Download Practice test (Chapters 10

Chapter 5A
1
Practice test for Midterm 3
Chapters 10, 11, 12, 13, 14
In preparation for the Midterm exam go through this and
the other practice tests, go through the homework
problems and through the problems we did in class.
Understand the concepts and what the formulas mean!!
---------------------------------------------------------Chapter 10
5.
(a)
(b)
(c)
(Chapter 10) Consider the arrangement of masses below. M = 0.50 kg, L = 1.0 m, and the mass of
each connecting rod shown is negligible. Treat the masses as particles.
What is the moment of inertia, I, about an axis that is perpendicular to the paper and that
goes through a point halfway between the masses M and M as shown?
If the object is rotating about this axis with an angular velocity of  = 10 rad/s what is the
rotational kinetic energy?
If the object is rotating about this axis with an angular velocity of  = 10 rad/s what is the
angular momentum?
CM
M
X
L = 1.0 m
M
4M
L = 1.0 m
© 2000 by Harcourt College Publishers. All rights reserved.
Chapter 5A
6. (Chapter 10) Two blocks, m1 = 1 kg and m2 = 2 kg, are connected by a light string as
shown in the figure. The string runs over the pulley without slipping. The radius of
the pulley is 0.1 m and it has a mass of M = 5 kg. Treat the pulley as a rotating
cylinder.
a.
b.
c.
What is the speed of mass m2 after it has fallen for 1.88 m?
What is the angular velocity  of the pulley at that point?
How many rotations has the pulley made at that point?
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2
Chapter 5A
7.
a.
b.
c.
3
(Chapter 10) Starting from the same point, a sphere and a disk of the same mass M = 1 kg and the
same radius R = 0.1 m are rolling down an incline of length 1.00 m. The angle between the incline and
the horizontal is  = 30º as shown.
What is the speed of the sphere at the end of the incline?
What is the speed of the disk at the end of the incline?
Which object will reach the end of the incline first?
 = 30º
27. The rigid object shown is rotated about an axis perpendicular to the paper and through point
P. The total kinetic energy of the object as it rotates is equal to 1.4 J. If M = 1.3 kg and L =
0.50 m, what is the angular velocity of the object? Neglect the mass of the connecting rods
and treat the masses as particles.
a.
b.
c.
d.
e.
48.
1.3 rad/s
1.5 rad/s
1.7 rad/s
1.2 rad/s
2.1 rad/s
The rigid body shown rotates about an axis through its center of mass and perpendicular
to the paper. If M = 2.0 kg and L = 80 cm, what is the kinetic energy of this object when its
angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod
and treat the masses as particles.
a.
18 J
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Chapter 5A
4
b. 15 J
c. 12 J
d. 23 J
e. 26 J
Chapter 11 (Vector product, torque, angular momentum)
3.
A particle located at the position vector r = (1i + 1j) m has a force F = (2i + 3j) N acting on it.
The torque about the origin is:
a.
b.
c.
d.
e.
5.
(1k)N m
(5k)N m
(–1k)N m
(–5k)N m
(2i + 3j)N m
A solid cylinder of radius R = 1.0 m and mass 10 kg rotates about its axis. When
its angular velocity is 10 rad/s, its angular momentum (in kg · m2/s) is
a.
b.
c.
d.
e.
15.
50.
20.
40.
25.
70.
A puck on a frictionless air hockey table has a mass of 5.0 g and is attached to a cord
passing through a hole in the surface as in the figure. The puck is revolving at a distance
2.0 m from the hole with an angular velocity of 3.0 rad/s. The cord is then pulled from
below, shortening the radius to 1.0 m. The new angular velocity (in rad/s) is
a.
b.
c.
d.
e.
4.0
6.0
12
2.0
8.0
(Note that angular momentum in this system is conserved, because no external torque is applied)
© 2000 by Harcourt College Publishers. All rights reserved.
Chapter 5A
5
What is the rotational kinetic energy before and after pulling on the string? Is the mechanical
energy conserved in this system? Why or why not?
Similar problem again. A puck on a frictionless air hockey table has a mass of 5.010-3 kg
and is attached to a cord passing through a hole in the surface as in the figure. The puck
is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The
cord is then pulled from below, shortening the radius to 1.0 m. Note that the angular
momentum of the puck is conserved, because no torque is applied to it.
d.
e.
f.
g.
h.
What is the angular momentum of the puck before the cord is pulled?
What is the angular momentum of the puck after the cord is pulled (Hint: No calculation
necessary)
What is the angular velocity  after the cord is pulled?
What is the rotational kinetic energy before the cord is pulled?
What is the rotational kinetic energy after the cord is pulled?
(10 points)
0.06 kgm2/s; 0.06 kgm2/s; 12 rad/s; 0.09 J; 0.36 J
17.
A skater extends her arms horizontally, holding a 5-kg mass in each hand. She is
rotating about a vertical axis with an angular velocity of one revolution per
second. If she drops her hands to her sides, what will the final angular velocity
(in rev/s) be if her moment of inertia remains approximately constant at
5 kg · m2, and the distance of the masses from the axis changes from 1 m to .1 m?
a.
b.
c.
d.
e.
6
3
9
4
7
© 2000 by Harcourt College Publishers. All rights reserved.
Chapter 5A
29.
