Download Kinetic Energy (Ek) Problems 1. A helicopter has a top speed of 111

Kinetic Energy (Ek) Problems
1. A helicopter has a top speed of 111 m/s. If its
kinetic energy at this speed is 21,000,000 J,
what is the helicopter’s mass?
4. The male polar bear is the largest land predator.
Its height when standing upright is over 3 m and
its mass can be as much as 680 kg. Even so, the
polar bear can reach speeds of up to 15.6 m/s.
Determine the kinetic energy of a running polar
bear.
2. In 1995, Karine Dubouchet of France reached a
record speed in downhill skiing. If her mass was
51.0 kg and she had a kinetic energy of 9960 J,
what was her speed?
5. The kinetic energy of a golf ball is measured to
be 1433 J. If the golf ball has a mass of 47.0 g,
what is the ball’s speed?
3. In 1987, the winner of the fastest auto race that
year had a speed of 88.3 m/s. Suppose the
kinetic energy of the winning car was 3,800,000
J, what was the mass of the car and its driver?
6. The leatherback turtle holds the record for the
fastest water speed of any reptile: 9.78 m/s.
Suppose the largest leatherback ever
discovered swims at top leatherback speed.
What is its mass if its kinetic energy is 60,800 J?
Gravitational Energy (Eg) Problems
7. In 1992, Ukrainian Sergei Bubka used a short
pole to jump to a height of 6.13 m. If the
maximum gravitational energy associated with
Bubka was 4800 J at the top of his jump, what
was his mass?
8. Situated 4080 m above sea level, La Paz, Bolivia,
is the highest capital in the world. If a car with a
mass of 905 kg is driven to La Paz from a
location that is 1860 m above sea level, what is
the increase in gravitational energy?
9.
What is the maximum gravitational energy of a
0.125 kg ball that is thrown to a maximum
height of 17.5 m?
10. A sandbag of mass 200 kg is hanging motionless
from a rope. If the gravitational energy stored
in it is 35,600 J, how high above the ground is
it?
11. A man of mass 63 kg climbs a set of stairs such
that his body is 13.5 m higher than it was
before. By how much has he increased his
gravitational energy?
12. A skydiver of mass 73 kg loses 12,543 J of
gravitational energy in 23 s. How much has he
fallen in this amount of time?
Elastic Energy (Eel) Problems
13. A produce scale at a supermarket uses a
stretched spring to indicate the weight of fruits
and vegetables. If five oranges with a total mass
of 0.76 kg are placed in the scale, the spring will
be stretched 2.3 cm. What is the force constant
of the spring if 0.175 J of elastic energy is
stored?
16. An arresting cable helps to slow jet planes as
they land on an aircraft carrier. This is
accomplished by two springs, each of which is
attached to one end of the cable. Suppose the
elastic potential energy stored in the springs
while a jet is landing is 57,000,000 J. If each
spring is stretched 102 m, what is the force
constant of each spring?
14. A pogo stick contains a spring with a force
constant of 15,000 N/m. Suppose the elastic
potential energy stored in the spring as the
pogo stick is pushed downward is 120 J. How far
is the spring compressed?
17. A 1750 kg weather satellite moves in a circular
orbit with a gravitational potential energy of
1.69 × 1010 J. At the satellite’s altitude above
Earth’s surface, the free-fall acceleration is only
6.44 m/s/s. How high above Earth’s surface is
the satellite?
15. An automobile to be transported by ship is
raised 7.0 m above the dock. If its gravitational
potential energy is 6.6 × 104 J, what is the
automobile’s mass?
18. The force constant of the spring in a child’s toy
car is 550 N/m. How much elastic potential
energy is stored in the spring if the spring is
compressed a distance of 1.2 cm?
Name
Date
Pd
Unit VII: Worksheet 1
Use pie charts to analyze the energy changes in each situation given.
• Designate your choice of system with a dotted line,
• Carefully label the pies to correspond with the positions of the objects given. (A, B, C, etc.)
• The pies should be accurately divided and labeled with the energy storage mechanisms involved.
1. A ball is held above the ground, and then is dropped so it falls straight down.
(Restrict your analysis to the ball moving in the air, BEFORE it hits the ground.)
2. A wind-up toy is wound up, then "walks" across a table and comes to a stop.
3. A baseball is thrown up in the air and then falls back down. Place velocity vectors beside each
image of the baseball in the drawing, and do a pie chart for each position.
