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Forces and Motion: Centripetal Motion

Explore the effects of forces on the motion of objects in circular motion and gravitation. Learn about centripetal acceleration, dynamics of uniform circular motion, and the forces acting on or between objects. Review equations and concepts related to forces and motion.

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Forces and Motion: Centripetal Motion

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  1. UEQ: How do forces affect the motion of objects? Day 1 Centripetal Motion

  2. †After Attendance(†EQ Sheet; Concept Map) Place HW on my desk †Pickup a new Essential Question Sheet and a Causes of Force Concept Map Pickup and sign out your computer Log into www.plutonium-239.com Select the Warm-Up link Complete today’s warm-up and submit it Logout and return the computer to the cart †Pull out your Effects of Force Concept Map

  3. Feed Back for Google Docs • Was anything confusing on google docs? • Noteworthy Student Responses

  4. Review of Materials • Effects of Forces Test

  5. UEQ #1: How do forces affect the motion of objects? UEQ #2: What affects the forces acting on or between objects? Chapter 5: Circular Motion; Gravitation

  6. UEQ #1: How do forces affect the motion of objects? UEQ #2: What affects the forces acting on or between objects? Review of Concept Map & Units of Chapter 5 • Kinematics of Uniform Circular Motion • Dynamics of Uniform Circular Motion • Highway Curves, Banked and Unbanked • Centrifugation • Newton’s Law of Universal Gravitation

  7. UEQ #1: How do forces affect the motion of objects? UEQ #2: What affects the forces acting on or between objects? Units of Chapter 5 • Gravity Near the Earth’s Surface; Geophysical Applications • Satellites and “Weightlessness” • Kepler’s Laws and Newton’s Synthesis • Types of Forces in Nature

  8. UEQ #1: How do forces affect the motion of objects? UEQ #2: What affects the forces acting on or between objects? Equations to Know: Causes of Force

  9. Causes of Forces: Centripetal Acceleration EQ(s): How does centripetal acceleration affect the motion of an object? Start: What forces are acting on the roller-coaster cars at the top of the loop?

  10. How does centripetal acceleration affect the motion of an object? 5-1 Kinematics of Uniform Circular Motion Uniform circular motion: motion in a circle of constant radius at constant speed Instantaneous velocity is always tangent to circle.

  11. How does centripetal acceleration affect the motion of an object? 5-1 Kinematics of Uniform Circular Motion The acceleration (called the centripetal or radial acceleration) points towards the center of the circle with a magnitude: Other important equations:

  12. How does centripetal acceleration affect the motion of an object? 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)

  13. How does centripetal acceleration affect the motion of an object? 5-2 Dynamics of Uniform Circular Motion We can see that the force must be inward by thinking about a ball on a string: A Let’s apply Newton’s Second Law of Motion: B

  14. How does centripetal acceleration affect the motion of an object? 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.

  15. How does centripetal acceleration affect the motion of an object? 5-2 Dynamics of Uniform Circular Motion Which direction will the ball go if it were released at the following points? B C A D

  16. How does centripetal acceleration affect the motion of an object? Famous Physics Students Watch closely to see if the point of release correct? http://www.youtube.com/watch?v=eIZGSkf7S1A

  17. How does centripetal acceleration affect the motion of an object? Famous Physics Students Watch closely to see if the point of release correct? IT GETS A BIT GROSS AT THIS POINT. WE SHOULD STOP WATCHING.

  18. Centripetal Apparatus Lab Work in groups of no more than 4 people. Return all supplies to the counter/cart. How does centripetal acceleration affect the motion of an object?

  19. WebAssign/Lab Time Work on WebAssign Problems 5.1 - 5.5 or Centripetal Apparatus Lab Final Copy Criteria State the problem (Ex. Find displacement) Draw a picture/diagram Provide a list or table of all given data (Ex. t = 2 s) Solve the problem symbolically (Ex. v=x/t  x = vt) Plug in numbers and units to obtain answer. (Ex. x = (5 m/s)(2 s)= 10 m) Notes about WebAssign: Positive vs. negative answers (Try a negative sign) Look at the final unit (hours or minutes or seconds) How does centripetal acceleration affect the motion of an object?

