section 5-2 circular motion; gravitation. reminder: ap test and solutions manual giancoli physics...
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Section 5-2
Circular Motion; Gravitation
Reminder: AP test and solutions manual
giancoli physics principles with applications 6th edition solution manual3rd site in google gives a pdf Physics – Comcast.net
Objectives: The student will be able to:
• identify the type of force supplying the centripetal force that acts on any object in uniform circular motion.
• determine the directions of the velocity, acceleration, and net force vectors for an object in uniform circular motion.
• identify centrifugal force as a fictitious force and explain how it results from an accelerated frame of reference.
• use Newton's laws of motion and the concept of centripetal acceleration to solve word problems.
April 20, 2023
Uniform Circular Motion: Observations Object moving along a
curved path with constant speed Magnitude of velocity:
same Direction of velocity:
changing Velocity : changing Acceleration is NOT zero! Net force acting on an
object is NOT zero “Centripetal force”
amFnet
v
5-2 Dynamics of Uniform Circular Motion
For an object to be in uniform circular motion, there must be a net force acting on it.
We already know the acceleration, so can immediately write the force:
(5-1)
Uniform Circular MotionNewton’s 2nd Law: : The net force on a body is equal to the product of the mass of the body and the acceleration of the body.
*The centripetal acceleration is caused by a centripetal force that is directed towards the center of the circle.
F ma mv2
r
5-2 Dynamics of Uniform Circular Motion
We can see that the force must be inward by thinking about a ball on a string:
Demo – penny and hanger
5-2 Dynamics of Uniform Circular Motion
There is no centrifugal force pointing outward; what happens is that the natural tendency of the object to move in a straight line must be overcome.
If the centripetal force vanishes, the object flies off tangent to the circle.
““Centrifugal ForceCentrifugal Force””
• ““centrifugal forcecentrifugal force”” is a is a fictitious forcefictitious force - - it is not an interaction between 2 it is not an interaction between 2
objects, and therefore objects, and therefore not not a real forcea real force..
• NothingNothing pulls an object away from pulls an object away from the center of the circle.the center of the circle.
““Centrifugal ForceCentrifugal Force””
• What is erroneously attributed to What is erroneously attributed to ““centrifugal forcecentrifugal force”” is actually the action is actually the action of the objectof the object’’s s inertiainertia - whatever - whatever velocity it has (speed + direction) it velocity it has (speed + direction) it wants to keep.wants to keep.
April 20, 2023
Centripetal Force• Acceleration:
– Magnitude: – Direction: toward the center
of the circle of motion
• Force: – Start from Newton’s 2nd Law
– Magnitude:
– Direction: toward the center of the circle of motion
r
vac
2
r
vac
2
amFnet
vac
r
mvmaF cnet
2
netF
netF
netF
vFnet
netc Fa
||
April 20, 2023
What provides Centripetal Force ?
• Centripetal force is not a new kind of force• Centripetal force refers to any force that
keeps an object following a circular path
• Centripetal force is a combination of – Gravitational force mg: downward to the
ground– Normal force N: perpendicular to the surface– Tension force T: along the cord and away from
object– Static friction force: fs
max = µsN
r
mvmaF cc
2
April 20, 2023
a
What provides Centripetal Force ?
r
mvT
maTFnet
2
r
vmmgN
mamgNFnet
2
mg
N
v
Example ProblemA 2.0-kg mass is attached to the end of a 3.0 m-long rope and spun in a vertical circle at a speed of 6.6 m/s. Determine the maximum and minimum tensions in the rope.
April 20, 2023
Problem Solving Strategy• Draw a free body diagram, showing and
labeling all the forces acting on the object(s)• Choose a coordinate system that has one axis
perpendicular to the circular path and the other axis tangent to the circular path
• Find the net force toward the center of the circular path (this is the force that causes the centripetal acceleration, FC)
• Use Newton’s second law – The directions will be radial, normal, and tangential– The acceleration in the radial direction will be the
centripetal acceleration
• Solve for the unknown(s)
Circular Motion Lab
• Looking at factors affecting velocity. (graph for each part)• Part 1: Changing hanging mass and radius constant (100g, 200g, 250g, 300g, 350g,
400g) -Select at least 3 different masses with 3 trials. • Looking at centripetal force formula which indicates that centripetal force and velocity
squared are directly related. Prepare a graph to support this.• Data Table: Hanging weight; radius, mass of twirling object, number of revolutions,
elapsed time, period, velocity of twirling mass, centripetal acceleration.• 2nd Data Table: Hanging weight, Centripetal force of the twirling mass, % error• Part 2: Changing radius and keeping hanging mass constant (40 cm, 60 cm, 80 cm)
– At least 3 trials.• 2nd graph – see 1st bullet (think of the independent and dependent variables)
– Use a paper clip as a marker (always keep 1 cm below tube)– Swinging must be horizontal.– Must use SI units!– Goggles must be worn.– What causes the centripetal force?
Homework for Section 5-2
• Be prepared for lab.
• Problems 7, 8,13, 16, 18
Kahoot
• Section 5-2 Giancoli Dynamics of Uniform Acceleration