versus-time graph for the
two bike trips.
The position of two blocks at successive 0.20-second time
intervals are represented by numbered squares in the figure
below. The blocks are moving toward the right.
1
1
2
2
3
4
3
5
4
5
6
6
Do the blocks ever have the same speed?
(A) No
(B) Yes, at instant 2.
(C) Yes, at instant 5.
(D) Yes, at instants 2 and 5.
(E) Yes, at some time during the interval 3 to 4.
7
7
8
1. Here is a graph of an object’s motion. Which sentence is a correct
interpretation?
(A) The object rolls along a flat surface. Then it rolls forward down a hill, and then finally stops.
(B) The object doesn’t move at first. Then it rolls forward down a hill and finally stops.
(C) The object is moving at constant velocity. Then it slows down and stops.
(D) The object doesn’t move at first. Then it moves backwards and then finally stops
(E) The object moves along a flat area, moves backwards down a hill, and then it keeps moving.
2. Here is a graph of an object’s motion. Which sentence is the best
interpretation?
(A) The object is moving with a constant, non-zero acceleration.
(B) The object does not move.
(C) The object is moving with a uniformly increasing velocity.
(D) The object is moving with a constant velocity.
(E) The object is moving with a uniformly increasing acceleration.
(F) Need more information
Here is a graph of an object’s motion. Which sentence is the best
interpretation?
(A) The object is moving with a constant, non-zero acceleration.
(B) The object does not move.
(C) The object is moving with a uniformly increasing velocity.
(D) The object is moving with a constant velocity.
(E) The object is moving with a uniformly increasing acceleration.
(F) Need more information
A ball is thrown straight up. At the
top of its trajectory, its
A. velocity is zero,
acceleration is zero.
B. velocity is non-zero,
acceleration is non-zero.
C. velocity is zero,
acceleration is non-zero.
D. velocity is non-zero,
acceleration is zero.
This graph shows velocity as a
function of time for a car of mass
1.5 x 103 kg. What was the
acceleration at the 90 s mark?
(A) 0.22 m/s2
(B) 0.33 m/s2
(C) 1.0 m/s2
(D) 9.8 m/s2
(E) 20 m/s2
A stone is thrown straight
upward with an initial
velocity v0. Sketch graphs:
(a) acceleration versus time
(b) velocity versus time
(c) position versus time.
Next questions refer to collisions between a
car and a truck. Choose the one answer from
the possibilities A though J that best
describes the forces between the car and the
truck.
If Vtruck = Vcar
If Vtruck << Vcar
If Vtruck = 0
A. Ftruck_on_car >Fcar_on_truck
B. Ftruck_on_car <Fcar_on_truck
C. Neither exerts a force on the other; the car
gets smashed simply because it is in the way
of the truck.
D. The truck exerts a force on the car but the
car doesn't exert a force on the truck.
E. Ftruck_on_car =Fcar_on_truck .
F. Not enough information is given to pick one
of the answers above.
J. None of the answers above describes the
situation correctly.
1. An elevator moves from the
basement to the tenth floor of a
building. The mass of the elevator
is 1000 kg and it moves as shown
in the velocity-time graph below.
How far does it move during the
first three seconds of motion?
2. The following represents an acceleration graph for an object
during a 5 s time interval.
Sketch the graph of
velocity versus time to
represent the object’s
motion during the same
time interval?
Which of these
represent(s) motion at
constant, non-zero
acceleration?
(A) I, II, and IV
(B) I and III
(C) II and V
(D) IV only
(E) V only
1. The following represents
an velocity-time graph for an
object. Sketch the graph of
acceleration versus time to
represent the object’s motion
during the same time
interval?
2. The following represents
an position-time graph for
an object. Sketch the graph
of velocity versus time to
represent the object’s
motion during the same
time interval?
A steel ball is attached to a string and is
swung in a circular path in a horizontal plane
as illustrated in the accompanying figure. At
the point P indicated in the figure, the string
suddenly breaks near the ball. If these
events are observed from directly above as
in the figure, which path would the ball most
closely follow after the string breaks?
A manikin exerts a constant horizontal
force on a large box. As a result, the
box moves across a horizontal floor at a
constant speed v0.
The constant horizontal force applied
by the manikin:
(A) has the same magnitude as the
weight of the box.
(B) is greater than the weight of the box.
(C) has the same magnitude as the total
force which resists the motion of the
box
(D) is greater than the total force which
resists the motion of the box
(E) is greater than either the weight of
the box or the total force which resists
the motion of the box.
