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Mechanics (2)

Mr. Klapholz Shaker Heights High School. Mechanics (2). Momentum, Energy, and Circular Motion . In nearly every physics textbook, this would be at least 3 chapters. For us, it’s half of a chapter. . Momentum ( p ). p = m v Momentum is a vector. Units: kg m s -1

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Mechanics (2)

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  1. Mr. Klapholz Shaker Heights High School Mechanics (2) Momentum, Energy, and Circular Motion. In nearly every physics textbook, this would be at least 3 chapters. For us, it’s half of a chapter.

  2. Momentum (p) • p = mv • Momentum is a vector. • Units: kg m s-1 • What is the momentum of a 2 kg object moving westward at 3 m/s? • p = mv = (2)(3) = 6 kg m/s, West

  3. Impulse and Momentum • Force is the thing that changes momentum. • The greater the duration of the force, the greater the change in momentum: • Change in Momentum = Force × Time • Definition: “Impulse” = Force × Time • So,… Dp = Impulse F×T= Dp

  4. Conservation of Momentum • Change in Momentum = Force × Time • What happens if there is no ‘external’ force acting on a system? • Change in Momentum = 0 × Time • Change in Momentum = 0 • That means the momentum does not change. • There are 7 conserved quantities in nature, and momentum is one of them.

  5. Conservation of Momentum • Can the momentum of an object change? • Yes, if a force acts on an object, then the momentum will change. • Can the momentum of a system of objects change? • Yes, if a force acts on the system, then the momentum can change. • But, if the total force that the world puts on a system is zero, then the total momentum of the system does not change.

  6. Conservation of Momentum • By far the most common types of momentum problems are ‘explosions’ and ‘collisions’. • In ‘explosions’ and ‘collisions’, the total momentum of the objects stays the same.

  7. Momentum vs. Energy • In every collision, momentum is conserved (the total momentum before equals the total momentum after). • In most collisions, energy does not appear to be conserved (the energy seems to decrease). • In one type of collision, even the energy is conserved: “elastic” collisions.

  8. Work • Work ≈ Force × Distance • Work is a scalar. • The work done by a particular force depends on how much of the force (Fcosq) is in the direction of the motion. • Work done by a force = {component of force in the direction of motion} × Distance • W = F × s × cosq • Units: Newtons × meters = Joules

  9. Example • Calculate the work done by a 100 N force if the object moves 10 m. • A) the angle between the force and the motion is 0˚. • B) the angle between the force and the motion is 45˚. • C) the angle between the force and the motion is 90˚.

  10. Solution • Work = Fscosq • Work = (100 N)(10 m)cos0˚ = (1000 J) 1 = 1000 J • Work = (100 N)(10 m)cos45˚ = (1000J)(.707)=707J • Work = (100 N)(10 m)cos90˚ = (1000 J) 0 = 0 • As the angle increases, the force is less involved in making the object move. • As the angle increases, the work done by that force decreases

  11. Kinetic Energy • Any moving object has energy. • EK = (½)Mv2 • Less commonly: EK = p2/(2M) • Motion matters more than mass.

  12. Gravitational Potential Energy • Any object with height has energy. • EP = Mgh (g = 9.8 m/s2) • What matters, is changes in height, and changes in Gravitational Potential Energy: • DEP = MgDh

  13. Work and Energy • The energy of a system, or of one object, can change. • Work done on a system increases the energy of the system. • Work done by a system decreases the energy of the system. Work = DEnergy

  14. Conservation of Energy • By far, the most common type of energy problem is when a system does not have energy added to it (or energy taken away). • For this kind of system, Work = 0. • Since Work = DEnergy, and Work = 0 in this case, … • 0 = DEnergy • So, if no work is done by (or on) a system, the total energy stays the same.

  15. Efficiency • In a perfect world, if you you drag a cart up a ramp, you would have done exactly as much work as if you had lifted it directly up to the top. • In the real world, friction makes the work we need to do greater than theoretical value. Efficiency = Ideal value ÷ Actual Value (memorize) • If the theoretical work required was 100 J, and it actually required 200 J, then what is the efficiency? • What is the greatest efficiency possible?

  16. Power • The rate at which energy changes from one form to another, is ‘power’. • Power = Energy ÷ Time • Power = Force × velocity • Units: Joules per second = Watts = W

  17. Circular Motion Intro (1 of 2) • Without exception, if an object is moving along a circular path, then the object is changing direction. • Since its direction is changing, its velocity is changing. • Since its velocity is changing, the object is accelerating (even if the speed is constant).

  18. Circular Motion Intro (2 of 2) • Acceleration requires a force. • That force is always toward the center. • That force can be due to a string, gravity, magnetism, electricity, friction, a wall,… but it always called a “centripetal” force. • At its core it is as simple as making a shopping cart turn left. To make circular motion, you must have a force toward the center.

  19. Centripetal Acceleration • The acceleration that an object has, due to its change in direction, is called centripetal acceleration. • Greater speed makes greater Centripetal acceleration. • Greater radius makes less Centripetal acceleration. • ac = v2 / R • ac= 4p2R / T2

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