Upload
stanley-dawson
View
216
Download
2
Embed Size (px)
Citation preview
Work and Energy
x
Work and Energy 06
A 500-kg elevator is pulled upward with a constant
force of 5500 N for a distance of 50.0 m. What is the
net work done on the elevator?
Ref: Sec. 6.1
Work and Energy 06
01
(A) 2.75 × 105 J
(B) -2.45 × 105 J
(C) 3.00 × 104 J
(D) -5.20 × 105 J
Work and Energy 06
x θcosFW Work
Matthew pulls his little sister Sarah in a sled on an icy
surface (assume no friction), with a force of 60.0 N at an
angle of 37.0° upward from the horizontal. If he pulls her
a distance of 12.0 m, what is the work done by Matthew?
Ref: Sec. 6.1
Work and Energy 06
02
(A) 185 J
(B) 433 J
(C) 575 J
(D) 720 J
Work and Energy 06
x θcosFW Work
A force moves an object in the
direction of the force. The graph
shows the force versus the object's
position. Find the work done when
the object moves from 0 to 6.0 m.
Ref: Sec. 6.2
Work and Energy 06
03
(A) 20 J
(B) 40 J
(C) 60 J
(D) 80 J
Work and Energy 06
Work is the product of force times distance
Work
A horizontal force of 200 N is applied to move a 55-kg
cart (initially at rest) across a 10 m level surface. What
is the final kinetic energy of the cart?
Ref: Sec. 6.3
Work and Energy 06
04
(A) 1.0 × 103 J
(B) 2.0 × 103 J
(C) 2.7 × 103 J
(D) 4.0 × 103 J
Work and Energy 06
FxW
Work
KEΔWnet Work/Energy Theorem
If it takes 50 m to stop a car initially moving at 25 m/s,
what distance is required to stop a car moving at 50 m/s
under the same condition?
Ref: Sec. 6.3
Work and Energy 06
05
(A) 50 m
(B) 100 m
(C) 200 m
(D) 400 m
Work and Energy 06
FxW
Work
2mv
KE2
Kinetic Energy
KEΔWnet
Work/Energy Theorem
A spring-driven dart gun propels a 10-g dart. It is cocked by
exerting a constant force of 20 N over a distance of 5.0 cm.
With what speed will the dart leave the gun, assuming the
spring has negligible mass?
Ref: Sec. 6.3
Work and Energy 06
06
(A) 10 m/s
(B) 14 m/s
(C) 17 m/s
(D) 20 m/s
Work and Energy 06
FxW
Work
2mv
KE2
Kinetic Energy
KEΔWnet
Work/Energy Theorem
A 100-N force has a horizontal component of 80 N and a
vertical component of 60 N. The force is applied to a box
which rests on a level frictionless floor. The cart starts
from rest, and moves 2.0 m horizontally along the floor.
What is the cart's final kinetic energy?
Ref: Sec. 6.3
Work and Energy 06
07
(A) 200 J
(B) 160 J
(C) 120 J
(D) zero
Work and Energy 06
x θcosFW Work
A 15.0-kg object is moved from a height of 7.00 m above a
floor to a height of 15.0 m above the floor. What is the
change in gravitational potential energy?
Ref: Sec. 6.4-6.5
Work and Energy 06
08
(A) 1030 J
(B) 1176 J
(C) 1910 J
(D) 2205
Work and Energy 06
yΔmgPEΔ g Gravitational Potential Energy
A 400-N box is pushed up an inclined plane. The plane is 4.0 m
long and rises 2.0 m. If the plane is frictionless, how much work
was done by the push?
Ref: Sec. 6.4-6.5
Work and Energy 06
09
(A) 1600 J
(B) 800 J
(C) 400 J
(D) 100 J
Work and Energy 06
yΔmgPEΔW g Gravitational Potential Energy
A spring is characterized by a spring constant of 60 N/m.
How much potential energy does it store, when stretched
by 1.0 cm?