A hockey puck slids with a
constant speed in a straight
line from point “a" to point “b"
along a frictionless horizontal
surface. When the puck
reaches point “b", it receives
an swift horizontal "kick" in the
direction of the heavy print
arrow, perpendicular to the
original sliding motion.
Which of the paths below
would the puck most
closely follow after
receiving the kick?
b
a
kick
A
C
B
D
E
a
b
kick
Along the frictionless path the
puck takes, the speed of the
puck after receiving the kick:
A. is constant.
B. continuously increases.
C. continuously decreases.
D. increases for a while and
decreases thereafter.
E. is constant for a while and
decreases thereafter.
Draw a motion diagram and
force diagram for a ball thrown
into the air for four different time
intervals:
a) The ball is in your hand as
you’re throwing it upwards.
b) The ball has left your hand
and traveling upwards to the top
of its trajectory.
c) The ball is traveling
downwards from the top of its
trajectory to the point just before
you catch it.
d) The ball is in contact with
your hand as you catch it and it
comes to a stop.
1. Sketch a position vs. time graph
for a system moving under a
constant net force.
2. A mosquito collides head on with
a car traveling 60 mph. How do
you think the size of the force the
car exerts on the mosquito
compares to the size of the force
that the mosquito exerts on the
car. Show free body diagrams for
the car and the mosquito at the
moment of collision showing only
the horizontal forces..
Smart and lazy horse
The man says to the horse
"Giddup" (which is horse for
"go"). The horse replies:
"There's no point. Newton's third
law says that the cart will exert a
force on me equal and opposite
to the force I exert on it. Sum of
forces = zero, so the
acceleration will be zero." How
would you answer the horse?
Hint 1: Choose the system and consider
external forces consistently!!!
Hint 2: Consider the role of the ground!
100 N
100 N


T3 ?
Three people are pulling on a ring
in a "2-D" tug of war. Shown is a
"top view". No one is winning the ring is sitting still.
What is the net force on the ring?
What is the T3
(v is down,
and constant)
An object is lowered by a
rope at a constant speed.
How does the tension T in the
string compare with the
weight "mg" of the object?
A: T=mg
B: T > mg
C: T < mg
D: Not enough information
given.
A child of mass m rides on a sled down a
slick, ice-covered hill inclined at an angle
 with respect to the horizontal.
a)What is the acceleration of the child
b)What is the normal force exerted on
the child by the sled
1. Draw a sketch
2. Draw a free body diagram
3. Set Cartesian coordinates (make a
smart choice)
4. Find all x and y components of all
forces and the acceleration
5. Write down Newton’s Second Law for
the components
Hint: Remember, that normal force is
always perpendicular to a surface
N
Ffr
a

W
A child of mass m rides on a sled down a
rough hill inclined at an angle  with respect
to the horizontal. The coefficient of the
kinetic friction is  k and static friction is 
a)What is the acceleration of the child
b)What is the normal force exerted on the
child by the sled
s
A block of mass m is projected
with an initial speed v0 along the
horizontal plane with coefficient
of kinetic friction k and of static
friction  s. How far will the block
go until it stops?
Does the force of friction
depend on the mass of the
block?
Does the coefficient of friction
depend on the mass of the block?
m
Fext
I push (with force Fext) on a block
(mass m) which sits on the table.
The block is not moving, because
there is static friction (coefficient s).
What can you say for sure about the
frictional force, f?
A: f = s mg
B: f = Fext
C: f > Fext
D: f < Fext
E: Not enough information (or, MORE
than one of the above)
A satellite is moving around Earth in a
circular orbit at a constant speed. Which
one of the following statements is true as
the satellite moves from point A to point B
in the orbit?
(a) The gravitational potential energy of the
satellite decreases as it moves from A to B.
(b) The work done on the satellite by the
gravitational force is negative for the
motion from A to B.
(c) The work done on the satellite by the
gravitational force is zero for the motion
from A to B.
(d) The velocity of the satellite remains
unchanged as it moves from A to B.
(e) None of the above.
A block 1 and block 2 are connected by a light
string that passes over frictionless and
massless pulley, as shown on the figure. There
is NO FRICTION between block 1 and the
surface of the table.
m1
m2
1. Draw a free body diagram for
a) block 1
b) block 2
2. Draw an acceleration vector for each block
3. Set Cartesian coordinates
4. Find all x and y components of all forces
and the accelerations for the both blocks
separately!!!
