Download Document

Topic 8: Work - Power - Springs - Energy
Work
● Work is done by individual Forces acting over a distance, it has UNITS of J, Joules
● Choose + or – for the sign of the work when F and d are same or opposite direction
● Force used must be parallel to the distance traveled, or use parallel component
(ex2: gravity does NO work on a box moved horizontally as none of the force is parallel)
● Power is the rate of work and is measured in Watts (joules per second)
Springs
● Springs that have no force acting are at the equilibrium position relaxed length.
● The force induced in the spring can be found by applying Hooke’s Law  Fsp = k Δx
● In a graph is F vs Δx the slope is the spring constant.
Energy
● Three key forms of energy  Potential (PE) , Kinetic (KE) and (Internal Energy) (Q)
● PE = Stored Energy - when you have height or springs, KE = Energy of Motion - when moving ,
Q = Heat Energy due to losses from friction
● Mechanical Energy is defined as Potential + Kinetic combined  ME = KE + PE (both types PE)
● The total energy of a system (ET) is the mechanical energy + the internal energy (heat)
ET = ME + Q
(ME = PE + KE)
ET = PE + KE + Q
Non-Conservative Forces: Friction, (fk), Applied forces (F)
These forces change the total ME (PE + KE). Usually this energy is lost to heat energy (Q)
Conservative Forces: Gravity (FG) , Spring Forces (Fsp)
These forces keep the total ME constant with no losses and simply transfer PE <-> KE
Mechanical Energy Conservation – Work Energy Theorem.
●When only Conservative forces act on an object (Fg, Fsp, Fn) the Mechanical Energy of that object must be
conserved: ME = ME at any two points in the problem. Changes in KE or PE must simply transfer from one to
another. The work done in the problems is equal the amount of energy transfer (ex: work done in compressing
spring equals final spring energy after compressed PEsp = 1/2 kx2)
● Using energy conservation - Pick a location where you have no unknowns (height, mass, velocity, spring
constants). Pick a second location where you are looking for something. Equate the ME at each spot and fill the
energy types, PE, PEsp and KE. Remember the three questions to determine which you have:
PE - is there height, KE - is it moving, PEsp = is there a stretched/compressed spring.
ME = ME
PE1 + PEsp(1) + KE1 = PE2 + PEsp(2) + KE2
● When Non-Conservative forces acts the Mechanical Energy will not be conserved. These changes are created
by transfers of heat/internal energy (Q) in the system. In the problem we add non conservative work into the
equation: Wnc is the work done (Fd) by the non conservative forces (usually friction)
PE1 + PEsp(1) + KE1 ±Wnc = PE2 + PEsp(2) + KE2
● This equation rearranged also show that W the work done by friction is simply the difference or missing amount
of mechanical energy between two points in a problem
Topic 9: Impulse, Momentum and Collisions
● Impulse (unit Ns) – Momentum (unit kg m/s)
#1 most important thing  opposite directions = make one of the velocities “-“
J = Ft
Jnet
= Δp
Ft
= mvf - mvi
● In collisions only, always start with ∑pi(tot) = ∑pf(tot) Fill in a “mv” term for each item that has momentum
● Elastic (KE & p conserved), Inelastic and Perfect Inelastic (only p conserved)
Physics Regents Review HW #3 – Work, Power, Energy, Springs, Momentum
Wells
Name: ___________________
THIS HW WILL COUNT AS A DOUBLE HW GRADE. THAT MEANS YOU GET TWO ZEROS IF YOU DON’T DO IT.
ANSWER SHEET. Place your answers to the attached assignment on this first sheet. Standard class homework
policies apply.
MULTIPLE
PROBLEMS
CHOICE
1.)
1.)
(a)
2.)
(b)
3.)
(c)
4.)
5.)
2.)
(a)
6.)
7.)
(b)
8.)
9.)
3.) put explanations on sheet, but show A,B,C answer here and on sheet
10)
(a)
11)
(b)
(c)
12)
13)
4.)
(a)
(c)
(b)
(d)
14)
15)
16)
5.)
(a)
17)
(b)
18)
(c)
19)
20)
6.)
(a)
21)
22)
(b)
23)
24)
25)
26)
27)
28)
7.)
(a)
(b)
(c)
MULTIPLE CHOICE
1.) Which graph best represents the kinetic energy KE of an object as a function of its speed v?
2.) The diagram below shows a 5.0-kilogram mass sliding 9.0 meters down an incline from a height of 2.0 meters
in 3.0 seconds. The object gains 90 joules of kinetic energy while sliding. How much work is done against friction
as the mass slides the 9.0 meters?
(1) 0 J
(2) 8 J
(3) 45 J
(4) 90. J
3.) A 500-newton girl lifts a 10-newton box vertically upward a distance of 0.50 meter. The work done on the box
is
(1) 5.0 J
(2) 50 J
(3) 250 J
(4) 2500 J
4.) A motor having a power rating of 500 watts is used to lift an object weighing 100 newtons. How much time
does the motor take to lift the object a vertical distance of 10.0 meters?
