Download 1. Five equal 2.0-kg point masses are arranged in the x

Sample exam 3:
Vectors: ax = acos;
ay = asin;
One-dimensional motion: x = vot +
Projectile motion: vox = vocos;
a=
ax  ay
2
 = tan-1
;
2
v y  v oy
v sin 2
R= o
;
;y
 2g
g
x = vox t ;
y = voy t -
2
Circular motion: aC =
gravitational potential energy: U = mg(y-y0) ; kinetic energy: K =
Wfr = -fk d;
power: P = F  v ; Pavg =
m1vi1 + m2vi2 = m1vf1 + m2vf2 ;
v2
  2 r;
r
I=
1
MR 2 ;
2
=  ;
ax
;
A + B = C  Cx = Ax + Bx , Cy = Ay +By;
1 2
gt ;
2
v2
;
R
T=
2R
;
v
 = 0 t +
rod: Irod(center) = 1/12 ML2
1
I
2 f
2

gx 2
2( v0 cos ) 2
Dynamic: F = ma;
weight: W = mg, ; g
mv 2
;
r
1
m v2; Ui + Ki = Uf + Kf work:
2
W
; momentum: p = mv;
t
v1  v 2
2
W = Fdcos;
Wtot = KEf -
Ft = mvf - mvI;
s
; 1 rev = 2 rad; v =  r; at =  r; ar =
r
2
 2  0
1

; K = I2
point mass: I = mr2
2
2
m1v1i + m2v2i = (m1 + m2)V; rotational motion:  
 = 0 + t;
Wtot=
x
vy = voy - gt; y  (tan )  x 
incline: Wx = mgsin, Wy = mgcos Friction: fs,max = sN; fk = kN; centrip. force: FC =
= 9.8 m/s2;
KEi ;
ay
1 2 2 2
1
at , v - v o = 2ax; v = vo + at ; y = vo t - gt2, v = vo - gt,
2
2
voy = vosin;
2
2
1 2
t ;
2
 = ½( + o)t;
Irod (end) = 1/3 ML2
sphere: I =
2
MR 2
5
torque:  = rFsin;
 = rF ;
disk:
 = I; work: W
1
Ii 2
2
__________________________________________________________________________________________________
1. A 0.025-kg ball is released from rest 80 m above the surface of Earth. Just before it hits the surface its speed is 20 m/s. During the fall,
how much mechanical energy of the ball has been lost?
A) 5.0 J
B) 10.8 J
C) 14.6 J
D) 24.0 J
E) 35.2 J
2. A 4-kg block moves from rest down a frictionless plane as shown. The final speed vf
of the block is most nearly
A. 1.41 m/s
B. 2.24 m/s
C. 4.43 m/s
D. 4.95 m/s
E. 9.81 m/s
3. A simple pendulum consists of a 8-kg mass attached to a string of length 2 m. It is released from rest at
0.2 m above the lowest point of the swing. What is the speed of the mass at the lowest point of the swing?
A) 2 m/s
B) 4 m/s
C) 6 m/s
D) 8 m/s
E) 10 m/s
A,
4. A 0.2-kg object is released from a height 2.2 m above the ground and slides along a frictionless loop-the-loop with a diameter of 1.4 m.
What is the object's speed at the top of the loop?
A) 2 m/s
B) 4 m/s
C) 6 m/s
D) 8 m/s
E) 10 m/s
5. A 4-kg block starts up a 250 frictionless incline with initial speed of 8 m/s. How far will it slide up the incline?
A.
B.
C.
D.
E.
2.5 m
4.2 m
6.0 m
7.7 m
22.7 m
6. 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 frictionless, horizontal surface. The
speed of the block is closest to
A. 2.2 m/s
B. 4.0 m/s
C. 6.4 m/s
D. 7.0 m/s
E. 8.0 m/s
7. A 5-kg block starts from rest and slides 4 m down a frictionless inclined plane with incline angle of 37 0, as shown. When it reaches the
horizontal surface, it encounters a friction force of 12 N. How far will it slide on the level surface before it stops?
A.
B.
C.
D.
E.
1.5 m.
3.0 m.
4.8 m.
6.9 m.
9.8 m.
37o
8. 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
9. Block A and block B are moving toward each other. Block A has a mass of 2 kg and a velocity of 50 m/s while block B has a mass of 4
kg and a velocity of 20 m/s. They collide and stick together. The common final speed is:
A.
B.
C.
D.
E.
3.3 m/s
20.0 m/s
30.0 m/s
40. 5 m/s
50 m/s
10. A 0.5-kg ball is dropped from rest at a point 1.25 m above the floor. The ball rebounds straight upward to a same height of 1.25 m. The
magnitude of the impulse applied to the ball during the collision with the floor is closest to :
2
A. 0.5 Ns
B. 1.5 Ns
C. 3.0 Ns
D. 5.0 Ns
E. 8.5 Ns
11. A solid sphere has a mass of 5 kg, and a radius of 0.2 m . If it rolls down the lane without slipping at a linear speed of
4 m/s, what is its total kinetic energy?
A.
B.
C.
D.
E.
6J
12 J
24 J
32 J
56 J
12. A 3-g bullet is fired horizontally into a 10-kg block of wood suspended by a rope form the ceiling. The block swings in an arc, rising 3
mm above its lowest position. The velocity of the bullet was:
A.
B.
C.
D.
E.
2.0x103 m/s
1.2x103 m/s
0.8x103 m/s
240 m/s
8 m/s
13. A wheel of diameter 3 cm has a 4-m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular
acceleration of 2 rev/s2. The cord will unwind in
A. 12.5 s
B. 8.5 s
C. 6.5 s
D. 3.5 s
E. 1.5 s
14. A disk with a rotational inertia of 5 kgm2 and a radius of 0.25 m rotates on a fixed axis perpendicular to the disk and through its center.
A force of 2 N is applied tangentially to the rim. As disk turns through half a revolution the work done by the force is
A. 1.6 J
B . 3.5 J
C. 6.3 J
D. 8.5 J
E. 9.8 J
15. A disk, with mass 4 kg and radius 0.6 m, initially has an angular velocity of 240 rev/min in clockwise direction and is slowing down at
a rate of =4.20 rad/s2. If the wheel rotates in a horizontal plane the total work done on the disk is:
A)
B)
C)
D)
E)
227 J
352 J
410 J
638 J
754 J
16. A Ferris wheel with rotational inertia 40000 kgm2 is to accelerate from rest to an angular velocity of 0.5 rev/s in 10 sec. The minimum
torque that its motor must provide to cause this acceleration is
A) 6280Nm
3
B)
C)
D)
E)
8500Nm
12560 Nm
16800 Nm
20000 Nm
17. An angular velocity of a disk with 2 kgm2 rotational inertia increases from 2 rev/sec to 6 rev/sec. The work done on the disk is closest
to
A)
B)
C)
D)
E)
1262 J
1440 J
1598 J
1880 J
2700 J
18. A grinding wheel with 10 kgm2 rotational inertia gains 2000 J of rotational kinetic energy after starting from rest. Its final angular
velocity is
A)
B)
C)
D)
E)
20 rad/s
40 rad/s
60 rad/s
80 rad/s
100 rad/s
3 kg
3 kg
19. Two equal masses m = 3 kg connected by a 4-kg rigid rod of length 1.2 m rotate about the
center of the rod at 60 rev/min. Find the kinetic energy of the system.
A) 52 J
B) 60 J
C) 98 J
D) 131 J
E) 180 J
4