Ref: Sec. 6.4-6.5
Work and Energy 06
10
(A) 3.0 × 10-3 J
(B) 0.30 J
(C) 60 J
(D) 600 J
Work and Energy 06
2kx
PE2
s
Spring Potential Energy
A spring with a spring constant of 15 N/m is initially
compressed by 3.0 cm. How much work is required to
compress the spring an additional 4.0 cm?
Ref: Sec. 6.4-6.5
Work and Energy 06
11
(A) 0.0068 J
(B) 0.012 J
(C) 0.024 J
(D) 0.030 J
Work and Energy 06
2kx
PE2
s
Spring Potential Energy
A skier, of mass 40 kg, pushes off the top of a hill with an
initial speed of 4.0 m/s. Neglecting friction, how fast will
she be moving after dropping 10 m in elevation?
Ref: Sec. 6.6-6.7
Work and Energy 06
12
(A) 7.3 m/s
(B) 15 m/s
(C) 49 m/s
(D) 196 m/s
Work and Energy 06
0PEΔKEΔ g Conservation of Energy
A 1.0-kg ball falls to the floor. When it is 0.70 m above
the floor, its potential energy exactly equals its kinetic
energy. How fast is it moving?
Ref: Sec. 6.6-6.7
Work and Energy 06
13
(A) 3.7 m/s
(B) 6.9 m/s
(C) 14 m/s
(D) 45 m/s
Work and Energy 06
KEPEg Energy
mgyPEg
Potential Energy
2mv
KE2
Kinetic Energy
A roller coaster starts with a speed of 5.0 m/s at a point 45 m
above the bottom of a dip as shown in the diagram. Neglect
friction, what will be the speed of the roller coaster at the top
of the next slope, which is 30 m above the bottom of the dip?
Ref: Sec. 6.6-6.7
Work and Energy 06
14
(A) 12 m/s
(B) 14 m/s
(C) 16 m/s
(D) 18 m/s
Work and Energy 06
0PEΔKEΔ g Cons. of Energy
mghPE
Potential Energy2
mvKE
2
Kinetic Energy
A pendulum of length 50 cm is pulled 30 cm away from the
vertical axis and released from rest. What will be its speed
at the bottom of its swing?
Ref: Sec. 6.6-6.7
Work and Energy 06
15
(A) 0.50 m/s
(B) 0.79 m/s
(C) 1.2 m/s
(D) 1.4 m/s
Work and Energy 06
0PEΔKEΔ g Cons. of Energy
mghPE
Potential Energy
2mv
KE2
Kinetic Energy
A 1500-kg car moving at 25 m/s hits an initially uncompressed
horizontal spring with spring constant of 2.0 × 106 N/m. What
is the maximum compression of the spring? (Neglect the mass
of the spring.)
Ref: Sec. 6.6-6.7
Work and Energy 06
16
(A) 0.17 m
(B) 0.34 m
(C) 0.51 m
(D) 0.68 m
Work and Energy 06
0PEΔKEΔ g Cons. of Energy
mghPE
Potential Energy
2mv
KE2
Kinetic Energy
The kinetic friction force between a 60.0-kg object and a
horizontal surface is 50.0 N. If the initial speed of the object
is 25.0 m/s, what distance will it slide before coming to a stop?
Ref: Sec. 6.8-6.9
Work and Energy 06
17
(A) 15.0 m
(B) 30.0 m
(C) 375 m
(D) 750 m
Work and Energy 06
KEΔWf Work/Energy Theorem
2mv
KE2
Kinetic EnergyWork/Friction
dfW kf
A force of 10 N is applied horizontally to a 2.0-kg mass on a
level surface. The coefficient of kinetic friction between the
mass and the surface is 0.20. If the mass is moved a distance
of 10 m, what is the change in its kinetic energy?
Ref: Sec. 6.8-6.9
Work and Energy 06
18
(A) 20 J
(B) 39 J
(C) 46 J
(D) 61 J
Work and Energy 06
netWKEΔ Work/Energy Theorem
FxW
WorkNμf kk
Friction
A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s.