6
The diagram below shows five cylinders, each cylinder rotating with constant
angular velocity about its central axis. The magnitude of the tangential velocity
of one point of each cylinder is shown, along with each cylinder’s radius and
mass. Which cylinder has the largest angular momentum?
Chapter 12 (Static equilibrium, elastic deformations)
2.
A horizontal meter stick supported at the 50-cm mark has a mass of 0.50 kg hanging from it
at the 20-cm mark and a 0.30 kg mass hanging from it at the 60-cm mark. Determine the
position on the meter stick at which one would hang a third mass of 0.60 kg to keep the
meter stick balanced.
a.
b.
c.
d.
4.
74 cm
70 cm
65 cm
86 cm
e. 62 cm
A uniform 100-lb beam is held in a vertical position by a pin at its lower end and
a cable at its upper end. A horizontal force (magnitude P) acts as shown in the
figure. If P = 75 lb, what is the tension in the cable?
a.
b.
c.
d.
e.
54 lb
69 lb
47 lb
61 lb
75 lb
© 2000 by Harcourt College Publishers. All rights reserved.
Chapter 5A
15.
The diagrams below show forces applied to a wheel that weighs 20 N. The symbol W
stands for the weight. In which diagram(s) is the wheel in equilibrium?
a.
b.
c.
d.
8.
A
B
C
D
e.
A and C
A 20-m long steel wire (cross-section 1 cm2, Young's modulus 2 x 1011 N/m2), is subjected
to a load of 25,000 N. How much will the wire stretch under the load?
a.
b.
c.
d.
e.
.25 cm
2.5 cm
12.5 cm
25 cm
1.25 cm
Chapter 13. The law of gravity, Kepler's laws of planetary motion
3.
A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 x 106 m.
What is the magnitude of the gravitational force on the satellite by planet Cruton?
a.
b.
c.
d.
e.
63 N
58 N
68 N
73 N
50 N
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7
Chapter 5A
9.Three 5.0-kg masses are located at points in the xy plane, as shown. What is the magnitude of
the resultant force (caused by the other two masses) on the mass at
x = 0.40 m, y = 0?
a.
b.
c.
d.
e.
2.2 x 10–8 N
1.9 x 10–8 N
1.4 x 10–8 N
1.6 x 10–8 N
2.5 x 10–8 N
Also go through the HW problems involving Kepler's laws
A satellite is 20,000 km above the earth of surface. How fast does it have to move so that its
centripetal force is equal to the gravitational pull it experiences.
What is a geosynchronous satellite? How far above earth does it have to be for this to work?
Chapter 14 Fluid Mechanics
9.
A blimp is filled with 200 m3 of helium. How much mass can the balloon lift? The density
of helium and air are given on the first page.
a.
b.
c.
d.
e.
15.
115 kg
215 kg
315 kg
415 kg
37 kg
The water level in a reservoir is maintained at a constant level. What is the exit velocity in
an outlet pipe 3.0 m below the water surface?
a.
b.
c.
d.
e.
2.4 m/s
3.0 m/s
5.4 m/s
7.7 m/s
49 m/s
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8
Chapter 5A
17.
Water pressurized to 3.5 x 105 Pa is flowing at 5.0 m/s in a pipe which contracts to 1/3 its
former area. What is the pressure and velocity of the water after the contraction?
a.
b.
c.
d.
e.
20.
9
2.5 x 105 Pa, 15 m/s
3.0 x 105 Pa, 10 m/s
3.0 x 105 Pa, 15 m/s
4.5 x 105 Pa, 1.5 m/s
5.5 x 105 Pa, 1.5 m/s
The pressure inside a commercial airliner is maintained at 1 ATM (10 5 N/m2). What is the
outward force exerted on a 1 m x 2 m cabin door if the outside pressure (at 10 km height) is
0.3 ATM?
a.
b.
c.
d.
e.
1.4 x 102 N
1.4 x 103 N
1.4 x 104 N
1.4 x 105 N
7.0 x 103 N
25. A cube of wood having a side dimension of 18.6 cm and a density of 653 kg/m3 floats on
water.
(a) What is the distance from the horizontal top surface of the cube to the water level?
(b) How much lead weight must be placed on top of the cube so that its top is just level
with the water?
26. What must be the contact area between a suction cup (completely exhausted) and a ceiling if
the cup is to support the weight of an 70.0 kg student?
How much weigh could be supported with such a device on the moon, where the air pressure is
0?
27. A balloon of radius 1.06 m floats at a constant height. If the density of air is 1.29 kg/m 3, what
is the mass of the balloon?
© 2000 by Harcourt College Publishers. All rights reserved.
Chapter 5A
© 2000 by Harcourt College Publishers. All rights reserved.
10
Chapter 5A
© 2000 by Harcourt College Publishers. All rights reserved.
11
Chapter 5A
Answers:
Chapter 10
Answers:
5.) 4.75 kgm; 237.5 J; 47.5 J
6.) 2.59 m/s; 25.9 rad/s; 3 rotation
7.) 2.64 m/s; 2.56 m/s, the sphere is faster
27c
48 no solution available
11. Angular momentum, torque, vector product
3a
5a
15c
17b
29e
12. Static equilibrium
2b
4a
15c
8b
13. Gravitation
3b
9d
14. Fluid mechanics
9b
15d
17a
20d
25 [6.45] cm [2.23] kg
26 [0.00677] m2; 0
27. 6.4 kg
© 2000 by Harcourt College Publishers. All rights reserved.
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