Section 6 3 Apparent Forces in Circular Motion

  • Slides: 29
Download presentation
Section 6. 3 Apparent Forces in Circular Motion (cont. ) © 2015 Pearson Education,

Section 6. 3 Apparent Forces in Circular Motion (cont. ) © 2015 Pearson Education, Inc.

Centrifugal Force? • If you are a passenger in a car that turns a

Centrifugal Force? • 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. © 2015 Pearson Education, Inc. A centrifugal force will never appear on a free-body diagram and never be included in Newton’s laws. Slide 6 -2

Apparent Weight in Uniform, Vertical Circular Motion © 2015 Pearson Education, Inc. Slide 6

Apparent Weight in Uniform, Vertical Circular Motion © 2015 Pearson Education, Inc. Slide 6 -3

Apparent Weight in Unif. Vert. Circular Motion • The force you feel, your apparent

Apparent Weight in Unif. Vert. 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. © 2015 Pearson Education, Inc. Slide 6 -4

Apparent Weight in Unif. Vert. Circular Motion • Newton’s second law for the passenger

Apparent Weight in Unif. Vert. Circular Motion • Newton’s second law for the passenger at the bottom of the circle gives that so her apparent weight is greater than her true weight, w. • Newton’s second law for the passenger at the top of the circle gives that Note that her apparent weight can exceed the true weight, but might not depending on the speed. © 2015 Pearson Education, Inc. Slide 6 -5

Apparent Weight in Unif. Vert. Circular Motion • As the car goes slower there

Apparent Weight in Unif. Vert. Circular Motion • 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 • The critical speed is the slowest speed at which the car can complete the circle. © 2015 Pearson Education, Inc. Slide 6 -6

Quick. Check 6. 10 A physics textbook swings back and forth as a pendulum.

Quick. Check 6. 10 A physics textbook swings back and forth as a pendulum. Which is the correct free-body diagram when the book is at the bottom and moving to the right? © 2015 Pearson Education, Inc. Slide 6 -7

Quick. Check 6. 10 A physics textbook swings back and forth as a pendulum.

Quick. Check 6. 10 A physics textbook swings back and forth as a pendulum. Which is the correct free-body diagram when the book is at the bottom and moving to the right? Centripetal acceleration requires an upward force. C. © 2015 Pearson Education, Inc. Slide 6 -8

Quick. Check 6. 11 A car that’s out of gas coasts over the top

Quick. Check 6. 11 A car that’s out of gas coasts over the top of a hill at a steady 20 m/s. Assume air resistance is negligible. Which free-body diagram describes the car at this instant? © 2015 Pearson Education, Inc. Slide 6 -9

Quick. Check 6. 11 A car that’s out of gas coasts over the top

Quick. Check 6. 11 A car that’s out of gas coasts over the top of a hill at a steady 20 m/s. Assume air resistance is negligible. Which free-body diagram describes the car at this instant? Now the centripetal acceleration points down. A. © 2015 Pearson Education, Inc. Slide 6 -10

Quick. Check 6. 12 • A roller coaster car does a loop-the-loop. Which of

Quick. Check 6. 12 • A roller coaster car does a loop-the-loop. Which of the free -body diagrams shows the forces on the car at the top of the loop? Rolling friction can be neglected. © 2015 Pearson Education, Inc. Slide 6 -11

Quick. Check 6. 12 • A roller coaster car does a loop-the-loop. Which of

Quick. Check 6. 12 • A roller coaster car does a loop-the-loop. Which of the free -body diagrams shows the forces on the car at the top of the loop? Rolling friction can be neglected. E. © 2015 Pearson Education, Inc. The track is above the car, so the normal force of the track pushes down. Slide 6 -12

Centrifuges © 2015 Pearson Education, Inc. Slide 6 -13

Centrifuges © 2015 Pearson Education, Inc. Slide 6 -13

Try It Yourself: Human Centrifuge If you spin your arm rapidly in a vertical

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 retard 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. © 2015 Pearson Education, Inc. Slide 6 -14

