Download Sponge - A 200 kg hockey player pushes a 150 kg official after

Sponge - A 200 kg hockey
player pushes a 150 kg
official after receiving a
penalty. If he pushes with
a force of 500 N, what is
the acceleration of each
person?
Newton’s Law of Universal
Gravitation - every particle in
the universe exerts a force on
every other particle by the
following equation:
F = G m1m2 /r2
G = 6.67259 x
-11
10
2
2
N•m /kg
G is the universal
gravitational constant.
It was first measured
by Henry Cavendish
(1731-1810) over 100
years after Newton
wrote the law.
The forces between
two particles are an
action-reaction pair,
as in Newton’s third
law.
Ex. 5 - What is the
magnitude of the
gravitational force that
acts on each particle,
assuming
m1 = 12 kg, m2 = 25 kg,
and r = 1.2 m?
The value “r” must
be measured from
the centers of the
objects if they are
not particles.
The weight of
an object is the
gravitational force
that the Earth exerts
on the object.
If “W” is weight,
Newton’s law of
gravitation becomes:
W = G MEm2
2
/r
Ex. 6 - The mass of the Hubble
space telescope is 11 600 kg.
Determine the weight of the
telescope
(a) when it was resting on the
Earth and
(b) as it is in its orbit 569 km
above the Earth’s surface.
Relation Between Mass
and Weight 2
W = G ME m2 /r
W=mg
g is determined by G, ME, and r.
The normal force FN is one
component of the force that
a surface exerts on an
object with which it is in
contact, namely, the
component that is
perpendicular to the
surface.
The forces on the block are
balanced. Adding another
downward force causes FN to
increase. Adding an upward force,
subtracts from W and FN decreases;
possibly to zero.
Ex. 8 - In a circus balancing act, a
woman performs a headstand on top
of a man’s head. The woman weighs
490 N, and the man’s head and neck
weigh 50 N. It is primarily the seventh
cervical vertebra in the spine that
supports all the weight above the
shoulders. What is the normal force
that this vertebra exerts on the neck
and head of the man (a) before the act
and (b) during the act?
When a person is
accelerated upward or
downward, the apparent
weight is greater or less
than the true weight.
FN = mg + ma
“a” is + if upward, - if downward
If a person is in free
fall, a = -g and by
FN = mg + ma,
FN = zero. The
apparent weight
in free fall is zero.
Friction is a
parallel force to
the direction of
intended motion.
Friction before an object
starts to move is static
friction. The maximum static
frictional force, fSMAX, is the
maximum frictional force that
can be applied before motion
and acceleration occur.
The ratio of fSMAX to FN
is called the coefficient
of static friction. It is
represented by µS.
fSMAX = µS FN
fSMAX = µS FN
This equation relates
only the magnitudes
of the vectors, not
the directions.
Ex. 8 - A sled is resting on a
horizontal patch of snow, and
the coefficient of static friction
is µS = 0.350. The sled and
its rider have a total mass of
38.0 kg. Determine the
horizontal force needed to
start the sled barely moving.
When two surfaces are moving
across each other, the friction is
called kinetic friction fK. It is
usually less than static friction.
µK is the coefficient of kinetic
friction.
fK = µK FN
Ex. 10 - A sled is traveling
at 4.00 m/s along a
horizontal stretch of
snow. The coefficient
of kinetic friction is mK =
0.0500. How far does the
sled go before stopping?