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Chapter 9 : Linear Momentum
8-5 The Law of Conservation of
Energy
Problem 38
38.(II) A 180-g wood block is firmly attached
to a very light horizontal spring, Fig. 8–35. The
block can slide along a table where the
coefficient of friction is 0.30. A force of 25 N
compresses the spring 18 cm. If the spring is
released from this position, how far beyond its
equilibrium position will it stretch on its first
cycle?
8-7 Gravitational Potential Energy and
Escape Velocity
Far from the surface of the Earth, the force of gravity is
not constant:
The work done on an object moving in
the Earth’s gravitational field is given
by:
8-7 Gravitational Potential Energy and
Escape Velocity
Because the value of the work depends only on the end points,
the gravitational force is conservative and we can define
gravitational potential energy:
8-7 Gravitational Potential Energy and
Escape Velocity
Example 8-12: Package dropped from high-speed rocket.
A box of empty film canisters is allowed to fall from a
rocket traveling outward from Earth at a speed of 1800
m/s when 1600 km above the Earth’s surface. The
package eventually falls to the Earth. Estimate its speed
just before impact. Ignore air resistance. The radius of
the earth is 6380km, and the mass of the earth is
5.98X1024kg
8-7 Gravitational Potential Energy and
Escape Velocity
Problem 50: (II) Two Earth satellites, A and B, each of mass of
950kg are launched into circular orbits around the Earth’s center.
Satellite A orbits at an altitude of 4200 km, and satellite B orbits
at an altitude of 12,600 km. (a) What are the potential energies of
the two satellites? (b) What are the kinetic energies of the two
satellites? (c) How much work would it require to change the orbit of
satellite A to match that of satellite B? The radius of the earth is
6380km, and the mass of the earth is 5.98X1024kg
8-7 Gravitational Potential Energy and
Escape Velocity
If an object’s initial kinetic energy is equal to the
potential energy at the Earth’s surface, its total energy
will be zero. The velocity at which this is true is called
the escape velocity; for Earth:
it is also the minimum velocity that prevent an object
from returning to earth.
8-8 Power
Power is the rate at which work is done.
Average power:
Instantaneous power:
In the SI system, the units of power
are watts:
8-8 Power
Power is the rate at which energy is
transformed
Units: Joules/s or Watts, W
In the British system, the basic
unit for power is the foot-pound per second,
but more often horsepower is used:
1 hp = 550 ft·lb/s = 746 W.
Puzzler:
kilowatt·hours [kW·h] are units
of what quantity?
8-8 Power
Example 8-14: Stair-climbing power.
A 60-kg jogger runs up a long flight of
stairs in 4.0 s. The vertical height of
the stairs is 4.5 m. (a) Estimate the
jogger’s power output in watts and
horsepower. (b) How much energy did
this require?
8-8 Power
Example 8-15: Power needs of a car.
Calculate the power required of a 1400-kg car
under the following circumstances: (a) the car
climbs a 10° hill (a fairly steep hill) at a steady
80 km/h; and (b) the car accelerates along a
level road from 90 to 110 km/h in 6.0 s to pass
another car. Assume that the average retarding
force on the car is FR = 700 N throughout.
9-1 Momentum and Its Relation to Force
Momentum is the property of a moving object to
continue moving
Momentum is a vector symbolized by the symbol p
and is defined as
The rate of change of momentum is equal to the
net force:
This can be shown using Newton’s second law.
Momentum, p
Vector
units: kg.m/s
Bowling Ball vs. Tennis Ball
p = mv
Mass
7 kg
57 g
Speed
9 m/s
60 m/s
63kg.m/s
3.42kg.m/s
momentum
9-1 Momentum and Its Relation to Force
Example: A system consists of three particles with these
masses and velocities:
mass 3.0 kg moving west at 5.0 m/s; mass 4.0 kg moving west at
10.0 m/s; and mass 5.0 kg moving east at 20.0 m/s.
What is total momentum of the system?
9-1 Momentum and Its Relation to Force
Example 9-1: Force of a tennis serve.
For a top player, a tennis ball
may leave the racket on the
serve with a speed of 55 m/s
(about 120 mi/h). If the ball
has a mass of 0.060 kg and
is in contact with the racket
for about 4 ms (4 x 10-3 s),
estimate the average force on
the ball. Would this force be
large enough to lift a 60-kg
person?
9-1 Momentum and Its Relation to Force
Example 9-2: Washing a car: momentum change
and force.
Water leaves a hose at a rate of 1.5 kg/s with
a speed of 20 m/s and is aimed at the side of a
car, which stops it. (That is, we ignore any
splashing back.) What is the force exerted by
the water on the car?
9-2 Conservation of Momentum
During a collision, measurements show that the
total momentum does not change:
9-2 Conservation of Momentum
Conservation of momentum can also
be derived from Newton’s laws. A
collision takes a short enough time
that we can ignore external forces.
Since the internal forces are equal
and opposite, the total momentum
is constant.
9-2 Conservation of Momentum
This is the law of conservation of linear
momentum:
when the net external force on a system
of objects is zero, the total momentum
of the system remains constant.
Equivalently,
the total momentum of an isolated
system remains constant.
9-2 Conservation of Momentum
Example 9-4: Rifle recoil.
Calculate the recoil velocity of a 5.0-kg rifle that
shoots a 0.020-kg bullet at a speed of 620 m/s.
(
9-2 Conservation of Momentum
Problem 12:(I) A 130-kg tackler moving at 2.5m/s
meets head-on (and tackles) an 82-kg halfback
moving at 5.0m/s. What will be their mutual speed
immediately after the collision?