What is the average power delivered by the engine?
(1 hp = 746 W)
Ref: Sec. 6.10
Work and Energy 06
19
(A) 60 hp
(B) 70 hp
(C) 80 hp
(D) 90 hp
Work and Energy 06
KEΔWnet Work/Energy Theorem
tW
P
Power Kinetic Energy
2mv
KE2
A 500-kg elevator is pulled upward with a constant
force of 5500 N for a distance of 50.0 m. What is the
net work done on the elevator?
01
Work and Energy 06
mg
F
xmgFWnet
m 05m/s 9.8 kg 500N 5500W 2net
J 000,03Wnet
xFW netnet Work
Matthew pulls his little sister Sarah in a sled on an icy
surface (assume no friction), with a force of 60.0 N at an
angle of 37.0° upward from the horizontal. If he pulls her
a distance of 12.0 m, what is the work done by Matthew?
02
Work and Energy 06
x
F
m 12 37 cos N 60W
J 755W
x θcosFW Work
A force moves an object in the
direction of the force. The graph
shows the force versus the object's
position. Find the work done when
the object moves from 0 to 6.0 m.
03
Work and Energy 06
20 J 40 J 20 J
80 JWork is equal to the area under under the curve
Work is the product of force times distance.
Work
A horizontal force of 200 N is applied to move a 55-kg
cart (initially at rest) across a 10 m level surface. What
is the final kinetic energy of the cart?
04
Work and Energy 06
KEFx
m 10N 200KE J 000,2
FxW
Work
KEΔWnet Work/Energy Theorem
If it takes 50 m to stop a car initially moving at 25 m/s,
what distance is required to stop a car moving at 50 m/s
under the same condition?
05
Work and Energy 06
0
2mv
Fx2
constantx
vmF2 2
2
22
1
21
x
v
x
v
21
22
12 v
vxx
2
2 m/s 25m/s 50
m50x
m 200x2
FxW
Work
2mv
KE2
Kinetic EnergyKEΔWnet
Work/Energy Theorem
A spring-driven dart gun propels a 10-g dart. It is cocked by
exerting a constant force of 20 N over a distance of 5.0 cm.
With what speed will the dart leave the gun, assuming the
spring has negligible mass?
06
Work and Energy 06
0
2mv
Fx2
mFx2
v
kg 0.010m 0.05 N 20 2 m/s .141
FxW
Work KEΔWnet
Work/Energy Theorem
2mv
KE2
Kinetic Energy
A 100-N force has a horizontal component of 80 N and a
vertical component of 60 N. The force is applied to a box
which rests on a level frictionless floor. The cart starts
from rest, and moves 2.0 m horizontally along the floor.
What is the cart's final kinetic energy?
07
Work and Energy 06
x
F
60
80
8060
θtan
8060
tanθ 1 o9.36
m 2.0 36.9 cos N 100W
m 2.0 36.9 cos N 100W
J 160W
x θcosFW Work
A 15.0-kg object is moved from a height of 7.00 m above a
floor to a height of 15.0 m above the floor. What is the
change in gravitational potential energy?
08
Work and Energy 06
m 7m 15 m/s 9.8 kg 15PEΔ 2g
J 1761PEΔ g
15 m
7 m
yΔmgPEΔ g Gravitational Potential Energy
A 400-N box is pushed up an inclined plane. The plane is 4.0 m
long and rises 2.0 m. If the plane is frictionless, how much work
was done by the push?
09
Work and Energy 06
yΔmgW
m 2.0 N 400W
J 800W
gPEΔW Gravitational Potential Energy
A spring is characterized by a spring constant of 60 N/m.
How much potential energy does it store, when stretched
by 1.0 cm?
10
Work and Energy 06
2
m 0.01 N/m 60PE
2
s
J 003.0PEs
2kx
PE2
s
Spring Potential Energy
A spring with a spring constant of 15 N/m is initially
compressed by 3.0 cm. How much work is required to
compress the spring an additional 4.0 cm?