5. Write down Newton’s Second Law for the
components
6. Find the acceleration
A block 1 and block 2 are connected by a light
string that passes over frictionless and
massless pulley, as shown on the figure. There
is FRICTION (coefficients µs and µk)between
block 1 and the surface of the table.
m1
m2
1. Draw a free body diagram for
a) block 1
b) block 2
2. Draw an acceleration vector for each block
3. Set Cartesian coordinates
4. Find all x and y components of all forces
and the accelerations for the both blocks
separately!!!
5. Write down Newton’s Second Law for the
components
6. Find the acceleration
A block 1 and block 2 are connected by a light
string that passes over frictionless pulley with
mass M and radius R, as shown on the figure.
The friction coefficients are µs and µk between
block 1 and the surface of the table.
m1
m2
1. Draw a free body diagram for
a) block 1
b) block 2
2. Draw an acceleration vector for each block
3. Set Cartesian coordinates
4. Find all x and y components of all forces
and the accelerations for the both blocks
separately!!!
5. Write down Newton’s Second Law for the
components
6. Find the acceleration
A 1000-kg elevator on the top
floor of a building starts at rest
and 2.0 sec later is moving
downward at speed 4.0 m/s.
Find the magnitude of the
tension in the cable pulling the
elevator as speed is increasing.
An object is moving down.
How does the tension T in the
string compare with the
weight "mg" of the object?
A: T=mg
B: T > mg
C: T < mg
D: Not enough information
given.
An object moves in a circular
path with constant speed. Which
of the following statements is
true concerning the object?
Remember that velocity and
acceleration are vectors.
A. Its velocity is constant, but
acceleration is changing
B. Its acceleration is constant,
but velocity is changing
C. Both its velocity and
acceleration are changing
D. Both its velocity and
acceleration remain constant
V
A car passes over a hill in the road
that has a circular cross-section.
How does the force exerted by the
road on the car compare with the
weight of the car?
A: N = mg
B: N > mg
C: N < mg
D: Not enough information
given.
V
A car passes over a low spot in the
road that has a circular crosssection. How does the force exerted
by the road on the car compare
with the weight of the car?
A: N = mg
B: N > mg
C: N < mg
D: Not enough information
given.
A mass is hanging from a rope and
swinging around a circular path at
constant speed. The situation is shown
in the figure. Draw a free body diagram
Support
rope
mass
circular
path
Pendulum Suspended from Spring Scale
A bob is hung by a string, attached to
a spring scale which is suspended
from a stand. First note the reading
on the spring scale when the bob is
not moving. The bob and string will
then be pulled back so that the string
makes an angle theta with the
vertical. The bob will then be released
and allowed to swing. Predict what
will happen to the reading on the
spring scale at the bottom of the
swing (more, less or same as when
the object is at rest).
L
s
A: s = L
B: s > L
C: s < L
A: VS = VL
B: VS > VL
C: VS < VL
A small wheel and a large wheel are
connected by a belt. The small wheel is
turned at a constant angular velocity s.
How does the magnitude of the angular
velocity of the large wheel L compare to
that of the small wheel?
There is a bug S on the rim of the small
wheel and another bug L on the rim of the
large wheel. How do their speeds
compare?
V
A car passes over a hill in the road
that has a circular cross-section with
a radius of 30m. The speed of the car
at the top of the hill is 10 m/s. What is
the force exerted by the seat of the
car on a 60kg passenger when the
car is at the top pf the hill?
Work
W = F d cosθ
You gave a very short kick
with force F = 200N to a
bowling ball at point A. The
ball started rolling along a
straight line.
a) How much work has been
done by force F trough a
distance D between points B
and C.
b) What work has been
done by kick force at
moment of the kick.
Very
short
kick
D = 1meter
F = 200N
A
B
C
While working out, a man
lifts a 10-kg object a
vertical distance of 0.80
m. He then carries it for
10 m where he sets it
down a vertical distance
of 0.80 m. How much
work does he do on the
object when he picks the
object up, when he
carries it, and when he
sets it back down? What
is the total work that he
does on it?
10m
0.8m
10 kg
You want to load a box into
the back of a truck. One way
is to lift it straight up through
a height h, doing work W1.
Alternatively, you can slide
the box up a loading ramp a
distance L, doing work W2.
Assuming that the box slides
on the ramp without friction
which of the following is
correct
(a) W1 < W2,
(b) W1 = W2,
(c) W1 > W2?
You want to load a box into
the back of a truck. One way
is to lift it straight up through
a height h, doing work W1.
Alternatively, you can slide
the box up a loading ramp a
distance L, doing work W2.
Assuming that the box slides
on the ramp WITH friction
which of the following is
correct
(a) W1 < W2,
(b) W1 = W2,
(c) W1 > W2?
