1. Problem Solving Read. Visualize and translate. Simplify.
Represent physically.
Represent mathematically.
Solve.
Evaluate the result.

3. 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 cos
A sin
A tan
sin/A
cos/A x A 

4. Three vectors are as shown. Which vector is ? B A C
Black: None of these!
Red
Blue
Green
Purple

5. An object goes from one point in space to another
An object goes from one point in space to another. After it arrives at its destination, the size of its displacement is:
than the distance it traveled.
A: could be smaller or larger
B: always equal to
C: either greater than or equal to
D: either smaller than or equal to

6. 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

7. Find the position and time when the two bikes meet
5 m/s
7 m/s
640m X
Find the position and time when the two bikes meet
Algebraically: Find the position and time using mathematical expressions.
Graphically: Construct a position-versus-time graph for the two bike trips.

8. Do the blocks ever have the same speed?
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 2 3 4 5 6 7 8
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.

10. (A) The object is moving with a constant, non-zero acceleration.
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

11. Here is a graph of an object’s motion
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

12. A ball is thrown straight up. At the top of its trajectory, its
velocity is zero, acceleration is zero.
velocity is non-zero, acceleration is non-zero.
velocity is zero, acceleration is non-zero.
velocity is non-zero, acceleration is zero.

13. This graph shows velocity as a function of time for a car of mass 1
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

14. (a) acceleration versus time (b) velocity versus time
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.

15. Next questions refer to collisions between a car and a truck
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.
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.
If Vtruck = Vcar
If Vtruck << Vcar
If Vtruck = 0

16. 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?

17. 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

18. 1. The following represents an velocity-time graph for an object
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?

19. 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) (B) (C) (D) (E)
                                                             

20. A manikin exerts a constant horizontal force on a large box
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.

21. 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. a b
kick A B
Which of the paths below would the puck most closely follow after receiving the kick? C D E

22. B. continuously increases. C. continuously decreases.
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.

23. 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.

24. Sketch a position vs. time graph for a system moving under a constant net force.
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..  

25. 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!

26. Three people are pulling on a ring in a "2-D" tug of war
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

27. An object is lowered by a rope at a constant speed
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.

28. What is the acceleration of the child
A child of mass m rides on a sled down a slick, ice-covered hill inclined at an angle  with respect to the horizontal.
What is the acceleration of the child
What is the normal force exerted on the child by the sled
Draw a sketch
Draw a free body diagram
Set Cartesian coordinates (make a smart choice)
Find all x and y components of all forces and the acceleration
Write down Newton’s Second Law for the components
Hint: Remember, that normal force is always perpendicular to a surface

29. What is the acceleration of the child x y N
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  s
What is the acceleration of the child
What is the normal force exerted on the child by the sled
Ffr  a W

30. 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?

31. Does the force of friction depend on the mass of the block?
Does the coefficient of friction depend on the mass of the block?

32. 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 ms).
What can you say for sure about the frictional force, f?
A: f = ms mg
B: f = Fext
C: f > Fext
D: f < Fext
E: Not enough information (or, MORE than one of the above)

33. 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.

34. Two identical stones, A and B, are shot from a cliff from the same height and with identical initial speeds v0. Stone A is shot vertically up, and stone B is shot vertically down. Which stone has a larger speed right before it hits the ground?
(a) A (because it travels a longer time).
(b) B (because it’s initial velocity is downward).
(c) Both stones have the same speed.

35. 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
Draw a free body diagram for
block 1
block 2
Draw an acceleration vector for each block
Set Cartesian coordinates
Find all x and y components of all forces and the accelerations for the both blocks separately!!!
Write down Newton’s Second Law for the components
Find the acceleration

36. 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
Draw a free body diagram for
block 1
block 2
Draw an acceleration vector for each block
Set Cartesian coordinates
Find all x and y components of all forces and the accelerations for the both blocks separately!!!
Write down Newton’s Second Law for the components
Find the acceleration

37. 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
Draw a free body diagram for
block 1
block 2
Draw an acceleration vector for each block
Set Cartesian coordinates
Find all x and y components of all forces and the accelerations for the both blocks separately!!!
Write down Newton’s Second Law for the components
Find the acceleration

38. A 1000-kg elevator on the top floor of a building starts at rest and 2
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.