  20. How does centripetal acceleration affect the motion of an object? Summary • Answer the Essential Questions. • Ticket out the Door: • What is the force equation for centripetal motion? • Draw a free body diagram for a “car” at the top of a rollercoaster loop. • Write the summation of forces for a “car” at the top of a rollercoaster loop. • HW: • Centripetal Apparatus Lab (5 Trials) • WebAssign Problems 5.1 - 5.5

  21. UEQ #1: How do forces affect the motion of objects? UEQ #2: What affects the forces acting on or between objects? Day 2 Banked and Unbanked Curves; Centrifugation

  22. After Attendance Place HW on my desk Pickup and sign out your computer Log into www.plutonium-239.com Select the Warm-Up link Complete today’s warm-up and submit it Logout and return the computer to the cart

  23. Feed Back for Google Docs • Was anything confusing on google docs? • Noteworthy Student Responses

  24. Causes of Forces: Centripetal Acceleration EQ(s): How does centripetal acceleration affect the motion of an object? Start: What force(s) keeps this race car on the track around Turn One at Indianapolis Motor Speedway?

  25. How does centripetal acceleration affect the motion of an object? So who is this guy Jerry? • Thought Question: Why does his car slide around the turns?

  26. How does centripetal acceleration affect the motion of an object? 5-3 Highway Curves, Banked and Unbanked When a car goes around a curve, there must be a net force towards the center of the circle of which the curve is an arc. If the road is flat, that force is supplied by friction.

  27. How does centripetal acceleration affect the motion of an object? 5-3 Highway Curves, Banked and Unbanked If the frictional force is insufficient, the car will tend to move more nearly in a straight line, as the skid marks show.

  28. How does centripetal acceleration affect the motion of an object? 5-3 Highway Curves, Banked and Unbanked • As long as the tires do not slip, the friction is static. If the tires do start to slip, the friction is kinetic, which is bad in two ways: • The kinetic frictional force is smaller than the static. • The static frictional force can point towards the center of the circle, but the kinetic frictional force opposes the direction of motion, making it very difficult to regain control of the car and continue around the curve.

  29. How does centripetal acceleration affect the motion of an object? 5-3 Highway Curves, Banked and Unbanked Banking the curve can help keep cars from skidding. In fact, for every banked curve, there is one speed where the entire centripetal force is supplied by the horizontal component of the normal force, and no friction is required. This occurs when: Solve for  in terms of r, g, & .

  30. How does centripetal acceleration affect the motion of an object? 5-5 Centrifugation A centrifuge works by spinning very fast. This means there must be a very large centripetal force. The object at A would go in a straight line but for this force; as it is, it winds up at B.

  31. Centripetal Apparatus Lab Work in groups of no more than 4 people. Return all supplies to the counter/cart. How does centripetal acceleration affect the motion of an object?

  32. WebAssign/Lab Time Work on WebAssign Problems 5.1 - 5.11 or Centripetal Apparatus Lab Final Copy Criteria State the problem (Ex. Find displacement) Draw a picture/diagram Provide a list or table of all given data (Ex. t = 2 s) Solve the problem symbolically (Ex. v=x/t  x = vt) Plug in numbers and units to obtain answer. (Ex. x = (5 m/s)(2 s)= 10 m) Notes about WebAssign: Positive vs. negative answers (Try a negative sign) Look at the final unit (hours or minutes or seconds) How does centripetal acceleration affect the motion of an object?

