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Dynamics

Dynamics. AP B: Chapter 4: 3-5, 12, 13 and Ch 5 PreAP: Ch4 and Ch7: 2,3. KEY CONCEPTS. The sum of the forces acting on objects at rest or moving with constant velocity is always ________. Zero  F = 0. Another KEY CONCEPT.

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Dynamics

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  1. Dynamics AP B: Chapter 4: 3-5, 12, 13 and Ch 5 PreAP: Ch4 and Ch7: 2,3

  2. KEY CONCEPTS The sum of the forces acting on objects at rest or moving with constant velocity is always ________. Zero F= 0

  3. Another KEY CONCEPT When a system is not in equilibrium, the sum of all forces acting must equal the __________that is acting on it . mass x acceleration F = ma

  4. Sum of forces: A crate rests on very low friction wheels. The crate and the wheels and stuff have a weight of 785 N. You pull horizontally on a rope attached to the crate with a force of 135 N. (a) What is the acceleration of the system? (b) How far will it move in 2.00 s? USE 9.8m/s2 Y Direction:Fy = 0 X Direction:Fx = ma

  5. We need to find the mass;

  6. (b) How far does it travel in 2.00 s?

  7. A 5.00 kg ball starting at rest slides down a 18.0 ramp.(a) What is the acceleration of the ball? Ignore friction. (b) If the ramp is 2.00 m long, how much time to reach the bottom? Draw FBD:

  8. Sum forces in the x direction Is it accelerating????? • Fx = ma • mg sin  = ma

  9. A 5.00 kg ball, starting at rest, slides down a 18.0 ramp. (b) If the ramp is 2.00 m long, how much time to reach the bottom?We know… acceleration = 3.03 m/s2distance it goes down the ramp Notice we pretty much ignored the y direction because there was no motion in that direction.

  10. TWO BODY PROBLEMS • Each body is treated separately • Draw a FBD of each • Analyze forces • Form equations Make sure you have your CALCULATOR today and EVERY DAY!!

  11. Two masses, 4.00 kg and 5.25 kg are connected by a light string to a frictionless pulley as shown. Find the tension in the string, and the acceleration on the system Heavy weight will move downward Lighter weight will move upward Treat as if in 1-dimension Each body experiences 2 forces Tension (T) = same magnitude for each Weight (m1g and m2g) Draw FBD

  12. For the forces on the rising mass, we use up as the positive direction: For the falling mass, down is positive Note that the acceleration on both masses is the same. Add the 2 equations:

  13. We’ve solved for the acceleration, so we can use that to find the tension:

  14. 2 blocks hang in an elevator as shown. The elevator accelerates upward at 3.00 m/s2. Find the tension in each rope. Both blocks will experience the same accelerations as the elevator, 3.00 m/s2 Look at the forces on the upper block in FBD: There is: T1 up T2 down m1g down We sum these forces: We can’t solve anything here because we have too many unknowns – the two tensions to be specific.

  15. Let us now look upon the lower block: This we can solve as there is only one unknown.

  16. Now we can find the tension on upper block:

  17. A 20.0 kg cart with very low friction wheels sits on a table. A light string is attached to it and runs over a low friction pulley to a 0.0150 kg mass. What is the acceleration experienced by the cart? Draw FBD of BOTH objects We shall choose the direction of motion to be positive. So for the cart, + = right and for the weight + = down.

  18. Sum the forces: Cart: Hanging mass: Both bodies experience the same acceleration. We can add the two equations together.

  19. 3 masses hang as shown, they are connected by light strings and your basic frictionless pulley. (a) Find the acceleration of each mass and (b) the tensions in the 2 strings. FBDs: Key point: Magnitude for the acceleration for each mass is the same. For falling masses (left side) down is positive. Up is positive on the upper mass.

  20. Sum the forces: m1 : m1g – T1 = m1a m2 : m2g + T1 – T2 = m2a m3 : T2 – m3g = m3a Add the equations and solve for the acceleration: m1g + m2g – m3g = m1a + m2 a + m3a

  21. Find the tensions:

  22. Some Friction Reminders:What is friction? • Force that resists the motion between two objects in contact with one another. Fancier definition: • Friction force caused by interaction of a body with its surroundings.

  23. Causes of Friction • Electrons of 2 surfaces in contact with each other form weak bonds • Surfaces 3) Deformation of surfaces … you have to dislodge it from the depressions … like fizzix students on a Monday…

  24. Frictional Forces • Always between two surfaces • Always parallel to the surface • In a direction that opposes motion

  25. Types of Friction • Sliding (the one we will be dealing with) • Rolling (much smaller) • Through fluids (air & water resistance)

  26. Magnitude depends on • Normal force • Heavy objects have more friction than very light ones • Material of two objects in contact • Wood on wood has different frictional force than steel on wood

  27. Types of sliding frictional forces • Static Friction (Fs): resistive force that opposes the start of motion between 2 surfaces • Kinetic Friction (Fk): resistive force between 2 surfaces which are in contact and moving

  28. Which force is BIGGER? STATIC FRICTION When at rest • microscopic surfaces of object are embedded in surface • Weak electron bonds • The depression deal When moving • Just rough surfaces bouncing off each other

  29. Frictional force is proportional to Normal Force F.U.N. Equation s coefficient of static friction k coefficient of kinetic friction coefficients depends on the two surfaces in contact

  30. Coefficients of Friction Materials Static Friction Kinetic Friction Steel on steel 0.74 0.57 Aluminum on steel 0.61 0.47 Wood on brick 0.60 0.45 Copper on steel 0.53 0.36 Rubber on concrete 1.0 0.80 Wood on wood 0.25 – 0.50 0.20 Glass on glass 0.94 0.40 Waxed wood on wet snow 0.14 0.10 Waxed wood on dry snow -- 0.040 Metal on metal (lubricated) 0.15 0.060 Ice on ice 0.10 0.030 Teflon on teflon 0.040 0.040 Synovial Joints in humans 0.010 0.0030

  31. A 0.500 kg block is on a ramp attached to a mass hanging over a low friction pulley via a light string. The ramp is elevated at 25.0. The block is accelerated up the ramp at 0.256 m/s2. What is the hanging mass? For k use 0.285.

  32. We can eliminate T by adding the two equations: We can now solve this equation for m2: But what is fk? Well, we know that it has to be:

  33. So we plug that into the equation we set up for m2:

  34. AP Physics Problem Blocks 1 and 2 of masses m1 and m2, respectively, are connected by a light string, as shown above. These blocks are further connected to a block of mass M by another light string that passes over a pulley of negligible mass and friction. Blocks 1 and 2 move with a constant velocity v down the inclined plane, which makes an angle with the horizontal. The kinetic frictional force on block 1 is f and that on block 2 is 2f. See handout for rest of question and ANSWERS!!!

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