Download Elastic potential energy

CH. 3 Energy and Conservation Laws
3.1 Conservation Laws:
The total mass in an isolated system is constant
3.2 Linear momentum: The mass of an object times
its velocity, P = mv
무거운 물체가 같은 속도로 움직이는
가벼운 물체보다 운동량이 더 크다
자전거와 사람의 질량: 80kg
자동차의 질량: 1,200kg
속력: 10m/s
 자전거의 운동량:
p  mv  80kg 10m / s  800kgm / s
 자동차의 운동량:
p  mv  1,200kg 10m / s  12,000kgm / s
Newton’s second Law of Motion
운동량의변화
force 
시간의 변화
(mv)
F
t
 If the mass of the object stays constant,
(mv)
v
F
m
 ma
t
t
 (mv)  Ft : impulse
The tennis racquet exerts a large force on the
tennis ball for a short time.
Ex 3.1 m = 0.06kg, v = 40m/s
 ( mv)  mv  0
 0.06kg  40m / s
 2.4kg  m / s
t  0.005s
(mv) 2.4kg  m / s
F

 480 N
t
0.005s
Law of Conservation of Linear Momentum : The total
linear momentum of an isolated system is constant.
The total linear momentum of the objects in the system before
the collision is the same as the total linear momentum after the
collision.
The most important use of the linear momentum conservation
law is in the analysis of collisions.
당구공, 자동차, 스케이터
Ex 3.2
m1  1,000kg, m2  1,500kg m v  1,000kg  v
1 1
1
v1  ?, v2  0
충돌후 v  4m/s
(m1  m2 )v  2,500kg  4m / s
2,500kg  4m / s
 v1 
 10m / s
1000kg
A bullet becomes embedded in a block of wood. If the speed
of the block and the masses of the block and the bullet are
measured, the initial speed of the bullet can be computed
using the conservation of linear momentum.
mv1  (m  M )v2
m
v2 
v1
mM
The mass of the cart on the right cart 2, is three times the
mass of the cart on the left, cart 1. After the spring is released,
the speed of the lighter cart is three times the speed of the
more massive cart.
(mv)전  (mv)후
(mv)전  0
(mv)후  0  m1v1  m2 v2
m1  v1  m2  v2
m2
v1  
 v2
m1
v1
m2

v2
m1
The ratio of the speeds of the two carts is the inverse of the
ratio of their masses.
Conservation of Liner Momentum: Newton’s third law of motion
The skater and the snowball
have the same amount of
momentum but in opposite
direction.
3.3 Work: The Key to Energy
FL  d L  FR  d R
들어올리는 힘 x 높이 = 굴리는 힘 x 경사로의 길이
Frolling  d rolling  Flifting  d lifting

Work: The force that acts times the distance moved in
the direction of the force: 1J 1N  m
work = Fd
Ex 3.3 Because of friction, a constant force of 100 N is
needed to slide a box across a room. If the box moves 3 m,
how much work is done?
Work = Fd
= 100N  3m
= 300Nm
= 300J
Ex 3.4 The barrel has a mass of 30kg and the height of the
dock is 1.2m. How much work would you do when lifting the
barrel?
F = W = mg
= 30kg x 9.8m/s2
= 294N
work = Fd = Wd
= 294N x 1.2m
= 353J
Ex 2.2
v 27m / s  0m / s
a