  33. Summary How does centripetal acceleration affect the motion of an object? • Answer the Essential Questions. • Ticket out the Door: • What is the force that allows a car to go around an unbanked curve? • What is the force that allows a car to go around an banked frictionless curve? • What is the equation that allows us to calculate the specific velocity, , for a car to go around an banked frictionless curve in terms of r, g, & ? • HW: • Centripetal Apparatus Lab (5 Trials) • WebAssign Problems 5.1 - 5.11

  34. UEQ #1: How do forces affect the motion of objects? UEQ #2: What affects the forces acting on or between objects? Day 3 Work Day

  35. After Attendance Place HW on my desk Pickup and sign out your computer Log into www.plutonium-239.com Select the Warm-Up link Complete today’s warm-up and submit it Logout and return the computer to the cart

  36. Feed Back for Google Docs • Was anything confusing on google docs? • Noteworthy Student Responses

  37. Causes of Forces: Centripetal Acceleration EQ(s): How does centripetal acceleration affect the motion of an object? Start: Write the summation of forces for the flat puck being rotated on a frictionless table being held in orbit by a light cord connected to a dangling block?

  38. Centripetal Apparatus Lab Work in groups of no more than 4 people. Return all supplies to the counter/cart. How does centripetal acceleration affect the motion of an object?

  39. WebAssign/Lab Time Work on WebAssign Problems 5.1 - 5.11 or Centripetal Apparatus Lab Final Copy Criteria State the problem (Ex. Find displacement) Draw a picture/diagram Provide a list or table of all given data (Ex. t = 2 s) Solve the problem symbolically (Ex. v=x/t  x = vt) Plug in numbers and units to obtain answer. (Ex. x = (5 m/s)(2 s)= 10 m) Notes about WebAssign: Positive vs. negative answers (Try a negative sign) Look at the final unit (hours or minutes or seconds) How does centripetal acceleration affect the motion of an object?

  40. Summary How does centripetal acceleration affect the motion of an object? • Answer the Essential Questions. • Ticket out the Door: • Derive an equation for the velocity, , of the flat puck in terms of m, g, R, and M? • HW: • Centripetal Apparatus Lab (5 Trials) • WebAssign Problems 5.1 - 5.11

  41. UEQ #1: How do forces affect the motion of objects? UEQ #2: What affects the forces acting on or between objects? Day 4 Newton’s Law of Gravity Coulomb’s Law

  42. After Attendance Place HW on my desk Pickup and sign out your computer Log into www.plutonium-239.com Select the Warm-Up link Complete today’s warm-up and submit it Logout and return the computer to the cart

  43. Feed Back for Google Docs • Was anything confusing on google docs? • Noteworthy Student Responses

  44. Causes of Forces: Gravity EQ(s): What affects the strength of forces that act at a distance? Start: What force(s) keeps this distant planet revolving around the sun?

  45. What affects the strength of forces that act at a distance? 5-6 Newton’s Law of Universal Gravitation If the force of gravity is being exerted on objects on Earth, what is the origin of that force? Newton’s realization was that the force must come from the Earth. He further realized that this force must be what keeps the Moon in its orbit.

  46. What affects the strength of forces that act at a distance? 5-6 Newton’s Law of Universal Gravitation The gravitational force on you is one-half of a Third Law pair: the Earth exerts a downward force on you, and you exert an upward force on the Earth. When there is such a disparity in masses, the reaction force is undetectable, but for bodies more equal in mass it can be significant.

  47. What affects the strength of forces that act at a distance? 5-6 Newton’s Law of Universal Gravitation Therefore, the gravitational force must be proportional to both masses. By observing planetary orbits, Newton also concluded that the gravitational force must decrease as the inverse of the square of the distance between the masses. In its final form, the Law of Universal Gravitation reads: where (5-4) The distance between the masses

  48. What affects the strength of forces that act at a distance? 5-6 Newton’s Law of Universal Gravitation The magnitude of the gravitational constant G can be measured in the laboratory. This is the Cavendish experiment.

  49. What affects the strength of forces that act at a distance? 5-7 Gravity Near the Earth’s Surface; Geophysical Applications Now we can relate the gravitational constant to the local acceleration of gravity. We know that, on the surface of the Earth: Solving for g gives: Now, knowing g and the radius of the Earth, the mass of the Earth can be calculated: (5-5)

  50. What affects the strength of forces that act at a distance? 5-7 Gravity Near the Earth’s Surface; Geophysical Applications The acceleration due to gravity varies over the Earth’s surface due to altitude, local geology, and the shape of the Earth, which is not quite spherical.

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