A rock of mass m is twirled on a
string in a horizontal plane. The
work done by the tension in the
string on the rock is..
A: + (positive)
B:  (negative)
C: 0
1. Define a system
Pendulum
2. Define the initial and final states
3. Draw an Energy Bar Chart (Work?!)
4. Write the Energy-Work Formula
Before (1) ΔE = W
KEi PEgi PEsi
+
1
2
0
-
W
After(2)
KEf PEgf PEsf
1. Define a system
2. Define the initial and final states
Roller Coaster
3. Draw an Energy Bar Chart (Work?!)
4. Write the Energy-Work Formula
Before
ΔE = W
KEi PEgi PEsi
+
0
-
W
After
KEf PEgf PEsf
1. Define a system
2. Define the initial and final states
3. Draw an Energy Bar Chart (Work?!)
4. Write the Energy-Work Formula
No Friction
ΔE = W
After
Before
Δx
KEi PEgi PEsi W
V-?
KEf PEgf PEsf
+
k
m
0
-
½ kx2 = ½ mv2
1. Define a system
2. Define the initial and final states
3. Draw an Energy Bar Chart (Work?!)
4. Write the Energy-Work Formula
No Friction
ΔE = W
After
Before
KEi PEgi PEsi W
V-?
Hmax ?
KEf PEgf PEsf
+
0
k
-
½ kx2 = ½ mv2+mgh
1. Define a system
2. Define the initial and final states
3. Draw an Energy Bar Chart (Work?!)
4. Write the Energy-Work Formula
ΔE = W
Friction: μs and μk
Before
KEi PEgi PEsi W
Δx
Hmax ?
+
θ
0
k
-
After
KEf PEgf PEsf
A: Yes
B: No
C: Need more
information
A hockey puck slides without friction
along a frozen lake toward an ice
ramp and plateau as shown. The
speed of the puck is 4m/s and the
height of the plateau is 1m. Will the
puck make it all the way up the
ramp?
v = 4 m/s
h = 1m
A hockey puck slides without friction
along a frozen lake toward an ice
ramp and plateau as shown. The
height of the plateau is 2m. With
what speed should the puck slide to
make it all the way up the ramp?
V–?
h = 2m
A ball is dropped from a tower
and attains a speed v at the
bottom. To achieve a speed 2v
at the bottom, how many times
as high must the new tower be?
momentum
p = mv
F=ma=mV/t
Vi=0
F=const
The block of mass m = 500g is at rest
on a frictionless surface. You start
pulling the block with a constant
force F = 10N and pull it for t=2sec.
Find the final velocity of the block,
and its final momentum.
An 80-kg man and his car are
suddenly accelerated from rest to
a speed of 5 m/s as a result of a
rear-end collision. Assuming the
time taken to be 0.3s, find the
a) impulse on the man and
b) the average force exerted on
him by the back seat of his car
A 3500 kg truck slams into the
back of a parked car with a
velocity of 14.3 m/s. The truck
comes to a halt, and the car, of
mass 1500 kg has no other forces
acting on it. What is the car’s
velocity?
Two goblins with identical mass
are traveling on a frictionless
surface at right angles to each
other with velocities v1 and v2
respectively (v1 = 2v2). The goblins
collide and stick together.
a. Draw momentum vectors for
both goblins before the collision.
b. Draw the momentum vector for
the combined body immediately
after the collision.
c. What is the impulse of the
system?
Ball 1 strikes stationary Ball 2 in 2D. The
initial momentum of Ball 1, p1i, (4,0) and
the final momentum of Ball 2, p2f (3,2) are
shown on the graph.
What is the xcomponent of p1f ?
A: 0
B: 1
C: 2
D: 3
E: None of these
p2f
p1i
A ball bounces off the floor
as shown. The direction of
the impulse on the ball, p,
is ...
A:
straight up 
B:
straight down 
C:
to the right 
D:
to the left 
A ball fall to the floor
and sticks to it. Find
p.
m
V
A ball bounces elastically off
the floor as shown. Find p.
m
p = mv
V
p = 2mv
A compact car and a large truck
collide head on and stick together.
Which undergoes the larger
momentum change?
A: car
B: truck
C: The momentum change is the
same for both vehicles.
D: Can’t tell without knowing the
initial velocities
A compact car and a large truck
collide head on and stick together.
Which undergoes the larger
acceleration?
A: car
B: truck
C: Both experience the same
acceleration
D: Can’t tell without knowing the
initial velocities
What is the initial speed of the bullet?
Ballistic pendulum
What do you need to know?
Mass of the bullet m
Mass of the block M
Height the block rises h
Elastic or Inelastic?
