Energy and Momentum

1. Energy and Momentum

2. Types of Energy • Energy is the capacity for an object to do work • For example, when a car moves, the engine performs work to get the car going. • There are many different types of energy, including: electrical, kinetic, gravitational potential, and elastic potential to name a few. • A more complete list can be found on p. 124

3. Energy Transformation • An energy transformation occurs whenever energy changes from one form into another. • Examples of this would be a ball being held above the ground (gravitational potential) and then being released to fall to the ground (kinetic).

4. Work

5. Work • This is the energy transferred to an object • The object must move a distance as a result of the force applied • Does it matter what direction the object moves??

6. How to calculate work • Work requires a force • Work requires a distance • This leads us to say: WαF and WαΔd • This gives us: W = F Δd • The units are Newton Meters (Nm) or, more commonly, Joules (J)

7. Examples • A 600 N force is applied by a person to a dresser that moves 2 m. Find the work done if the force and the displacement are • Parallel • At right angles • Oppositely directed

8. A horse pulls a barge along a canal with a rope in which the tension is 1000N. The rope is at an angle of 10° with the towpath and the direction of the barge • How much work is done by the horse in pulling the barge 100m? • What is the net force on the barge?

9. Remember!!!! • For there to be work,

10. Positive and Negative Work • Any force applied in the same plane causes work to be done • If the force makes the object increase in speed, then it is positive work • If the force makes the object slow its speed, then it is negative work. These forces are called Dissipative Forces • All friction is negative work.

11. Gravity • When we lift something up, we do work, why is this? • When we look at this type of work, we still must look at the force we are working with • Fg = mg • This lead to the following • W = Fgd • W = mgd

12. Example • A bag of groceries of mass 8.1 kg is raised vertically without acceleration from the floor to a counter top, over a distance of 92 cm. Determine • The force needed to raise the bag without acceleration. • The work done on the bag against the force of gravity

13. Mechanical Energy

14. Mechanical energy • There are 2 types of mechanical energy • Gravitational Potential Energy • Kinetic Energy • Gravitational Potential Energy • This is energy that can be used to do work at a lower level • Kinetic Energy • This is the energy of motion

15. Determining Potential energy • To hit a nail with a hammer, what must you do? • By lifting the hammer, Δh, you also need to apply a force. • The height is measured from a starting point or equilibrium position. • The force is found by lifting the mass against gravity • Ep = FΔh • Ep = mg(-)

16. example • Assume that a 59 kg pole vaulter must raise their center of mass from 1.1 m off the ground to 4.6 m off the ground. What is the jumper’s gravitational potential energy at the top of the bar relative to where the jumper started to jump? • Ep = mgΔh • Ep = (59)(9.81)(4.6-1.1) • Ep = 2.0 x 103 J

17. Applications of mechanical energy • Grain Auger • Pile Drivers • Hydro Dams • We use this in Red Lake everyday

18. Determining kinetic energy • If you are interested in how the formula is generated, see p. 134 • Kinetic energy is the energy of motion, so what do we need? • Ek = ½ mv2

19. example • Determine the amount of kinetic energy of a 48 g dart travelling at a speed of 3.4 m/s. • Ek = ½ mv2 • Ek = ½ (.048)(3.4)2 • Ek = 0.28 J

20. Law of conservation of energy

21. Energy conservation • We know that there are many types of energy transformations • When energy changes forms, energy is conserved • What does this mean? • Energy is never lost, it just changes form • Example

22. Simple Harmonic Motion

23. Periodic Motion • Motion that repeats itself over and over • Ex: heart beats, ticking clock, moving on a swing • The time it takes for one complete cycle of the motion is called the ……. Period

24. Other Terms to Know • Cycle – One complete back and forth motion • Frequency – the number of cycles per unit time. It is measured in Hertz (Hz) • Displacement – the distance an object moves from the equilibrium position • Amplitude – the maximum displacement

25. Simple Harmonic Motion (SHM) • A type of periodic motion • Objects that vibrate with SHM are called Simple Harmonic Oscillators • An example of this is a mass on a spring, pendulums, and waves

26. Mass on a spring • When there is a mass on a spring, there are 2 forces that are acting on it. • Gravity and the Tension of the spring • Tension on the spring is governed by Hooke’s Law

27. F is Force k is the spring constant X is the displacement When the spring is stretched FT > Fg then the mass moves upwards When the spring is compressed Fg> FT then the mass moves downwards Hooke’s Law

28. A mass of 15.0 kg is suspended from a spring. If the spring has a spring constant is 6.00 N/m, what is the restoring force of the spring when the mass is 0.30 m from equilibrium? F = -kx F = -(6.00 N/m)(0.30 m) F = -1.8 N Hooke’s Law Example

29. MASS ON A SPRING e M A Stretch & Release k = the spring constant in N/m

30. Mass on a Spring Example • A 0.23 kg object vibrates at the end of a horizontal spring (k = 32 N/m) along a frictionless surface. What is the period of the vibration? T = 0.53 s

31. Hooke’s Law Cont. • If there was no force to slow the motion down, it would continue forever • The force that causes the slowing of the motion is called the Restoring Force • The Restoring force is governed by the spring constant, k

32. INITIAL AMPLITUDE time DAMPING DISPLACEMENT THE AMPLITUDE DECAYS EXPONENTIALLY WITH TIME

33. Hooke’s Law Cont. • When there is a Restoring force, the systems will become damped • Where is this idea of a damped system used in your daily life???

34. l THE PENDULUM The period, T, is the time for one complete cycle.

35. Pendulum Example • Find the length of a pendulum that has a period of 0.90 s. = 0.20 m

36. Energy in SHM • Work is done on an object when we apply a force over a distance • For a spring, the work is moving the object to its maximum displacement

37. Energy in SHM Cont. • Potential Energy stored in the spring is • Ep = ½ x • And k x • So • But the mass moves on the spring back and forth changing from Kinetic to potential Energy • Kinetic Energy is: • Total Mechanical Energy is: • ET = Ep + Ek • ET = ½ k x2 + ½ mv2

38. Circular motion and SHM • Applet

39. Impulse and Momentum

40. Impulse and Momentum Impulse and momentum play important roles in sports.

41. Bowling

42. Baseball

43. Tennis

44. Soccer

45. Karate

46. Foot ball

47. Golf

48. Impulse, p The impulse J of a force is the product of the average force and the time interval Dt during which the force acts: Impulse is a vector quantity and has the same direction as the average force. SI Unit of Impulse: newton · second = (N · s)

49. Momentum, p The linear momentum p of an object is the product of the object’s mass m and velocity v: Linear momentum is a vector quantity that points in the same direction as the velocity. SI Unit of Linear Momentum: kilogram · meter/second = (kg · m/s)

50. So What’s Momentum ? • Momentum = mass x velocity • Momentum is a measure of inertia in motion • This can be abbreviated to : momentum = mv • Or, if direction is not an important factor : momentum = mass x speed • So, A really slow moving truck and an extremely fast roller skate can have the same momentum.