Physics 111
Fall 2008
Final Exam
A y j
2
A
A
Adding vectors
Ax
Linear motion v v o
Ay
2

a t
tan
B y j
Ay
1  2
at
2
v o  cos  o
v o t
x xo
Projectile motion components: v xo
v x is_constant
Projectile motion
1
Ax
A x B x i
B
L 2   r
Ay
circle A   r
 means difference: final - initial
A A x i
Name ________________________________
2
Two vectors are equal if both components are equal
dot product A  B A x B x A y  B y A  B  cos A  B
1
2
2
2 a  x x o v v o
x x o  v v o t
2
v yo v o  sin  o
v y v yo
g t
2
v o  sin ( 2   )
R
Circular motion
T period time_for_single_rotation
f
max height at
g
g t 0
v y v yo
1
 2   f
v  R
ar
T
ar
2
2
A
v
2
R
R
T
Fnet
Newton Laws
Fnet m a
Fi
F i addition_of_vectors
all
all
a a i
Hint: always choose one axis in the direction of acceleration vector then the acceleration vector is:
weight w vertical_down
Forces: Normal N perpendicular_to_surface
0 j
friction
Fr parallel_to_surface perpendicular_to_ N
weight
w
m g
friction
def: W F  d
F  d  cos F  d
work by gravity W
Fr s
 s N
Fr smax
 s N
k x
Hook's Law F spring
Work
 k N
Fr k
F x d x F y  d y
mgh (if h positive)
work by spring W s
1  2
kx
2
W net Fnet  d
F i d
all
1  2
1 2
 K W net
gravitational U g m g  h
elastic U s  k  x
mv
2
2
W
dW 
P avg
Power
P
F v F  v  cos F  v
dt
t
Work - Energy Principle
if W = 0 then
Ug Us K
W Ug Us K
initial
final
Energy
Ug
Us
kinetic K
K
Ug
initial
Us
K
final
n
Center of mass
r com M
n
m i r i
n
v com M
i= 1
m i v i
a com M
i= 1
Linear momentum for single mass p m v
impulse I
m i a i
i= 1
I F net  t  p
n
For many masses
P
pi
I F net ( external )  t  P
If no external forces or t=0:
P 0
means
i= 1
P final P initial
1
Physics 111
Fall 2008
Elastic collision
v initial
Final Exam
V1
V final
m 1 v 1
Fully inelastic collision
m 2 v 2
m1
m2
m1
m2
1
2
11  N  m
G 6.67  10
kg

Rotation
s
  o
 t
2
I
Rot. inertia
I mr

 avg
radians
R

t
2
r dm
2
2
m i r i
2
I net
 o
t
s
dt
v R 
2
m h
I Io
rad
d

2   
2
0.105
60

 avg

rev 2 
min
d
1  2
 t
2
n
1
g 9.8
dt
 o t
 o
A
m 2 V
m1
1 rev 2  radians 360 deg
Constants
v
Name ________________________________

2 m2
2 m 1
m2 m1
v
v
v
V
2
2
1
2
m1 m2
m1 m2
m1 m2
rot. energy
a R 
1  2
I
2
Kr
i= 1
n

torque 
r
 net I  
 net
F
i= 1
2
W
1
W  
n
orbital momentum = l
l r
p m r
for system: L
v
oscillations
phase   t
L
 net
t
i= 1
 net   t 0 then L i L f
M m
F G
2
r
gravitation
L I
li
U
G M  m
T
R
x( t ) x m cos (   t
)
2
4  3
r
G M
2
v
 d
conservation: if
altitude = above the surface
R
  x m sin(   t
v( t )
2  G M
 i
)
a( t )
2
  x m cos (   t
)
2
  x( t )


