6.3 Apparent Forces in Circular Motion ­ 6.4 Circular Orbits and Weightlessness.notebook
October 21, 2016
Centrifugal Force?
Section 6.3 Apparent Forces in Circular Motion
• If you are a passenger in a car that turns a corner quickly, it is the force of the car door, pushing inward toward the center of the curve, that causes you to turn the corner.
• What you feel is your body trying to move ahead in a straight line as outside forces (the door) act to turn you in a circle.
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Apparent Weight in Circular Motion
A centrifugal force will never appear on a free­body diagram and never be included in Newton’s laws.
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Apparent Weight in Circular Motion
• The force you feel, your apparent weight, is the magnitude of the contact force that supports you. • When the passenger on the roller coaster is at the bottom of the loop:
> The net force points upward, so n > w.
> Her apparent weight is wapp= n, so her apparent weight is greater than her true weight.
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Apparent Weight in Circular Motion
Nov 3­3:15 PM
Apparent Weight in Circular Motion
• Newton’s second law for the passenger at the bottom of the circle is
• Newton’s second law for the passenger at the top of the circle is
• From this equation, the passenger’s apparent weight is
• Note that wx is now positive because the x­axis is directed downward. We can solve for the passenger’s apparent weight:
• Her apparent weight at the bottom is greater than her true weight, w.
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• If v is sufficiently large, her apparent weight can exceed the true weight.
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6.3 Apparent Forces in Circular Motion ­ 6.4 Circular Orbits and Weightlessness.notebook
October 21, 2016
Apparent Weight in Circular Motion
QuickCheck 6.10
• As the car goes slower there comes a point where n becomes zero:
• The speed for which n = 0 is called the critical speed vc. Because for n to be zero we must have , the critical speed is
A physics textbook swings back and forth as a pendulum. Which is the correct free­body diagram when the book is at the bottom and moving to the right? • The critical speed is the slowest speed at which the car can complete the circle.
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QuickCheck 6.12
QuickCheck 6.10
A physics textbook swings back and forth as a pendulum. Which is the correct free­body diagram when the book is at the bottom and moving to the right? A roller coaster car does a loop­the­loop. Which of the free­body diagrams shows the forces on the car at the top of the loop? Rolling friction can be neglected.
Centripetal acceleration requires an upward force.
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Nov 3­3:15 PM
QuickCheck 6.12
Centrifuges
A roller coaster car does a loop­the­loop. Which of the free­body diagrams shows the forces on the car at the top of the loop? Rolling friction can be neglected.
The track is above the car, so the normal force of the track pushes down.
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6.3 Apparent Forces in Circular Motion ­ 6.4 Circular Orbits and Weightlessness.notebook
October 21, 2016
Try It Yourself: Human Centrifuge
If you spin your arm rapidly in a vertical circle, the motion will produce an effect like that in a centrifuge. The motion will assist outbound blood flow in your arteries and impede inbound blood flow in your veins. There will be a buildup of fluid in your hand that you will be able to see (and feel!) quite easily.
Example 6.10 Analyzing the ultracentrifuge
An 18­cm­diameter ultracentrifuge produces an extraordinarily large centripetal acceleration of 250,000g, where g is the free­fall acceleration due to gravity. What is its frequency in rpm? What is the apparent weight of a sample with a mass of 0.0030 kg?
prepare The acceleration in SI units is
The radius is half the diameter, or r = 9.0 cm = 0.090 m.
solve We can rearrange to find the frequency given the centripetal acceleration:
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Example 6.10 Analyzing the ultracentrifuge (cont.)
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Example 6.10 Analyzing the ultracentrifuge (cont.)
Converting to rpm, we find
The acceleration is so high that every force is negligible except for the force that provides the centripetal acceleration. The net force is simply equal to the inward force, which is also the sample’s apparent weight:
assess Because the acceleration is 250,000g, the apparent weight is 250,000 times the actual weight. This makes sense, as does the fact that we calculated a very high frequency, which is necessary to give the large acceleration.
The 3 gram sample has an effective weight of about 1700 pounds!
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QuickCheck 6.13
Nov 3­3:15 PM
QuickCheck 6.13
A coin sits on a turntable as the table steadily rotates counterclockwise. What force or forces act in the plane of the turntable? Nov 3­3:15 PM
A coin sits on a turntable as the table steadily rotates counterclockwise. What force or forces act in the plane of the turntable? Nov 3­3:15 PM
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6.3 Apparent Forces in Circular Motion ­ 6.4 Circular Orbits and Weightlessness.notebook
October 21, 2016
QuickCheck 6.14
QuickCheck 6.14
A coin sits on a turntable as the table steadily rotates counterclockwise. The free­body diagrams below show the coin from behind, moving away from you. Which is the correct diagram? A coin sits on a turntable as the table steadily rotates counterclockwise. The free­body diagrams below show the coin from behind, moving away from you. Which is the correct diagram? C
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QuickCheck 6.15
Nov 3­3:15 PM
QuickCheck 6.15
A car turns a corner on a banked road. Which of the diagrams could be the car’s free­body diagram? A car turns a corner on a banked road. Which of the diagrams could be the car’s free­body diagram? Nov 3­3:15 PM
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Orbital Motion
Section 6.4 Circular Orbits and Weightlessness
The force of gravity on a projectile is directed toward the center of the earth.
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6.3 Apparent Forces in Circular Motion ­ 6.4 Circular Orbits and Weightlessness.notebook
October 21, 2016
Orbital Motion
Orbital Motion
• If the launch speed of a projectile is sufficiently large, there comes a point at which the curve of the trajectory and the curve of the earth are parallel.
• The force of gravity is the force that causes the centripetal acceleration of an orbiting object:
• An object moving in a circle of radius r at speed vorbit will have this centripetal acceleration if
• Such a closed trajectory is called an orbit.
• An orbiting projectile is in free fall.
• That is, if an object moves parallel to the surface with the speed
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Weightlessness in Orbit
Orbital Motion
• The orbital speed of a projectile just skimming the surface of a smooth, airless earth is
• Astronauts and their spacecraft are in free fall.
• We can use vorbit to calculate the period of the satellite’s orbit:
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QuickCheck 6.19
QuickCheck 6.19
Astronauts on the International Space Station are weightless because
Astronauts on the International Space Station are weightless because
A. There’s no gravity in outer space.
B. The net force on them is zero.
C. The centrifugal force balances the gravitational force.
D. g is very small, although not zero.
E. They are in free fall.
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A. There’s no gravity in outer space.
B. The net force on them is zero.
C. The centrifugal force balances the gravitational force.
D. g is very small, although not zero.
E. They are in free fall.
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6.3 Apparent Forces in Circular Motion ­ 6.4 Circular Orbits and Weightlessness.notebook
October 21, 2016
The Orbit of the Moon
• The moon, like all satellites, is simply “falling” around the earth.
• If we use the distance to the moon, r = 3.84 × 108 m, in:
we get a period of approximately 11 hours instead of one month.
• This is because the magnitude of the force of gravity, and thus the size of g, decreases with increasing distance from the earth.
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