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Sample Final Exam
Phys 111
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Vectors: Ax = A cos; Ay = A sin; A = A x  A y
2
One-dimensional motion: x = vot +
v2  v0
 2g
1 2
at ,
2
2
2
y max 
v0
2g
t tot 
v2  v0
2a
x
2v0
g
Ay
Ax
; A + B = C  Cx = Ax + Bx ,
A x B = (AxBy - AyBx)k ;
2
;
x
v = vo + at;
projectile motion: vox = vocos;
2
2( v0 cos ) 2
y
voy = vosin;
v y  v oy
W
Pavg =
t
Wmg = mg(y0 - y) ,
1
Kinetic energy: K = m v2;
2
Ugi + Usi + KI = Ugf + Usf + Kf
y = voy t -
v2
;
R
Fnet = ma;
ac =
fk = kN;
centripetal force: F =
Wtot = Kf - Ki ;
 = rFsin;
Ipoint mass = mr2
Ishell =
 = I;
Idisck =
2
mR 2
3
Pi = Pf ;
Ihoop = mR2
I = Icom + MD2
2R
;
v
Oscillations:
= 2
m
;
k
Etot =/2 kxm2
v esc 
Fnet = m
v2
,
R
2GM p
R
1
T
Tpend =
GM p
R
K=
FG
Etot =1/2kx2 + 1/2mv2
l
g
1
I
2
;
Uspr =
Etot = 1/2mvmax2
m1  m 2
2
2
1
mR 2
3
;
Iball =
1
m vcom 2
2
+
L = I
R
4 2 3
T2 
R ;
GM
v = -  xm sin(t)
2
Irod(end) =
l =m (rxvy - ryvx)k
W = mg,
v sat 
1
mR 2
12
vcom = R
l = mrvsin ;
x = xmcos(t)
f=
Irod =
Rolling:
Angular momentum: lpoint mass = mrxv
period T =
weight: W
mv 2
; work:
r
Wfr = -Fk d;
m 1vi1 + m2vi2 = m1vf1 + m2vf2 ;
2  0
1 2
 = 0 + t;  = 0 t + t ;  
2
2
W
1
1
2
2
W=
Pavr =
I  Ii
2 f
2
t
work: W =  ;
1
mR 2
2
G = 6.67x10-11Nm2+/kg2
vy =
Ugi + Usi + KI + Wnc = Ugf + Usf + Kf
s
rotational motion:   ; v =  r; at =  r;1 rev = 2 rad;
r
= r x F;
1 2
gt ;
2
Us = 1/2 kx2,
Ug = mg(y-y0)
Fnet t = mvf - mvi
momentum: p = mv;
;
Wspring = 1/2k(x02 -x2)
Fspring = -kx ;
x = vox t ;
2
 2g
= mg, ; g = 9.8 m/s2; incline: Wx = mgsin, Wy = mgcos, Friction: fs,max = sN;
W = F  d = Fdcos;
A = Axi + Bxj
1
v1  v 2
t ; y = vo t - gt2, v = vo - gt,
2
2
2
v sin 2
R= o
;
g
gx 2
y  (tan )  x 
voy - gt;
;  = tan-1
A  B  ABcos   A x Bx  A y By ; A x B = ABsin ;
Cy = Ay + By;
y
2
gG
; K=
2

 = fsR
LI = Lf
Mp
R
2
;
U  G
M E mo
;
R
 = 2f =
2
T
ME = 5.98x1024 kg.
F = -kx
1 2
kx
2
vmax = xm 
1
I
2
2
mR 2
5
RE = 6.37x106 m ,
a = - 2 xmcos(t)
2
amax = xm 2
=
k
m
period: T spring
Sample Final Exam
Phys 111
1. A cart with an initial velocity of 20 m/s to the right experiences a constant acceleration of a = 2 m/s 2 to the left. What is its velocity
after traveling 64 m?
A. 32 m/s
B) 24 m/s
C) 18 m /s
D) 12 m /s
E) 4 m /s
2. A projectile is fired over level ground at an angle of 350 above the horizontal. It strikes the ground at a distance 280 m from the
release point. What is the magnitude of its initial velocity?
A)
B)
C)
D)
E)
40 m/s
54 m/s
82 m/s
120 m/s
146 m/s
3. A projectile is fired over level ground toward a wall with an initial velocity of 25 m/s at an angle of 40 0 .The wall is 36 m from the
release point. How far above the ground does the projectile hit the wall?
A)
B)
C)
D)
E)
1.2 m
4.4 m
8.0 m
10.5 m
12.9 m
4. A ball thrown horizontally from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m
With what speed was it thrown?
A.
B.
C.
D.
E.
6.1 m/s
7.4 m/s
8.1 m/s
10.8 m/s
15.0 m/s
5. Forces of 10 N north, 20 N east, and 15 N south are simultaneously applied to a 4- kg mass. The magnitude of the resultant
acceleration is closest to:
A.