4. A ball rolls to a stop on the floor.
©Modeling Workshop Project 2006
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Unit VII ws1 v3.0
5. A superball is dropped and bounces up and down. Do a pie chart for each position of the ball
shown.
Why does the ball not bounce as high each time? Where did the energy "go"?
6. An object rests on a coiled spring, and is then launched upwards.
7. A piece of clay is dropped to the floor.
8. A truck is driven at constant speed down the street.
©Modeling Workshop Project 2006
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Unit VII ws1 v3.0
Name
Date
Pd
Unit VII: Worksheet 3a
For each situation shown below:
1. Show your choice of system in the energy flow diagram, unless it is specified for you.
**Always include the earth in your system.
2. Decide if your system is frictionless or not, and state this.
3. Sketch an energy bar graph for the initial situation.
4. Then complete the analysis by showing energy transfers and the final energy bar graph.
1.
Initial
EK Eg Eel
Final
Energy Flow
Diagram
EK
Final
Eg Eel Eint
Initial
0
0
2.
Initial
EK Eg Eel
Energy Flow
Diagram
EK
Final
Eg Eel Eint
Final
Initial
0
0
3.
y
vo>0
yo=0
y>0
v=0
Initial
EK Eg Eel
Energy Flow
Diagram
EK
Final
Eg Eel Eint
0
0
0
©Modeling Workshop Project 2006
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Unit VII ws3a v3.0
4. A person pushes a car, with the parking brake on, up a hill.
v=0
y>0
y
Initial
EK Eg Eel
vo=0
yo=0
Energy Flow
Diagram
EK
Final
Eg Eel Eint
0
0
0
5. A load of bricks rests on a tightly coiled spring, then is launched into the air.
y
vo=0
yo=0
Initial
EK Eg Eel
v>0 Final
0
Energy Flow
Diagram
EK
Final
Eg Eel Eint
0
0
Initial
EK
Final
Eg Eel Eint
6. A crate is propelled up a hill by a tightly coiled spring.
y
vo=0
yo=0
0
Initial
EK Eg Eel
v>0
Energy Flow
Diagram
Final
Initial
©Modeling Workshop Project 2006
0
0
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Unit VII ws3a v3.0
7. A bungee jumper falls off the platform and reaches the limit of stretch of the cord.
y
Initial
EK Eg Eel
v=0
0
Initial
Final
Energy Flow
Diagram
EK
Final
Eg Eel Eint
EK
Final
Eg Eel Eint
0
0
8. An elevator, initially moving downward, is brought to rest on the ground floor.
y
system
boundary
Initial
EK Eg Eel
yo>0
vo>0
0
y=0
v=0
Energy Flow
Diagram
0
0
9. Create your own situation and construct corresponding energy bar graphs and system schema.
System = ______________________
Initial
EK Eg Eel
EK
Final
Eg Eel Eint
0
0
©Modeling Workshop Project 2006
Energy Flow
Diagram
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Unit VII ws3a v3.0
Name
Date
Pd
UNIT VII: WS 3b Quantitative Bar Graphs and Problems
For each situation shown below:
1. In the energy flow diagram show the system you choose to analyze. Assume the systems to be frictionless unless stated
otherwise.
2. Complete the energy bar graph QUANTITATIVELY (numerically accurate).
3. In the space below each diagram use conservation of energy equations to solve for the quantity called for in the question.
1. A moving cart hits a spring, traveling at 5.0 m/s at the time of contact. At the instant the cart is
motionless, by how much is the spring compressed?
Final
Energy Flow
Initial
Diagram
EK Eg Eel Eint
EK Eg Eel
0
0
height (m)
2. Determine final velocity of the cart, assuming that 10% of the energy is dissipated by friction.
v=0
Final
Energy Flow
Initial
Diagram
EK Eg Eel Eint
EK Eg Eel
5
m = 20 kg
v=?
0
0
0
3. A block is placed on a spring, compressing it 0.30m. What height does the block reach when
launched by the spring?
m = 500
v=0
k = 100 mN
x = 0.30 m
Initial
0
Fina
©Modeling Workshop Project 2006
Initial
EK Eg Eel
Energy Flow
Diagram
EK
Final
Eg Eel Eint
0
0
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Unit VII ws3b v3.0
4. The bullet strikes a block of wood which exerts, on average, a force of 50,000N opposing the motion
of the bullet. How far does the bullet penetrate?