k
m
m
T 2 
k
E
1  2
k xm
2
I
T 2 

T 2  
I
m g  L
As a student at NJIT I will conduct myself in a professional manner and will comply with the provisions of
the NJIT Academic Honor Code. I also understand that I must subscribe to the following pledge: On my
honor, I pledge that I have not violated the provisions of the NJIT Academic Honor Code.
__________________________________
2
Physics 111
Fall 2008
Final Exam
Name ________________________________
A
1. A car travels along a straight stretch of road. It proceeds for 11 mi at 60 mi/h then 23 mi at 40 mi/h. What is the car's average
velocity during the entire trip?
A. 45 mi/h
B. 42 mi/h
C. 48 mi/h
D. 50 mi/h
E. 55 mi/h
2. A bolt is dropped from a bridge under construction, falling 46 m to the river below the bridge. What is its speed when it
reaches the water beneath the bridge?
A. 10 m/s
B. 20 m/s
C. 30 m/s
D. 40 m/s
E. 50 m/s
3. Two blocks are in contact on a frictionless table. A horizontal force is applied to the larger block, as shown in fig.
If m1 = 2 kg and m2 = 4 kg, and F = 30 N find the magnitude of the force between the two blocks.
A. 10 N
B. 20 N
C. 30 N
D. 40 N
E. 50 N
4. The figure shows a man sitting in a chair that dangles from a massless rope which runs over a
massless, frictionless pulley and back down to the man's hand. The combined mass of man and
chair is 100 kg. With what force must the man pull on the rope if he is to rise with a constant velocity
A. 450 N
B. 500 N
C. 550 N
D. 600 N
E. 650 N
5. A stone is thrown vertically upward from the ground with an initial velocity of 25 m/s. How long is
required for the stone to reach its maximum height?
A. 2.5 s
B. 3.0 s
C. 3.5 s
D. 4.0 s
E. 4.5 s
3
Physics 111
Fall 2008
Final Exam
Name ________________________________
A
6. A falling object requires 1.5 s to travel the last 30 m before hitting the ground. From what height above the ground did it fall?
A. 33 m
B. 38 m
C. 43 m
D. 48 m
E. 53 m
7. Find the dot product of the two vectors A = 6i +j -2k
A. -3
B. 0
C. 2k
D. 7
E. -2k
and B = -i +3j. (where i, j, k are unit vectors).
.
8. Find the cross product between two vectors A = 6i +j
A. 19i
B. 27j
C. -7i+8j
D. 19k
E. -33k
and B = -i +3j
9. In flat, open country a hiker travels due east for 5.12 km and then turns due south proceeding for another 3.87 km before
resting. How far is this rest position (bee line) relative to the starting point?
A. 9.1 km
B. 8.7 km
C. 7.6 km
D. 6.4 km
E. 5.3 km
10. A particle travels with uniform speed in a circular path with a radius R = 2m and a period T = 0.75 s. What is the centripetal
acceleration of the particle?
A. 140 m/s
B. 220 m/s
C. 340 m/s
D. 430 m/s
E. 570 m/s
4
Physics 111
Fall 2008
Final Exam
Name ________________________________
11. A flat disk with a mass of 2 kg slides across the frozen surface of a lake with an initial speed of 5 m/s. If the
frictional force on the disk has a constant value of 4 N. in what distance will the disc come to rest?
A. 3.7 m
B. 5.2 m
C. 6.3 m
D. 8.4 m
E. 9.7 m
A
12. A block of wood rests on an inclined plane, also of wood, with an adjustable angle of inclination . The angle is slowly
increased from zero, and the block is observed to start sliding when = 33 deg. What is the coefficient of static friction ms
between the block and plane?
A. 0.22
B. 0.35
C. 0.17
D. 0.42
E. 0.65
13. A 5 kg block is initially at rest on an inclined
 = 60 deg) A force F = 20 N is applied to the block in a direction
parallel to and up the plane. Determine the acceleration of the block if the coefficient of kinetic friction k = 0.42.
A. 6.5 down the plane
B. 2.4 down the plane
C. 2.5 up the plane
D. 1.5 up the plane
E. 1.5 down the plane
14. A pendulum bob is displaced from its equilibrium position and is raised to a vertical height h as shown. If the bob is
released from this height from rest, what amount of work has been done by the gravitational force when the bob arrives at the
bottom of its swing?
A. mgh
B. mghsin()
C. mghcos()
D. mgh/sin()
E. mgh/cos()
15. A spring with a spring constant k = 50N/m moves a block by contracting from a stretched length of 30 cm to a length of 5
cm. The block slides on a horizontal frictionless surface. What is the amount of work done on the block by the spring?
A. 0.5 J
B. 0.9 J
C. 1.4 J
D. 1.8 J
E. 2.2 J
5
Physics 111
Fall 2008
Final Exam
Name ________________________________
A
