Download Circular-Motion and forces

10/28/2014
Angular Position
Circles
Phy 114
Eyres
The qualitative velocity change method for
circular motion
Circles
•
Instantaneous velocity is tangent to the displacement for any instant.
– In circular motion, the system object travels in a circle and the velocity is
tangent to the circle at every instant.
•
Even if an object is moving at constant speed around a circle, its velocity
changes direction.
– A change in velocity means there is acceleration!
C = 2πr
v=
2πr
T
T is time to go
around once
© 2014 Pearson Education, Inc.
Using the velocity change method to
estimate the direction of acceleration
• This method is used to estimate the direction
of acceleration of any object during a short
time interval Δt = tf – ti.
Circles
∆s ∆v
=
r
v
(∆s )v = (∆v )r
r
r
vi
vf
r
r
Δs
(∆s )v (∆v)r
=
∆t
∆t
2
v = ar
a=
v2
r
© 2014 Pearson Education, Inc.
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10/28/2014
Radial and Tangential
• Always draw a picture where you can see the
center of the circle
• Use radial and tangential coordinate axes.
• Set positive toward the center
• Remember that radial acceleration is:
Testing Experiment 1: The sum of the forces exerted
on an object moving at constant speed along a
circular path points toward the center of that circle in
the same direction as the object's acceleration
=
© 2014 Pearson Education, Inc.
Driving over a Rise
Roller-Coaster
A car of mass 1500 kg goes over a
hill at a speed of 20 m/s. The shape
of the hill is approximately circular,
with a radius of 60 m, as in the figure
at right. When the car is at the
highest point of the hill,
• A roller-coaster vehicle
has a mass of 500 kg
when fully loaded with
passengers. If the
vehicle has a speed of
20.0 m/s at point A,
what is the force of the
track on the vehicle at
this point?
a. What is the force of gravity on
the car?
b. What is the normal force of the
road on the car at this point?
Slide 6-26
Example
Example 4.5: Toy airplane
• A toy airplane flies around in a horizontal circle at constant
speed. The airplane is attached to the end of a 46-cm string,
which makes a 25° angle relative to the horizontal while the
airplane is flying. A scale at the top of the string measures the
force that the string exerts on the airplane.
• Predict the period of the airplane's motion (the time interval for
it to complete one circle).
In the hammer throw, an
athlete spins a heavy mass in a
circle at the end of a chain,
then lets go of the chain. For
male athletes, the “hammer” is
a mass of 7.3 kg at the end of
a 1.2 m chain.
A world-class thrower can get the hammer up to a speed of 29
m/s. If an athlete swings the mass in a horizontal circle centered
on the handle he uses to hold the chain, what is the tension in the
chain?
© 2014 Pearson Education, Inc.
Slide 6-25
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Example 4.7: Texas Motor Speedway
Newton's law of universal gravitation
• Texas Motor Speedway is a
2.4-km (1.5-mile)-long oval
track. One of its turns is about
200 m in radius and is banked
at 24° above the horizontal.
• How fast would a car have to
move so that no friction is
needed to prevent it from
sliding sideways off the
raceway (into the infield or off
the track)?
© 2014 Pearson Education, Inc.
Example 4.8: Geostationary satellite
• You are in charge of
launching a geostationary
satellite into orbit.
• At which altitude above the
equator must the satellite
orbit be to provide
continuous communication
to a stationary dish antenna
on Earth?
• The mass of Earth is 5.98 x
1024 kg.
© 2014 Pearson Education, Inc.
Answers
• Drive over a rise: n=4700 N
• Roller Coaster: n=24900 N.
• Hammer throw: T=5116 N
© 2014 Pearson Education, Inc.
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