B.
C.
D.
E.
1.75 m/s2.
2.75 m/s2
5. 15 m/s2.
6.30 m/s2
8.00m/s2
6. Traveling at a speed of 21 m/s, the driver of a car suddenly locks the wheels by slamming on the brakes. The coefficient of kinetic
friction between the tires and the road is 0.72. How much time does it take for the car to come to stop?
A. 1 sec
B. 2 sec
C. 3 sec
D. 4 sec
E. 5 sec
2
7. A hanging block M is connected by a string over a massless pulley to a 10-kg block
sitting at rest on a flat table. The coefficient of static friction between the table and the
block is 0.3. What minimum mass of the hanging block is needed to start the system
moving?
A. 1 kg
B. 2 kg
C. 3 kg
D. 4 kg
E. 5 kg
8. An ideal Atwood's machine has a 7-kg and 5-kg mass at the ends of the string as has been shown in the figure.
The magnitude of acceleration of both masses is closest to
A. 9.80 m/s2
B. 7.52 m/s2
C. 5.20 m/s2
D. 2.85 m/s2
E. 1.63 m/s2
9. A 4-kg block is placed on a plane inclined at 350 with respect to the horizontal. If the block slides down the plane with an acceleration
of 2 m/s2, determine the coefficient of kinetic friction between the block and plane.
A) 0.22
B) 0.38
C) 0.45
D) 0.69
E) 0.85
10. A 0.2-kg object is released from a height 1.8 m above the ground and slides along a frictionless loop-the-loop with a diameter of 1.4
m. The normal force on the object at the top of the loop is:
A. 0.40 N
B. 1.00 N
C. 1.55 N
D. 2.52 N
E. 8. 48 N
11. A floating ice block is pushed through a displacement d = (10 m) i -(8 m) j bu rushing water that exerts a force of
F = (200 N)i + (100) Nj on the block. The work done by this force on the block is closest to:
A) 800 J
B) 1200 J
C) 1600 J
D) 2000 J
E) 2400 J
12. A horizontal spring with a 10000 N/m spring constant is compressed 0.08 m, and a 12-kg block is
placed against it. When the block is released, the block shoots forward along a horizontal surface that
exerts 8 N friction force on the block. How far from the original position does the block travel before
coming to a stop?
A.
B.
C.
D.
E.
3.2 m
4.0 m
6.4 m
7.0 m
8.0 m
3
13. A 4-kg block is projected up a 250- inclined plane with initial speed vo = 6 m/s. If the coefficient of kinetic friction between the block
and the plane is 0.2, how far up the plane does it go?
A) 3.0 m
B) 4.5 m
C) 6.5 m
D) 7.0 m
E) 9.0m
14. A 5-kg ball is dropped from a height y0 above the top of a vertical spring whose spring constant is 2000
N/m. The spring is compressed 0.4 m. The height y0 is closest to
A) 1.25 m
B) 2.86 m
C) 6.81 m
D) 8.29 m
E) 9.40 m
15. A simple pendulum consists of a 5-kg mass attached to a string of length 2 m. It is released from rest at A, 0.2 m above the lowest
point of the swing. The tension in the string at the lowest point B is closest to:
A)
B)
C)
D)
E)
36 N
48 N
60 N
88 N
96 N
16. A 10 - g bullet moving directly upward at 1000 m/s strikes and passes
through the center of mass of a 5-kg block initially at rest. The bullet emerges
from the block moving directly upward at 400 m/s. Find the magnitude of
impulse exerted on the block by the bullet.
A. 2.0 Ns
B. 3.0 Ns
E. 4.0 Ns
D. 5.0 Ns
E. 6.0 Ns
17. A 10 kg sphere is glued to a massless stick that is tangent to it and then spun about the axis formed
by the stick. What is the sphere's rotational inertia I about this axis, if its radius is 0.2 m ? The
rotational inertia of a sphere about its center is Icm = 2/5 MR2 .
A. 0. 24 kg.m2
B. 0.56 kg.m2
C. 1.52 kg.m2
D. 1.75 kg.m2
E. 1.25 kg.m2
18. A multi-level pulley of rotational inertia I = 0.2 kgm 2 is pivoted about a frictionless axis through O
and perpendicular to the pulley, as shown. If a = 20 cm and b = 25 cm (see the figure) what is the
angular acceleration of the pulley ?
A. 0. 75 rad/s2 clockwise
B. 0.75 rad/s2 counterclockwise
C. 2.00 rad/s2 counterclockwise
D. 2.50 rad/s2 clockwise
E. 3.50 rad/2 clockwise
4
19. A bowling ball has a mass of 5 kg, and a radius of 0.2 m . If it rolls down the 250 incline, 5 m long, without slipping. The speed of
the ball at the bottom of the incline is closest to:
A.
