Transcript Driving on Curves - Wappingers Central School

A vs m, a vs 1/m, F vs m, F vs a
F = ma
F
F = am
m
a
a
m
a = F(1/m )
1/m
F
F = ma
a
A vs m, a vs 1/m, F vs m, F vs a
F = ma
F
F = am
m
a
a
m
a = F(1/m )
1/m
F
F = ma
a
Driving on Curves
Transportation: Ch. 1, Act. 7
Motion & Forces
– Velocity – a measure of the change in distance over
time with direction (v = Δd/Δt).
– Mass – A measure of the amount of matter an object
contains (m).
– Acceleration – A measure of the change in velocity
over change in time (a = Δv/Δt).
– Force – A push or pull that is equal to the mass of the
object multiplied by its acceleration (Fc = mac).
Uniform Circular Motion
• If an object is moving at constant speed in a
circular path, can it be accelerating?
– YES!
» Although the speed may be constant, the direction is
changing.
» If direction is changing over time, then the velocity
must be changing.
» Acceleration, by definition, is the change in velocity
over time (a = v/t).
» If the velocity is changing over time, then the
object must be accelerating.
Newton’s
st
1
Law
• In order to make an object move in a circular path,
an outside force must be must exist.
– Newton’s 1st Law says that an object will attempt to
remain in motion in a straight line at a constant speed
unless an unbalance force acts on it.
– To make an object move in a circular path, centripetal
force must be applied to the object.
– Centripetal force always acts toward the center of the
circle that the object moves.
Circular Motion – Centripetal Force
• Centripetal force acts perpendicular or at
right angles to its direction of motion.
Instantaneous
direction of velocity
Direction of force
required to make
object move in a
circular path
(towards the center)
Centripetal Force
• Centripetal force is affected by:
– The mass of the object (m).
– The speed of the object around the circle (v).
– The radius of the circle (r).
• Using Newton’s 2nd Law of Motion (F = ma),
centripetal force is mathematically represented as
follows:
mv 2
F
r
Where: ac = v2/r
What do you think?
• You are driving along a road at the posted speed
limit of 40 mph (20 m/s). A road sign warns you
that you are approaching a curve and tells you to
slow down to 20 mph (10 m/s).
– Why are they telling you to slow down?
» If your speed is too fast, you may lose grip with the road while
going around the turn.
» Factors such as rain and snow need to be considered while
negotiating turns.
What Factors Affect Centripetal
Force and How?
• Centripetal force will increase as:
– the mass of the object increases.
– The speed of the object increases.
– The radius of the circle decreases.
Mass
Speed
Radius
The path of objects.
• If the centripetal force were suddenly removed
from an object moving in a circular path, what
trajectory (or path) would it follow? Why?
The object would go straight due to inertia
Determining the Speed
• How would you determine the speed of an object
moving in a circular path?
– What you already know:
» v = Δd/Δt
» Circumference of a circle: C = 2πr
• If you know the time (T) it takes an object to
make one full revolution and the radius of the
circle it traverses, then the objects speed can be
determined as follows:
– v = C/T
– v = 2πr/T
Example 1
• A person at the equator travels once around
the circumference of the Earth in 24 hours.
The radius of the Earth is 6,400 km. How
fast is the person going?
–
–
–
–
v = d/t
d = 2πr = 2•π•6,400 km = 40,192 km
t = 24 hours = 24 • 60 min/hr • 60 sec/min = 86,400 s
v = 40.192 km/86,400 s = 465 m/s (~1,000 mph)
Example 2
• Earth travels in a circular path around the
sun. The radius of the orbit of the Earth’s
path around the sun is about 1.5 x 108 km.
What is the speed of the Earth in its orbit?
–
–
–
–
d = 2πr = 2•π•1.5 x 108 km = 9.42 x 1011 km
t = 365 days x 24 hr/day = 8,760 hr
v = d/t = 9.42 x 1011 m/8,760 x 103 hr
v = 107,589 km/hr (~66,705 mph)
Example 3
• Friction can hold a car on the road when it
is traveling at 20 m/s and the radius of the
turn is 15 m. What happens if:
– The turn is tighter?
» The force due to friction will need to increase.
– The speed is increased?
» The car will likely go off the road is a straight path.
– The road is more slippery.
» The car will likely go off the road in a straight path.
Objects that travel in circular paths.
What is the cause of the force?
• The Earth – Sun System:
– Gravity.
• A racecar traveling around a turn on the
racetrack:
– Friction.
• An athlete throwing the hammer:
– Tension in the cable attached to the hammer.
Key Ideas
• Roller Coaster:
– ac > g or you will die. (ac = v2/r)
• In going around in a circle
– As you go faster you need more force to hold
you in place
– Friction.
• As you go tighter in a circle at the same
speed, you need more force to hold you in
place
Just For Fun
• https://www.youtube.com/watch?v=J7k8Oz
_73mw&t=12s