(1) 0.500 s (3) 5.00 s
(2) 2.00 s (4) 50.0 s
5.) A 10-newton force is required to hold a stretched spring 0.20 meter from its rest position. What is the
potential energy stored in the stretched spring?
(1) 1.0 J (3) 5.0 J
(2) 2.0 J (4) 50. J
6.) A 0.50-kilogram ball is thrown vertically upward with an initial kinetic energy of 25 joules.
Approximately how high will the ball rise? [Neglect air resistance.]
(1) 2.6 m (3) 13 m
(2) 5.1 m (4) 25 m
7.) The diagram below shows a 0.1-kilogram apple attached to a branch of a tree 2 meters above a
spring on the ground below. The apple falls and hits the spring, compressing it 0.1 meter from its rest position. If
all of the gravitational potential energy of the apple on the tree is transferred to the spring when it is
compressed, what is the spring constant of this spring?
(1) 10 N/m (3) 100 N/m
(2) 40 N/m (4) 400 N/m
8.) Which graph best represents the elastic potential energy stored in a spring (PEs) as a function of its
elongation, x?
9.) What is the maximum height to which a 1200-watt motor could lift an object weighing 200 newtons in 4.0
seconds?
(1) 0.67 m (3) 6.0 m
(2) 1.5 m (4) 24 m
10.) The diagram below shows a moving, 5.00-kilogram cart at the foot of a hill 10.0 meters high. For
the cart to reach the top of the hill, what is the minimum kinetic energy of the cart in the position
shown? [Neglect energy loss due to friction.]
(1) 4.91 J (3) 250. J
(2) 50.0 J (4) 491 J
11.) The graph below shows elongation as a function of the applied force for two springs, A and B.
Compared to the spring constant for spring A, the spring constant for spring B is
(1) smaller
(2) larger
(3) the same
12.) One watt is equivalent to one
(1) N•m (3) J•s
(2) N/m (4) J/s
13.) The spring of a toy car is wound by pushing the car backward with an average force of 15 newtons through
a distance of 0.50 meter. How much elastic potential energy is stored in the
car’s spring during this process?
(1) 1.9 J (3) 30. J
(2) 7.5 J (4) 56 J
14.) A 1.0-kilogram rubber ball traveling east at 4.0 meters per second hits a wall and bounces
back toward the west at 2.0 meters per second. Compared to the kinetic energy of the ball
before it hits the wall, the kinetic energy of the ball after it bounces off the wall is
(1) one-fourth as great (3) the same
(2) one-half as great (4) four times as great
15.) The graph below represents the kinetic energy, gravitational potential energy, and total mechanical energy
of a moving block.
Which best describes the motion of the block?
(1) accelerating on a flat horizontal surface (3) falling freely
(2) sliding up a frictionless incline (4) being lifted at constant velocity
16.) When a force moves an object over a rough, horizontal surface at a constant velocity, the work done against
friction produces an increase in the object’s
(1) weight (3) potential energy
(2) momentum (4) internal energy
17.) As shown in the diagram below, a student exerts an average force of 600. newtons on a rope to lift a 50.0kilogram crate a vertical distance of 3.00 meters.
Compared to the work done by the student, the gravitational potential energy gained by the crate is
(1) exactly the same (3) 330 J more
(2) 330 J less (4) 150 J more
18.) A vertical spring 0.100 meter long is elongated to a length of 0.119 meter when a 1.00-kilogram mass is
attached to the bottom of the spring. The spring constant of this spring is
(1) 9.8 N/m (3) 98 N/m
(2) 82 N/m (4) 520 N/m
19.) A 55.0-kilogram diver falls freely from a diving platform that is 3.00 meters above the surface of the water in
a pool. When she is 1.00 meter above the water, what are her gravitational potential energy and kinetic energy
with respect to the water’s surface?
(1) PE = 1620 J and KE = 0 J
(2) PE = 1080 J and KE = 540 J
(3) PE = 810 J and KE = 810 J
(4) PE = 540 J and KE = 1080 J
20.) The diagram below shows two carts initially at rest on a horizontal frictionless surface being pushed apart
when a compressed spring attached to one of the carts is released. If the 1.0-kilogram cart moves to the left with
a speed of 6.0 meters per second, then the 2.0-kilogram cart moves to the right with a speed of
(1) 6.0 m/s
(2) 2.0 m/s
(3) 3.0 m/s
(4) 12 m/s
21.) A mother pushes her 120-newton child, who is sitting on a swing. If the mother exerts a 10-newton force on
the child for 0.50 second, what is the magnitude of the impulse imparted to the child by the mother?
(1) 5.0 N•s
(2) 20. N/s
(3) 60. N•s
(4) 240 N/s
22.) A 1,200-kilogram car traveling at 10. meters per second hits a tree and is brought to rest in
0.10 second. What is the magnitude of the average force acting on the car to bring it to rest?
4
(1) 1.2 x 102 N (3) 1.2 x
N
3
5
N (4) 1.2 x
N
23.) Which is an acceptable unit for impulse?
(1) N•m (3)J•s
(2) J/s (4) kg•m/s
24.) A 50.-kilogram student threw a 0.40-kilogram ball with a speed of 20. meters per second. What was the
magnitude of the impulse that the student exerted on the ball?