B.
C.
D.
E.
5 m/s
12 m/s
25 m/s
32 m/s
56 m/s
20. A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms:
A. his angular velocity increases
B. his angular velocity decreases
C. his rotational inertia decreases
D. his rotational inertia remains the same
E. his kinetic energy remains the same
21. A wheel starts from rest and has an angular acceleration of 4.0 rad/s 2 . The time it takes to make 10 revolutions is:
A.
B.
C.
D.
E.
0.50 s
0.71 s
1.4 s
1.8 s
5.6 s
22. Three identical objects of mass M are fastened to a massless rod of length L as shown. The
rotational inertia about one end of the rod of this array is:
A.
B.
C.
D.
E.
ML2/2
ML2
3ML2/2
5ML2/4
3ML2
23. A disk with a rotational inertia of 5.0 kg ×m2 and a radius of 0.25 m rotates on a fixed axis perpendicular to the disk and through its
center. A force of 2.0 N is applied tangentially to the rim. As the disk turns through half a revolution the work done by the force is:
A.
B.
C.
D.
E.
1.6 J
2.5 J
6.3 J
10 J
40 J
24. A 6-kg particle moves to the right at 4 m/s as shown. Its angular momentum in kg ×m 2 /s2 about the point O is:
A.
B.
C.
D.
E.
zero
288
144
24
249
25. A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg × m2 . It is initially spinning at 0.80 rad/s
when a 20-kg child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merry-go-round is:
A. 0.61 rad/s
B. 0.73 rad/s
C. 0.80 rad/s
D. 0.89 rad/s
E. 1.1 rad/s
5
26. A projectile of mass m = 1.3 kg moves to the right with speed v 0 = 23 m/s. The
projectile strikes and sticks to the stationary rod of mass M = 9 kg and length d = 1.3 m
that is pivoted about a frictionless axle through its center. Find the angular speed of the
system right after the collision
A) 4.3 rad/s
B) 5.8 rad/s
C) 7.8 rad/s
D) 10.7 rad/s
E) 12.4 rad/s
27. What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 800 km
km
/s
B) 3.3 /s
km
C) 7.5 /s
km
D) 10.2 /s
km
E) 13.7 /s
A) 1.2
km
28. The planet X requires 2.44 years to orbit the sun, which has a mass of 2.0 .1030 kg, in an almost circular trajectory. Calculate the
radius of the orbit of X as it circles the sun. Answer in units of m.
A) 2.7.1011 m
B) 3.2 .1011 m
C) 5.5.1011 m
D) 7.8.1011 m
E) 9.1.1011 m
29. A uniform ladder is 10 m long and weighs 250 N. It leans against a frictionless wall as shown. The
angle  = 40 0. Find the force exerted on the ladder by the wall.
A) 149 N
B) 198 N
C) 281 N
D) 355 N
E) 500 N
30. If weight of the block is 200 N , T 1 = 150 N and 1 = 250 , what is the magnitude of T2 and 2 ?
A) 150 N, 350
B) 192 N, 450
C) 284 N, 550
D) 315 N, 650
E) 386 N, 650
T2
T1
1
2
29. A cylinder of mass 4 kg and diameter 0.3 m rolls without slipping on a horizontal surface. At the instant its center of mass has a
speed of 13 m/s determine the total energy of the cylinder
A) 507 J
B) 611 J
C) 722 J
D) 831 J
E) 911 J
6
30. A satellite is in circular orbit 520 km above the surface of the Mars (radius of Mars is 3395 km). It is observed to have a period of
124 min. What is the mass of Mars?
A. 6.4x1023 kg
B. 1.4x1024 kg
C. 5.0x1025 kg
D. 2.4x1026 kg
E. 8.0x1027 kg
31. The motion of a piston in an auto engine is simple harmonic. The piston travels back and forth over a distance of 18 cm, and the
piston has a mass of 1.6 kg. What is the maximum speed of the piston when the engine is running at 5000 rpm?
A)
B)
C)
D)
E)
21 m/s
34 m/s
47 m/s
59 m/s
72 m/s
A 0.25-kg block is attached to the end of the spring and executes simple harmonic motion according to the equation
x = 5cmcos [(25rad/s)t]
32. The total mechanical energy of the mass-spring system is closest to
A.
B.
C.
D.
E.
0.05 J
0.15 J
0.20 J
0.35 J
0.50 J
33. What is the velocity of the mass at t = 2.8 s?
A. 0.46 m/s
B. 0.95 m/s
C. 1.28 m/s
D. 2.65 m/s
E. 3.15 m/s
34. What is the velocity of the mass when x = 2.2 cm?
A. 0.1 m/s
B. 0.2 m/s
C. 0.3 m/s
D. 0.4 m/s
E. 0.5 m/s
7