Final
Energy Flow
Initial
Diagram
EK Eg Eel Eint
EK Eg Eel
Initial
Fina
0
0
5. A 200. kg box is pulled at constant speed by the little engine pictured below. The box moves a
distance of 2.5 m across a horizontal surface.
a) Draw a force diagram of all relevant forces acting on the box.
b) Construct a qualitative energy bar graph/flow diagram for this situation. Be sure to specify your
system.
c) How much energy is transferred by the engine?
d) What type of motion would occur if the engine pulled with a force of 500 N?
Modify your force diagram and apply Newton's 2nd Law.
6. How far could the box in problem 5 be pulled at constant velocity with the expenditure of 8,000 J of
energy?
©Modeling Workshop Project 2006
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Unit VII ws3b v3.0
7. A person pulls a 50. kg box pictured below with a force of 100. N. The coefficient of kinetic friction
is 0.15.
a. Sketch a force diagram for the box.
b. How much of the force acts in the direction of motion? How much energy is transferred (via
working) by the person who pulls the box a distance of 10. m?
c. Is the box moving at constant speed? Explain how you know. What does this tell you about the
kinetic energy Ek of the system?
d. How much energy is stored as internal energy due to friction in the pulling process?
What eventually happens to this energy?
e. Show that energy is conserved in the system, accounting for all the energy stored and transferred in
the process.
Final
Energy Flow
Initial
Diagram
EK Eg Eel Eint
EK Eg Eel
0
0
©Modeling Workshop Project 2006
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Unit VII ws3b v3.0
Conservation of Energy Problems
1. A 2.4 kg bowling ball is dropped from a height
of 12.2 m. Eventually, it strikes the ground.
Assuming there is no friction, how fast is it
moving the moment it touches the ground?
2. A 0.75 kg book is thrown into the air with a
velocity of 8.25 m/s. Assuming there is zero air
resistance and that it was thrown from ground
level, to what maximum height does it rise?
3. A 2.4 kg bowling ball is rolled horizontally with a
velocity of 3.0 m/s and eventually runs into a
horizontal spring that stretches 0.35 m while
bring the ball to rest. Assuming zero friction,
what is the spring constant of the spring?
4. A spring with a spring constant of 735 N/m is
set vertically into a hole in the ground and
compressed so that a baseball of mass 0.15 kg
can be set on the spring and be level with the
ground. If releasing the spring launches the ball
4.5 m into the air, how much was it
compressed? No air resistance.
5. How fast is the baseball in question #4 moving
the very instant it leaves the spring? (Hint: the
spring raises it a little above the ground before
it stops touching the baseball). No friction.
6. A diver with a mass of 76 kg dives and strikes
the water with a velocity of 14.1 m/s. What is
the diver’s initial height? Assume no air
resistance.
7. How fast is the diver in problem #6 moving
when he is 5.0 m above the water (halfway
down)? Assume no air resistance.
8. A man pushes a stationary car 5.5 m. The mass
of the car is 1200 kg. At the end of this
distance, the car has a speed of 1.75 m/s. With
what force does the man push? (Hint: make the
car the system and assume zero friction).
9.
A bow and arrow are held 1.5 m above the
ground. If the mass of the arrow is 0.100 kg and
it is pulled back 55 cm how high does it rise?
(k=950 N/m and there is zero friction).
10. How much force does the water apply on the
diver in problem #7 if the diver comes to a stop
underwater in 1.35 m?
Momentum Problems
1. An 8-kilogram bowling ball is rolling in a straight
line toward you. If its momentum is 16 kg·m/s,
how fast is it traveling?
6. A 0.14-kilogram baseball is thrown in a straight
line at a velocity of 30 m/s. What is the
momentum of the baseball?
2. A beach ball is rolling in a straight line toward
you at a speed of 0.5 m/s. Its momentum is 0.25
kg·m/s. What is the mass of the beach ball?
7. Another pitcher throws the same baseball in a
straight line. Its momentum is 2.1 kg·m/s. What
is the velocity of the ball?
3. A 4,000-kilogram truck travels in a straight line
at 10.0 m/s. What is its momentum?
8. A 1-kilogram turtle crawls in a straight line at a
speed of 0.01 m/s. What is the turtle’s
momentum?