Example 6. 10 Analyzing the ultracentrifuge An 18 -cm-diameter ultracentrifuge produces an extraordinarily large

Example 6. 10 Analyzing the ultracentrifuge An 18 -cm-diameter ultracentrifuge produces an extraordinarily large centripetal acceleration of 250, 000 g, where g is the free-fall acceleration due to gravity. a) What is its frequency in rpm? b) What is the apparent weight of a sample with a mass of 0. 0030 kg? © 2015 Pearson Education, Inc. Slide 6 -15

Example 6. 10 Analyzing the ultracentrifuge PREPARE The acceleration in SI units is The

Example 6. 10 Analyzing the ultracentrifuge PREPARE The acceleration in SI units is The radius is half the diameter, or r = 9. 0 cm = 0. 090 m. We can rearrange Equation 6. 5 to find the frequency given the centripetal acceleration: SOLVE Converting to rpm, we find © 2015 Pearson Education, Inc. Slide 6 -16

Example 6. 10 Analyzing the ultracentrifuge (cont. ) The acceleration is so high that

Example 6. 10 Analyzing the ultracentrifuge (cont. ) 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: A 3 g sample has apparent weight around 1700 pounds! Because the acceleration is 250, 000 g, 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. ASSESS © 2015 Pearson Education, Inc. Slide 6 -17

Quick. Check 6. 13 • A coin sits on a turntable as the table

Quick. Check 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? © 2015 Pearson Education, Inc. Slide 6 -18

Quick. Check 6. 13 • A coin sits on a turntable as the table

Quick. Check 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? A. © 2015 Pearson Education, Inc. Slide 6 -19

Example Problem A car of mass 1500 kg goes over a hill at a

Example Problem 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. When the car is at the highest point of the hill, 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? © 2015 Pearson Education, Inc. Slide 6 -20

Section 6. 4 Circular Orbits and Weightlessness © 2015 Pearson Education, Inc.

Section 6. 4 Circular Orbits and Weightlessness © 2015 Pearson Education, Inc.

Orbital Motion The force of gravity on a projectile is directed toward the center

Orbital Motion The force of gravity on a projectile is directed toward the center of the earth. © 2015 Pearson Education, Inc. Slide 6 -22

Orbital Motion • If the launch speed of a projectile is sufficiently large, there

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. • Such a closed trajectory is called an orbit. • An orbiting projectile is in free fall. © 2015 Pearson Education, Inc. Slide 6 -23

Orbital Motion • The force of gravity is the force that causes the centripetal

Orbital Motion • 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 • That is, if an object moves parallel to the surface with the speed © 2015 Pearson Education, Inc. Slide 6 -24

Orbital Motion • The orbital speed of a projectile just skimming the surface of

Orbital Motion • The orbital speed of a projectile just skimming the surface of a smooth, airless earth is • We can use vorbit to calculate the period of the satellite’s orbit: • This gives T = 2. 2 hours. © 2015 Pearson Education, Inc. Slide 6 -25

Weightlessness in Orbit • Astronauts and their spacecraft are in free fall. © 2015

Weightlessness in Orbit • Astronauts and their spacecraft are in free fall. © 2015 Pearson Education, Inc. Slide 6 -26

Quick. Check 6. 19 Astronauts on the International Space Station are weightless because A.

Quick. Check 6. 19 Astronauts on the International Space Station are weightless because A. B. C. D. E. There’s no gravity in outer space. The net force on them is zero. The centrifugal force balances the gravitational force. g is very small, although not zero. They are in free fall. © 2015 Pearson Education, Inc. Slide 6 -27

Quick. Check 6. 19 Astronauts on the International Space Station are weightless because A.

Quick. Check 6. 19 Astronauts on the International Space Station are weightless because A. B. C. D. E. There’s no gravity in outer space. The net force on them is zero. The centrifugal force balances the gravitational force. g is very small, although not zero. They are in free fall. © 2015 Pearson Education, Inc. Slide 6 -28

The Orbit of the Moon • The moon, like all satellites, is simply “falling”

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. © 2015 Pearson Education, Inc. Slide 6 -29