(1) 8.0 Ns (3) 4.0 x102 Ns
3
Ns
25.) The diagram below shows a 4.0-kilogram cart moving to the right and a 6.0-kilogram cart moving to the left
on a horizontal frictionless surface.
When the two carts collide they lock together. The magnitude of the total momentum of the two-cart system
after the collision is
(1) 0.0 kg•m/s (3) 15 kg•m/s
(2) 6.0 kg•m/s (4) 30. kg•m/s
26.) A 2.0-kilogram laboratory cart is sliding across a horizontal frictionless surface at a constant velocity
of 4.0 meters per second east. What will be the cart’s velocity after a 6.0-newton westward force acts on it for
2.0 seconds?
(1) 2.0 m/s east (3) 10. m/s east
(2) 2.0 m/s west (4) 10. m/s west
27.) At the circus, a 100.-kilogram clown is fired at
15 meters per second from a 500.-kilogram
cannon. What is the recoil speed of the cannon?
(1) 75 m/s (3) 3.0 m/s
(2) 15 m/s (4) 5.0 m/s
28.) In the diagram below, a block of mass M initially at rest on a frictionless horizontal surface is struck by a
bullet of mass m moving with horizontal velocity v.
What is the velocity of the bullet-block system after the bullet embeds itself in the
block?
PROBLEMS
1.) A 250.-kilogram car is initially at rest at point A on a roller coaster track. The car carries a 75-kilogram
passenger and is 20. meters above the ground at point A. [Neglect friction.]
(a) Calculate the total gravitational potential energy, relative to the ground, of the car and the passenger at
point A. [Show all work, including the equation and substitution with units.] [2]
(b) Calculate the speed of the car and passenger at point B. [Show all work, including the equation and
substitution with units.] [2]
(c) Compare the total mechanical energy of the car and passenger at points A, B, and C. [1]
2.) The graph below represents the relationship between the force applied to each of two springs, A and B, and
their elongations.
(a) What physical quantity is represented by the slope of each line? [1]
(b) A 1.0-kilogram mass is suspended from each spring. If each mass is
at rest, how does the potential energy stored in spring A compare to
the potential energy stored in spring B? [1]
3.) A mass, M, is hung from a spring and reaches equilibrium at position B.
The mass is then raised to position A and released. The mass oscillates
between positions A and C. [Neglect friction.]
(a) At which position, A, B, or C, is mass M located when the kinetic energy
of the system is at a maximum? Explain your choice. [1]
(b) At which position, A, B, or C, is mass M located when the gravitational
potential energy of the system is at a maximum? Explain your choice. [1]
(c) At which position, A, B, or C, is mass M located when the elastic potential energy of the system is
at a maximum? Explain your choice. [1]
4.) The driver of a car made an emergency stop on a straight horizontal road. The wheels locked and the car
skidded to a stop. The marks made by the rubber tires on the dry asphalt are 16 meters long, and the car’s
mass is 1200 kilograms.
(a) Determine the weight of the car. [1]
(b) Calculate the magnitude of the frictional force the road applied to the car in stopping it. [Show
all work, including the equation and substitution with units.] [2]
(c) Calculate the work done by the frictional force in stopping the car. [Show all work, including the
equation and substitution with units.] [2]
(d) Using work energy theorem considerations, calculate the speed of the car before the brakes were applied.
[Show all work, including the equation and substitution with units.] [2]
5.) A 50-kilogram child running at 6.0 meters per second jumps onto a stationary 10.-kilogram sled. The sled is
on a level frictionless surface.
(a) Calculate the speed of the sled with the child after she jumps onto the sled. [Show all work, including the
equation and substitution with units.] [2]
(b) Calculate the kinetic energy of the sled with the child after she jumps onto the sled. [Show all
work, including the equation and substitution with units.] [2]
(c) After a short time, the moving sled with the child aboard reaches a rough level surface that exerts a
constant frictional force of 54 newtons on the sled. How much work must be done by friction to
bring the sled with the child to a stop? [1]
6.) An 8.00-kilogram ball is fired horizontally from a 1 x 103 -kilogram cannon initially at rest. After having been
fired, the momentum of the ball is 2.40 x 103 kilogram•meters per second east. [Neglect friction.]
(a) Calculate the magnitude of the cannon’s velocity after the ball is fired. [Show all work, including
the equation and substitution with units.] [2]
(b) Identify the direction of the cannon’s velocity after the ball is fired. [1]
7.) A 1000.-kilogram empty cart moving with a speed of 6.0 meters per second is about to collide with a
stationary loaded cart having a total mass of 5000. kilograms, as shown. After the collision, the carts lock and
move together. [Assume friction is negligible.]
(a) Calculate the speed of the combined carts after
the collision. [Show all work, including the equation
and substitution with units.] [2]
(b) Calculate the kinetic energy of the combined carts after the collision. [Show all work, including
the equation and substitution with units.] [2]
(c) How does the kinetic energy of the combined carts after the collision compare to the kinetic
energy of the carts before the collision? [1]