Transcript Acceleration is equal to Δv/Δt. Velocity is a vector and there are two

Acceleration is equal
to Δv/Δt. Velocity is a
vector and there are
two ways a vector
can be changed: by
changing magnitude or
by changing direction.
An acceleration
due to a change in
direction is called
a centripetal
acceleration.
The equation is:
ac =
2
vt /r.
vi and vf are equal
and can be called v.
Also, ∆d = v ∆t.
Therefore, ∆v/ vi = ∆d/r
becomes: ∆v/v = v∆t/r
∆v/v = v∆t/r
becomes:
∆v/∆t =
2
v /r
∆v/∆t =
∆v/∆t = a
a=
2
v /r
SO,
2
v /r
A test car moves at
constant speed around a
circular track. If the car is
48.2 m from the track’s
center and has a
centripetal acceleration of
2
8.05 m/s , what is its
tangential speed?
The direction of
centripetal
acceleration is
toward the center
of the circle.
An object can have a
centripetal acceleration
and a tangential
acceleration. These two
accelerations are
perpendicular to each
other.
When both these
components exist
simultaneously, the total
acceleration can be
found using the
Pythagorean theorem.
A Hot Wheels‘ car moves around
a curve in the track. The curve
has a radius of 0.20 m, the
instantaneous velocity is 1 m/s,
and friction is causing a
tangential acceleration of -0.5
m/s2. What is the aC and what
is the total acceleration?
A force is required to
accelerate an object:
F = ma. A centripetal force
is required to cause a
centripetal acceleration.
Fc = mac
Fc = mac
2
Fc = mv /r
Fc is measured in newtons.
A pilot is flying a small
plane at 30.0 m/s in a
circular path with a radius
of 100.0 m. If a force of 635
N is needed to maintain the
pilot’s circular motion, what
is the pilot’s mass?
The centripetal force
needed to pull an object
into a curved path is
directed toward the
center of the circle
formed by the path.
Inertia is often
misrepresented
as a force:
centrifugal force.
Centrifugal force is a
fictitious force.
Gravitational
force is what pulls
orbiting objects
into a elliptical
path.
The magnitude
of this force can be
calculated from
Newton’s
Law of Universal
Gravitation.
The force of attraction
between two objects is
directly proportional to the
product of the masses of the
objects and inversely
proportional to the square of
the distance between their
centers of mass.
F=
2
Gm1m2\d
F is force of gravitation
m1 & m2 are masses
d is distance
G is the universal gravitational
constant
Henry Cavendish
measured G
in 1797.
G = 6.67 x 10-11
N•m2/kg2
Find the distance between a
0.300 kg billiard ball and a 0.400
kg billiard ball if the magnitude
of the gravitational force is 8.92
x 10-11 N.
We can use this law
to find the
mass of the earth:
Fw = Gmemp
2
/d
Fw = Gmemp
2
/d
divide both sides by mp
Fw /mp=
2
Gme/d
Fw /mp=
Fw = mp g,
g=
2
Gme/d
or Fw /mp = g, so
2
Gme/d
G & me are
constant,so g
is determined
only by d.
g=
2
Gme/d ,
solve for me,
me =
2
gd /G
me =
2
gd /G
g = 9.81 m/s2
d = 6.37 x 106 m
G = 6.67 x 10-11 N•m2/kg2
me = 5.96 x
24
10
kg
Weight is the
measure of the
force of attraction
between the object
and the Earth.