 2.7m / s 2
t
10s
F  ma  1,000kg  2.7m / s 2  2,700 N
Ex 3.5 How much work is done?
10초 동안 2.7m/s2로 가속되었으므로,
1 2 1
d  at  (2.7m / s)(10s ) 2  135m
2
2
work = Fd
= 2,700N x 135m
= 364,500J
The force is always toward the center of the circle and
perpendicular to the object’s velocity at each instant. Therefore,
the force does not do work on the object.
Work is also done when a force causes something to slow
down. When you catch a ball, your hand exerts a force on the
ball. As the ball slows down, it pushes your hand back with
equal and opposite force. In this case, the ball does work on
your hand.
The work that the force of gravity does on an object as it falls
is equal to the work that was done to lift the object the same
distance.
3.4 Energy: The measure of a system’s capacity to do work.
Kinetic Energy: Energy due to motion.
1 2
KE  mv
2
Ex. 3.6 1,000kg의 차가 정지상태
에 27m/s로 가속된다
The car’s kinetic energy when it
is traveling 27m/s is
1
KE 
2
mv 2
1
 1,000kg  (27m / s ) 2
2
 500kg 729m 2 / s 2
 364,500 J
A spinning dancer(far left) has kinetic energy, even though she
stays in one place.
This transparent toy car (left) and shaver (right) use rotational
kinetic energy stored in spinning flywheels.
Potential Energy: Energy due to an object’s position
or orientation.
PE= work done = weight x height = Wd=mgd
Ex 3.7 3kg brick is lifted to a height of 0.5m above a table. Its
positional energy relative to the table is
PE = mgd
=
3kg  9.8m / s 2  0.5m  14.7 J
Its potential energy to the floor is
PE=mgd= 3kg  9.8m / s 2 1.5m  44.1J
The potential energy of golf ball A is positive relative to the
ground. The potential energy of B is zero and that of c is
negative because it is below ground level. Balls A and b can
move horizontally while C is restricted to the hole.
Elastic potential energy
Olympic archer Joanne
Edens. While pulling the
bowstring back, she
does work bending the
bow. This gives the bow
elastic potential energy.
This mechanical bird
uses energy stored in
the rubber band inside.
Patricia is holding the
crank used to wind it
up.
3.5 The Conservation of Energy
Energy cannot be created or destroyed, only converted from
one form to another. Therefore, the total energy in an isolated
system is constant.
This wind generator converts kinetic energy of the wind into
electrical energy plus some internal energy because of friction.
A basketball rolls off the rim and falls to the floor. Initially, it
has potential energy only. As it falls, its potential energy
decreases as its kinetic energy increases. Just before it hits
the floor, it has kinetic energy only. At each point as it falls, its
total energy, kinetic plus potential, is the same, 18 joules.
E  KE  PE  일정
공이 떨어지기 시작할 때( KE  0)
E  KE  PE  PE
PE  mgd
공이 마루에 닿는 순간( PE  0)
E  KE  PE  KE
KE 
1 2
mv
2
The potential energy the object had when it was released
equals the kinetic energy it has just before impact.
1 2
mv  mgd
2
2
v  2 gd
v  2 gd
Ex 3.8 The height of the falls is about 53m.Estmiate their
speed when they hit the water at the bottom of the falls.
v  2 gd
 2  9.8m / s 2  53m
 1039m 2 / s 2
 32.2m / s
As a roller coaster travels down a hill, its potential energy is
converted into kinetic energy. If there is no friction, its kinetic
energy at the bottom equals its potential energy at the top. Its
speed at the bottom is the same as that of an object dropped
from the same height.
1 2
mv  mgd
2
v 2  2 gd
v  2 gd
The motion of a pendulum involves the continuous conversion
of gravitational potential energy in kinetic energy and back
again.
A golf ball at rest in the small valley has negative potential
energy. Hitting the golf ball gives it kinetic energy but it
oscillates inside the valley if its total energy is negative, (a)
and (b). If the golf ball is given enough kinetic energy to
make its total energy zero, it rolls out of the valley and
stops (c).
3.6 Collisions: An Energy Point of View
An Elastic Collision is one in which the total kinetic energy of
the colliding bodies after the collision equals the total kinetic
energy before the collision.
An Inelastic Collision is one in which the total kinetic energy of
the colliding bodies after collision is not equal to the kinetic
energy before. The total kinetic energy after can be greater
than, or less than, the total kinetic energy before.
Ex 3.9 Compare the amount of
kinetic energy in the system before
and after the collision.
1
KE전  1,000kg  (10m / s ) 2
2
 50,000 J
1
2
KE후   2,500kg  (4m / s )
2
 20,000 J
30,000J (60%) of the kinetic energy before the collision was
converted into other forms of energy.
A cart 2 has energy stored in its spring-loaded plunger. When
this cart is struck by cart 1, this potential energy is converted
into kinetic energy, which then shared by both carts. The total
kinetic energy after the collision is greater than the total
kinetic energy before the collision.
Elastic collisions involving the force of gravity (and no physical
contact) are used in the space exploration. Called the slingshot
effect or gravity assist, the technique involves having a
spacecraft overtake a planet and pass it on its side away from
the Earth.
Gravitational Slingshot Effect - YouTube.url
3.3 Power: The rate of doing work. The rate at which energy is
transferred or transformed. Work done divided by the time.
Energy transferred divided by the time. P[watt] =W[J]/t[s]
예) 지게차로 1ton의 벽돌을 1.2m의 높이에 싣는 경우
m  1ton  103 kg
d  1.2m
W  Fd
 103 kg  9.8m / s 2 1.2m
 11,760 J
t  10 s,
W 11,760 J
P

t
10 s
 1,176 J / s
 1,176W
A 60W light bulb uses electrical energy at the rate of 60 J
each second. A 1,600 W hair dryer uses 1,600 J of energy
each second.
1 hp=746W
Ex 3.10 We can determine the required power output of the
engine. The work, 364,500 J, is done in 10 s. Hence the
power is
P=일/시간 = 364,500J/10s
=36,450W=48.9hp
The human body has a maximum power output that varies
greatly from person to person. In the act of jumping, an
outstanding athlete can develop more than 8,000 W, but only
for a fraction of a second. The same person would have a
maximum of less than 800W if the power level had to be
maintained for an hour. The average person can produce
800W or more for a few seconds and perhaps 100-200 W for
an hour or more.
The Gossamer Albatross, 2시간 49분 동안 250W의 출력
To measure your power output when going up a flight of stairs,
multiply the height of the stairs by your weight, and divides
this by the times it takes you to climb the stairs.
P=mgh/t
3.5 Rotation and Angular Momentum
Law of Conservation of Angular Momentum:
The angular momentum of an isolated system is constant.
L= rxP=mvr(원궤도)
A satellite in orbit about the Earth is twice as from the Earth’s
center at point A as it is at point B. Conservation of angular
momentum then tells us that its speed at A is one-half its
speed at B.
Conservation of angular momentum
L  mvr
The person spins faster when the weight are pulled in
closer to the body because angular momentum is
conserved.
Ch. 3
1. Questions: 3, 6
2. Problems: 6, 8, 15, 21, 22, 28, 33
3. Challenges: 4