4. A 1,400-kilogram car is also traveling in a
straight line. Its momentum is equal to that of
the truck in the previous question. What is the
velocity of the car?
5. The momentum of a car traveling in a straight
line at 20 m/s is 24,500 kg·m/s. What is the
car’s mass?
9.
Which would take more force to stop in 10
seconds: an 8.0-kilogram ball rolling in a straight
line at a speed of 0.2 m/s or a 4.0-kilogram ball
rolling along the same path at a speed of 1.0
m/s?
10. Which would take more force to stop in 10
seconds: a 2.0-kilogram ball rolling in a straight
line at a speed of 2.5 m/s or a 1.0-kilogram ball
rolling along the same path at a speed of 5.0
m/s?
Impulse Problems
1. A net force of 100 N is applied to a 20-kilogram
cart that is already moving at 3 m/s. The final
speed of the cart was 8 m/s. For how long was
the force applied?
4. A 60-kg high jumper lands on a mat after her
jump. The mat brings her to a stop after 1 s. She
was traveling at 5.0 m/s when she landed on
the mat. Note: The speed of the jumper at the
top of her jump, before she started to fall
toward the mat, was 0 m/s.
a. What is the change in momentum for the
jumper?
2. In A 3-kilogram ball is accelerated from rest to a
speed of 10 m/s.
a. What is the ball’s change in momentum?
b. What is the force felt by the jumper upon
impact with the mat?
b. What is the impulse?
c. If a constant force of 40 N is applied to
change the momentum in this situation, for
how long does the force act?
5. A 0.5-kg soccer ball is kicked with a force of 50
N for 0.2 seconds. The ball was at rest before
the kick. What is the speed of the soccer ball
after the kick?
3. A 2,000-kilogram car uses a braking force of
12,000 N to stop in 5 s.
a. What impulse acts on the car?
b. What is the change in momentum of the car?
c. What is the initial speed of the car?
6. A baseball player hits a 0.155-kg fastball
traveling at 44.0 m/s into center field at a speed
of 50.0 m/s. If the impact lasts for 0.00450 s,
with what force does he hit the baseball?
7. Tom Sawyer launches his 180-kg raft on the
Mississippi River by pushing on it with a force of
75 N. How long must Tom push on the raft to
accelerate it to a speed of 2.0 m/s?
8. In terms of impulse, why is the ride much more
comfortable when an airplane is flying at
constant speed versus when it is taking off or
landing?
9.
If identical bullets are shot from a pistol and a
rifle, a bullet shot from the rifle will travel at a
higher speed than a bullet from the pistol.
Why? (Hints: Assume shooting force is the same
in each case. The barrel of the rifle is longer
than the barrel of the pistol.)
10. Show that the relationship between impulse
and the change in momentum is another way of
stating Newton's second law of motion.
11. Boxers attempt to move with an opponent’s
punch when it is thrown. In other words, a
boxer moves in the same direction as their
opponent's punch. This movement may prevent
a knockout blow being delivered by their
opponent. Explain how.
12. Mats in a gym, airbags, and padding in sports
uniforms are used to protect people from being
injured. Explain why these soft objects used
instead of rigid objects using your
understanding of impulse and change of
momentum.
Conservation of Momentum Problems
1. A 63.0 kg astronaut is on a spacewalk when the tether line to the shuttle breaks. The astronaut is able to throw a
spare 10.0 kg oxygen tank in a direction away from the shuttle with a speed of 12.0 m/s, propelling the
astronaut back to the shuttle. Assuming that the astronaut starts from rest with respect to the shuttle, find the
astronaut’s final speed with respect to the shuttle after the tank is thrown.
2. An 85.0 kg fisherman jumps from a dock into a 135.0 kg rowboat at rest on the west side of the dock. If the
velocity of the fisherman is 4.30 m/s to the west as he leaves the dock, what is the final velocity of the fisherman
and the boat?
3. A 38.0 kg boy on a 2.0 kg skateboard initially at rest tosses an 8.0 kg jug of water in the forward direction. If the
jug has a speed of 3.0 m/s relative to the ground how fast and in what direction do the boy and skateboard
move?
4. A student stumbles backward off a dock and lands in a small boat. The student isn’t hurt, but the boat drifts
away from the dock with a velocity of 0.85 m/s to the west. If the boat and student each have a mass of 68 kg,
what is the student’s initial horizontal velocity?