16. A block with a mass m = 8 kg is pushed up a frictionless inclined plane ( = 320) by a force F = 48 N that acts parallel to the
plane. If the block starts from rest, how much work is done on the block when it has been moved 0.65 m up the plane
A. 21 J
B. 31 J
C. 42 J
D. 53 J
E. 61 J
17. A block with a mass of 0.5 kg is suspended (vertically) from a spring that has a spring constant k = 50N/m. The block is
pulled down a distance of 50 cm to a point xA and released. What is the velocity of the block when it is 20 cm above release
point?
A. 2.0 m/s
B. 2.5 m/s
C. 3.0 m/s
D. 3.5 m/s
E. 4.0 m/s
18. A block with a mass m = 4 kg slides starting from rest, down an inclined plane (=35deg) from an initial height h0 = 6 m. the
friction coefficient is k = 0.25. Find the kinetic energy of the block when it has reached the height h = 2m
A. 40 J
B. 60 J
C. 80 J
D. 100 J
E. 120 J
19. Two particles with masses m1 = 2 kg and m2 = 5 kg are free to slide on a straight horizontal frictionless guide wire. The
particle m1 is moving with a speed of 17 m/s and overtakes the larger particle, which is moving in the same direction with a
speed of 3 m/s. What are the final velocities of the particles if the collision was fully elastic?
A. -4 m/s and 5 m/s
B. -3 m/s and 11 m/s
C. -2 m/s and 5 m/s
D.-8 m/s and 3 m/s
E. -2 m/s and 8 m/s
20. A massless string is wrapped around a uniform solid cylinder that has a mass m = 15 kg and a radius r = 20 cm. The
cylinder is free to rotate about its axis on frictionless bearings. One end of the string is attached to the cylinder and the free end
is pulled tangentially by a force that maintains a constant tension of 2 N in the string. What is the angular acceleration  of the
cylinder?
A. 1.3 rad/s2
B. 1.7 rad/s2
C. 0.45 rad/s2
D. 6.3 rad/s2
E. 4.8 rad/s2
6
Physics 111
Fall 2008
Final Exam
Name ________________________________
A
21. Two solid uniform disks are attached to a common axis which is free to rotate without friction. A massless string is wrapped
around each disk and supports a hanging block. Disc A has mass of 4 kg and a radius of 8 cm; the mass of the block hanging
from A is 6 kg. Disc B has a mass of 6 kg and a radius of 10 cm. The mass of the block hanging from disc B is 5 kg. Find the
angular acceleration of the system assuming the rod has negligible inertia.
A. 1.2 rad/s2
B. 2.7rad/s2
C. 3.8 rad/s2
D. 4.6 rad/s2
E. 5.8 rad/s2
22. A uniform cylinder with a mass M rolls without slipping down an inclined plane. Find the linear velocity of the cylinder at the
bottom of the incline.
A. 2.25 m/s
B. 3.25 m/s
C.4.25 m/s
D. 5.25 m/s
E. 6.25 m/s
23. Consider the wheel-and-axle system shown below. Which of the following expresses the
condition required for the system to be in static equilibrium?
A. am1 = bm2
B. m1 = m2
C. am2 = bm1
D. a2m1 = b2m2
E. b2m1 = a2m2
24. A(n) 34 kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole. A
cable at an angle of 300 with the beam helps to support the light. Find the tension in the cable.
A. 666 N
B. 732 N
C. 456 N
D. 388 N
E. 525 N
25. A 10 g bullet is fired into and embeds itself in a 2 kg block. What is the velocity of the block with bullet after the collision?
The bullet has a speed of 300 m/s just before it strikes the block, and the block slides on a frictionless surface.
A. 0.5 m/s
B. 0.8 m/s
C. 1.2 m/s
D. 1.5 m/s
E. 1.8 m/s
7
Physics 111
Fall 2008
Final Exam
Name ________________________________
A
26. A 5.0-kg block travels around a 0.50-m radius circle with an angular velocity of 6 rad/s. The magnitude of its angular
momentum about the center of the circle is:
A. 7.5kg·m2/s
B. 11 kg·m2/s
C. 18 kg·m2/s
D. 22 kg·m2/s
E. 36 kg·m2/s
27. A 0.7 kg block attached to a spring of force constant k =120 N/m oscillates with an amplitude of 8 cm. Find the maximum
speed of the block.
A. 1.0
B. 1.5
C. 2.0
D. 2.5
E. 3.0
28. Two objects are moving in the x, y plane as shown. The
magnitude of their total angular momentum (about the origin O) is:
A. zero
B. 6 kg • m2/s
C. 12 kg • m2/s
D. 30 kg • m2/s
E. 78 kg • m2/s
29An ice skater with rotational inertia I0 is spinning with angular speed 0. She pulls her arms in, thereby
increasing her angular speed to 40. Her rotational inertia is then:
A. I0
B. I0/2
C. 2I0
D. I0/4
E. 4I0
30. The position of a 0.64-kg mass undergoing simple harmonic motion is given by x(t) = (0.60 m) cos(20t+600).
What is its period of oscillation?
a.
0.10 s
b.
0.34 s
c.
0.17 s
d.
2.0 s
e.
0.5 s
8