Inelastic collision
Pi = Pf
mV = (m+M)Vf
V = Vf · (m+M)/m
Vf2 = 2gh
V
Quiz
All three collisions
in the figure shown
here are totally
inelastic. What is the
velocity of the car on
the left?
V= 0 in all three cases
A pendulum is launched in
two different ways. During
both launches, the bob has
an initial speed of 3.0 m/s.
On launch 1, the speed is up
On launch 2, the speed is
down
Which launch will cause
the pendulum to swing
the largest angle from
the equilibrium position
on the left side?
f
v1
v2 ( = -v1 )
TOP VIEW
hinge
Big F
The door does not move.
Assuming the hinge is
well-greased (no friction
there) is this situation as
shown physically
possible?
small F
A: Sure, why not?
B: No.
You are using a
wrench and trying to
loosen a rusty nut.
Which of the
arrangements shown
is most effective in
loosening the nut?
Least effective in
loosening the nut?
You are using a
wrench and trying to
loosen a rusty nut.
Which of the
arrangements shown
is less effective in
loosening the nut?
Least effective in
loosening the nut?
A ladybug is clinging to the rim
of a spinning wheel starts
spinning CCW and speeds up.
At the moment shown, what is
the approximate direction of the
ladybug's acceleration?
A)
B)
C)
D)
E) None of these
A ladybug is clinging to the rim
of a spinning wheel which is
spinning fast CCW and is
slowing down. At the moment
shown, what is the approximate
direction of the ladybug's
acceleration?
A)
B)
C)
D)
E) None of these
A mass is hanging from the end
of a horizontal bar which pivots
about an axis through it center,
but it being held stationary. The
bar is released and begins to
rotate. As the bar rotates from
horizontal to vertical, the
magnitude of the torque on the
bar..
A: increases
B: decreases
C: remains constant
As the bar rotates from horizontal to
vertical, the magnitude of the angular
acceleration  of the bar..
A: increases
B: decreases
C: remains constant
R
m
A mass m hangs from string
wrapped around a pulley of
radius R. The pulley has a
moment of inertia I and its
pivot is frictionless. Because
of gravity the mass falls and
the pulley rotates.
The magnitude of the torque on
the pulley is..
A: greater than mgR
B: less than mgR
C: equal to mgR
(Hint: Is the tension in the string
= mg?)
M, R, L
Moment of
inertia is larger
in situation:
A
B
C
the same
A
B
C
Moment of
inertia is larger
in situation:
A
B
the same
A)    t
B)    t(1/2) t2
C) 2=2+2
A student sees the following
question on an exam:
A flywheel with mass 120 kg, and
radius 0.6 m, starting at rest, has
an angular acceleration of 0.1
rad/s2. How many revolutions has
the wheel undergone after 10 s?
Which formula should the student
use to answer the question?
A: IA= 2IB
B: 2IA = IB
C: IA = IB
D: IA = 4IB
E: 4IA=IB
Consider two masses, each of size m
at the ends of a light rod of length L
with the axis of rotation through the
center of the rod. The rod is doubled
in length. What happens to I?
m
m
2L
L
L
m
A
2L
m
B
A: IA= 2IB
B: 2IA = IB
C: IA = IB
D: IA = 4IB
E: 4IA=IB
Consider two masses, each of size m
at the ends of a light rod of length L
with the axis of rotation through the
center of the rod. The rod is doubled
in length. What happens to I?
2m
m
2L
L
L
2m
A
2L
m
B
Cup A
Cup B
The same
Cup A contains 100 grams of
water and cup B contains twice
as much water. The water in
both cups was initially at room
temperature 25C. Cup A was
heated to 75C and cup B was
heated to 50C.
Which cup had more heat
energy transferred to it?
A) Lower than 0C
B) 0C
C) between 0C and 25C
D) 25C
E) Between 25C and 50C
F) 50C
G) Higher than 50C
Cup A contains 100 grams
of water at 0C and cup B
contains 100 grams of
water at 50C.
The contents of the two
cups are mixed together in
an insulated container (no
heat can transfer in or out).
What is the final
temperature of the water in
the container?
A) Lower than 0C
B) 0C
C) between 0C and 25C
D) 25C
E) Between 25C and 50C
F) 50C
G) Higher than 50C
Cup A contains 100 grams
of water at 0C and cup B
contains 200 grams of
water at 50C.
The contents of the two
cups are mixed together in
an insulated container (no
heat can transfer in or out).
What is the final
temperature of the water in
the container?
The water in a cup is initially at
55C, and the cup is in a room
where the temperature is 25C.
A