5. A child jumps from a moving sled with a speed of 2.2 m/s and in the direction opposite the sled’s motion. The
sled continues to move in the forward direction, but with a new speed of 5.5 m/s. If the child has a mass of 38 kg
and the sled has a mass 68 kg, what is the initial velocity of the sled?
6. A 50.0 g shell fired from a 3.00 kg rifle has a speed of 400.0 m/s. With what speed does the rifle recoil in the
opposite direction?
7. Momentum conservation often assumes that the mass of an object remains constant throughout a process or
event. However, a change in momentum can also occur when mass changes. Consider an automobile with a full
tank of gasoline traveling at a velocity of 24.44 m/s to the east. The mass of the car when the fuel tank is full is
1292 kg. By the time the car has traveled this distance, its mass is 1255 kg. What is the car’s velocity at the end
of the journey?
8. An ice skater at rest catches a bag of sand moving to the north with a speed of 5.4 m/s. This causes both the
skater and the bag to move to the north at a speed of 1.5 m/s. If the skater’s mass is 63 kg, what is the mass of
the bag of sand?
9. A 1500 kg car traveling at 15.0 m/s to the south collides with a 4500 kg truck that is initially at rest at a stoplight.
The car and truck stick together and move together after the collision. What is the final velocity of the twovehicle mass?
10. A 15,000 kg railroad car moving at 7.00 m/s to the north collides with and sticks to another railroad car of the
same mass that is moving in the same direction at 1.50 m/s. What is the velocity of the joined cars after the
collision?
Mixed Problems: Set 1
1. A car traveling through the mountains passes through three semi-circular curves in the road. Curve A has a
radius of 14 m, Curve B has a radius of 25 m and Curve C has a radius of 8 m. Answer (a) in which curve does
the car change direction more quickly, (b) in which curve does the car feel the most centripetal force, and (c)
what is the source of this centripetal force?
2. Object A is placed 3 m away from Object B and the gravitational force between them is measured to be 40,500
N. Then object B is moved to a location such that the gravitational force between the objects is 4,500 N. (a)How
far from object A is object B? (b) What principle do you have to know to predict this answer?
3. A 2.5 kg flowerpot falls from a balcony 12.5 m above the ground and hits a passing pedestrian in the head while
it is moving at 14.66 m/s. (a)How tall was the passing pedestrian? (b) How fast would it have been moving if it
had hit the ground instead? You must show all work including LOL charts.
4. A stalled motorist pushes his 1400 kg car with a force of 815 N for 65 m until it is on the shoulder of the
highway. (a)How much working was done on the car? (b) How fast was the car moving at the end?
5. A stationary cue ball of mass 0.155 kg is struck by a cue stick giving the ball a velocity of 3.04 m/s. (a)What was
the impulse provided by the cue stick? (b)If the force applied was 2.14 N how long was the cue stick in contact?
6. A 4.5 kg bowling moving to the right at 1.2 m/s strikes a 3.25 kg bowling ball moving to the left at 1.92 m/s.
After the collision, the 4.5 kg ball moves to the left with a velocity of 1.4 m/s. (a) What is the velocity of the 3.25
kg ball? (b) The 4.5 kg ball is quickly slowed to a stop in 0.5 s by a man’s shoe. How much force did the show
apply?
7. A 2400 kg truck moving at 14.5m/s runs head on into a 1150 kg car moving in the opposite direction at 16.5 m/s.
The vehicles stick together. (a)What is the velocity of the combined vehicles after the collision? (b) The truck’s
bumper was not designed to crumple, but the car’s was. Who felt the most force? Prove it.
8. A steak is sealed and placed into a freezer. (a) Describe what happens to the heat energy inside of it and its
temperature. A week later it is thawed at room temperature. (b) Describe what happens to the heat energy
inside of it and its temperature. Use only physics appropriate language.
9. A heat engine uses 1350 J of heat and does 675 J of working with it. (a) How much heat is expelled from the
heat engine? (b) How much input heat is needed if the same engine did 833 J of working while expelling 450 J of
waste heat?
10. (a) What is entropy? (b) What does the 2nd Law of Thermodynamics state? (c) Give examples of situations with
high/low entropy. (d) A messy room is tidied up. Explain how the 2 nd Law remains true.