39. An object is moving down
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.

40. An object moves in a circular path with constant speed
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.
Its velocity is constant, but acceleration is changing
Its acceleration is constant, but velocity is changing
Both its velocity and acceleration are changing
Both its velocity and acceleration remain constant

41. D: Not enough information given.
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? V
A: N = mg
B: N > mg
C: N < mg
D: Not enough information given.

42. D: Not enough information given.
A car passes over a low spot 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? V
A: N = mg
B: N > mg
C: N < mg
D: Not enough information given.

43. 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

44. 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).

45. A small wheel and a large wheel are connected by a belt
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?
A: s = L
B: s > L
C: s < L
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?
A: VS = VL
B: VS > VL
C: VS < VL

46. 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? V

47. 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
Need play dough and a block
F = 200N C A B

48. While working out, a man lifts a 10-kg object a vertical distance of 0
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

49. You want to load a box into the back of a truck
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
W1 < W2,
(b) W1 = W2,
(c) W1 > W2?

50. You want to load a box into the back of a truck
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
W1 < W2,
(b) W1 = W2,
(c) W1 > W2?

51. A rock of mass m is twirled on a string in a horizontal plane
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

52. Pendulum ΔE = W 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 + -
Before (1)
After(2)
KEi
PEgi
KEf
PEgf W
PEsi
PEsf 1 2

53. Roller Coaster ΔE = W 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
ΔE = W + -
Before
After
KEi
PEgi
KEf
PEgf W
PEsi
PEsf

54. ΔE = W k m 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 + -
Before
After
KEi
PEgi
PEsi
KEf
PEgf
PEsf W Δx
V-? k m
½ kx2 = ½ mv2

55. ΔE = W 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
No Friction
ΔE = W + -
Before
After
KEi
PEgi
PEsi
KEf
PEgf
PEsf W
V-?
Hmax ? k
½ kx2 = ½ mv2+mgh

56. ΔE = W k 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
After
KEi
PEgi
PEsi
KEf
PEgf
PEsf W
Hmax ? Δx θ k

57. 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?
A: Yes
B: No
C: Need more information
h = 1m
v = 4
m/s

58. 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?
h = 2m
V – ?

59. A ball is dropped from a tower and attains a speed v at the bottom
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?

60. momentum Vi=0 F=const p = mv
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.
F=ma=mV/t

61. 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

62. 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?

63. 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?

64. Ball 1 strikes stationary Ball 2 in 2D
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 x-component of p1f ?
A: 0
B: 1
C: 2
D: 3
E: None of these

65. A ball bounces off the floor as shown
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 

66. A ball fall to the floor and sticks to it. Find p.
A ball bounces elastically off the floor as shown. Find p. m m
p = mv
p = 2mv V V

67. A compact car and a large truck collide head on and stick together
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

68. A compact car and a large truck collide head on and stick together
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

69. 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 V
mV = (m+M)Vf
V = Vf · (m+M)/m
Vf2 = 2gh

70. 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

71. A pendulum is launched in two different ways
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?

72. The door does not move.
Assuming the hinge is well-greased (no friction there) is this situation as shown physically possible?
A: Sure, why not?
B: No.

73. You are using a wrench and trying to loosen a rusty nut
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?

74. You are using a wrench and trying to loosen a rusty 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?

75. A) B) C) D) E) None of these
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) D) C) B)
E) None of these

76. 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) D) C) B)
E) None of these

77. 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

78. As the bar rotates from horizontal to vertical, the magnitude of the angular acceleration  of the bar..
A: increases
B: decreases
C: remains constant

79. A mass m hangs from string wrapped around a pulley of radius R
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. R m
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?)

80. Moment of inertia is larger in situation:
M, R, L
Moment of inertia is larger in situation: A B C
the same A B C

81. Moment of inertia is larger in situation:B
the same

82. 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)    t
B)   t(1/2) t2
C) 2=2+2

83. 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?
A: IA= 2IB
B: 2IA = IB
C: IA = IB
D: IA = 4IB
E: 4IA=IB m L A m 2L B

84. 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?
A: IA= 2IB
B: 2IA = IB
C: IA = IB
D: IA = 4IB
E: 4IA=IB 2m L A m 2L B

85. 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?
Cup A
Cup B
The same

86. 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 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

87. 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?
A) Lower than 0C
B) 0C
C) between 0C and 25C
D) 25C
E) Between 25C and 50C
F) 50C
G) Higher than 50C

88. The water in a cup is initially at 55C, and the cup is in a room where the temperature is 25C.