11
Work and Energy 06
2kx
ΔPEΔ2
s
2
kx
2
kxPEΔ
21
22
s
22s m 0.03m 0.07
2 N/m 15
PEΔ
21
22 xx
2k
J 03.0
2kx
PE2
s
Spring Potential Energy
A skier, of mass 40 kg, pushes off the top of a hill with an
initial speed of 4.0 m/s. Neglecting friction, how fast will
she be moving after dropping 10 m in elevation?
12
Work and Energy 06
0PEΔKEΔ g Conservation of Energy
00mgy2
mv
2
mv 2i
2f
gy2vv 2if
m 10 m/s 9.8 2m/s 4.0v 22f m/s 14.6
A 1.0-kg ball falls to the floor. When it is 0.70 m above
the floor, its potential energy exactly equals its kinetic
energy. How fast is it moving?
13
Work and Energy 06
2mv
mgy2
gy2v
m 0.70 m/s 9.8 2v 2 m/s 3.7
yv
KEPEg Energy
mgyPEg
Potential Energy
2mv
KE2
Kinetic Energy
A roller coaster starts with a speed of 5.0 m/s at
a point 45 m above the bottom of a dip as shown
in the diagram. Neglect friction, what will be
the speed of the roller coaster at the top of the
next slope, which is 30 m above the bottom of
the dip?
14
Work and Energy 06
21212 yyg2vv
0mgymgy2
mv
2
mv12
21
22
y2
y1
m 30m 45 m/s 9.8 2m/s 5 22
m/s 9.17v2
0PEΔKEΔ g Cons. of Energy
mghPE
Potential Energy
2mv
KE2
Kinetic Energy
A pendulum of length 50 cm is pulled 30 cm away from the
vertical axis and released from rest. What will be its speed
at the bottom of its swing?
15
Work and Energy 06
0mgy002
mv2
gy2v
L
yx
v
H
HLy
22 xLH
22 m 3.0m 5.0H m 40.0
m 40.0m 50.0y m 10.0
m 0.10 9.8m/s 2v 2
m/s 1.4v
0PEΔKEΔ g Cons. of Energy mghPE
Potential Energy
2mv
KE2
Kinetic Energy
A 1500-kg car moving at 25 m/s hits an initially uncompressed
horizontal spring with spring constant of 2.0 × 106 N/m. What
is the maximum compression of the spring? (Neglect the mass
of the spring.)
16
Work and Energy 06
002
kx2
mv0
22
kmv
x2
N/m 10x 2.0
m/s 25 kg 15006
2
m 68.0x
0PEΔKEΔ g Cons. of Energy
mghPE
Potential Energy
2mv
KE2
Kinetic Energy
The kinetic friction force between a 60.0-kg object and a
horizontal surface is 50.0 N. If the initial speed of the object
is 25.0 m/s, what distance will it slide before coming to a stop?
17
Work and Energy 06
2mv
0df2
k
k
2
f2mv
d N 50 2
m/s 25 kg 60 2
m 375d
KEΔWf Work/Energy Theorem
2mv
KE2
Kinetic EnergyWork/Friction
dfW kf
A force of 10 N is applied horizontally to a 2.0-kg mass on a
level surface. The coefficient of kinetic friction between the
mass and the surface is 0.20. If the mass is moved a distance
of 10 m, what is the change in its kinetic energy?
18
Work and Energy 06
fF WWKEΔ
Ffk
x
xfFxKEΔ kmgμf kk
mgxμFxKEΔ k
10m m/s 9.8 kg 2 0.20m 10N 10KEΔ 2
J 8.06KEΔ
netWKEΔ Work/Energy Theorem
FxW
Work
Nμf kk Friction
A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s.
What is the average power delivered by the engine?
(1 hp = 746 W)
19
Work and Energy 06
tKE
P
t2mv
P2
s 7.0 2
m/s 25 kg 1500 2
hp 8.89P
KEΔWnet Work/Energy Theorem
tW
P
Power
Kinetic Energy
2mv
KE2