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Work and Energy

Work and Energy. Scalars are back. Review. Equations for Motion Along One Dimension. Review. Motion Equations for Constant Acceleration. 1. 2. 3. 4. Review. 3 Laws of Motion If in Equilibrium If not in equilibrium Change in Motion is Due to Force

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Work and Energy

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  1. Work and Energy Scalars are back

  2. Review • Equations for Motion Along One Dimension

  3. Review • Motion Equations for Constant Acceleration • 1. • 2. • 3. • 4.

  4. Review • 3 Laws of Motion • If in Equilibrium • If not in equilibrium • Change in Motion is Due to Force • Force causes a change in acceleration

  5. Springs and other problems • Force exerted by a spring is dependent on amount of deformity of the spring • Amount of force applied changes continuously over time • What is the velocity of an object launched from the spring?

  6. Work • Work done on an object by all forces is equal to the change in kinetic energy of the object. • This definition is valid even if the force is not constant

  7. Work – Constant Force • When a force, F, is doing work on an object, the object will move and be displaced. • The work done, by the force, F, is defined as • Where d is the objects displacement

  8. Work – Constant Force • We are only interested in the component of the force that is parallel to the direction of motion

  9. Work – Constant Force • We are only interested in the component of the force that is parallel to the direction of motion • or

  10. Joule • Work done by 1N of force to move an object 1 meter in the same direction

  11. James Prescott Joule • December 24, 1818- October 11, 1889 • The mechanical equivalent of heat • 838 ft.lbf of work to raise temperature of 1 lb of water by 1 degree farenheit • Led to the theory of conservation of energy • Helped Lord Kelvin develop the absolute scale of temperature

  12. Work – Zero, Negative, Positive • When defining work done, its always important to specify which force is acting on what object • Work done by man • Work done by gravity • Work done by barbell

  13. Total Work • Compute work done by forces individually • Then just add to get total work done on the object • Note: work is scalar

  14. Example • Farmer hitches a tractor with firewood and pulls it a distance 20m on level ground. Total weight of the sled and wood is 14700N and the tractor pulls with a constant force of 5000N at an angle 36.9o above the horizontal. There is a 3500N friction force opposing the motion. Find the work done by each of the forces and the total work done by all forces.

  15. Example

  16. Work done by non-constant force • Requires the use of integrals

  17. Energy • Energy is a hard to define concept • Simplified definition • The ability of a physical system to do work on another physical system • Many types of energy- these are much easier to define

  18. Kinetic Energy • Energy of motion • When work is done to an object the object moves • It also affects an objects speed • W>0 – object speeds up • W<0 – object slows down • W=0 – no effect

  19. Kinetic Energy • Newton’s 2nd Law

  20. Kinetic Energy

  21. Kinetic Energy • Work done is the change in kinetic energy of an object • This is translational kinetic energy

  22. Work – Energy Theorem • Assuming mass is constant • Unit of work is Joules • Unit of energy is also Joules • Note: Energy is also scalar

  23. Example • Farmer hitches a tractor with firewood and pulls it a distance 20m on level ground. Total weight of the sled and wood is 14700N and the tractor pulls with a constant force of 5000N at an angle 36.9o above the horizontal. There is a 3500N friction force opposing the motion. Suppose it’s initial speed is 2.0 m/s, what is its final speed after travelling 20m.

  24. Example

  25. Example • A 15kg block is placed on a 40o incline and allowed to slide for 5m. What is it’s final speed?

  26. Potential Energy • Energy due to a body’s configuration or surroundings. • Many different types • Springs • Electrical • Gravitational

  27. Gravitational Potential • An object held in the air has the “potential” to do work once released. • Assume object at some height • After travelling some distance y

  28. Gravitational Potential • An object held in the air has the “potential” to do work once released. • KE after travelling some distance y

  29. Gravitational Potential • An object held in the air has the “potential” to do work once released. • Amount of potential work

  30. Gravitational Potential • An object held in the air has the “potential” to do work once released. • Note: choose your origin and be consistent

  31. Example- Giancoli 6-28 • By how much does the gravitational potential energy of a 64-kg pole vaulter change if his center of mass rises 4.0m?

  32. Example- Giancoli 6-28 • By how much does the gravitational potential energy of a 64-kg pole vaulter change if his center of mass rises 4.0m?

  33. Work Done Example • What is work done to lift a block by 5 m? • If a 40o was used?

  34. Conservative and Non-conservative force • Conservative Force • Work Done is independent of the path taken • Gravity • Elastic • Electric • You can “store” energy in these types of systems by doing work on the system • Non Conservative Force • Work done depends on the path taken • Friction • Air resistance • Tension • Push-Pull from a person • Cannot define potential energy for these types of forces

  35. Conservation of Mechanical Energy • If only gravity is acting on the object • Valid for all conservative forces • If only conservative forces are acting, the total mechanical energy of a system neither increase nor decrease in any process. It stays constant- it is conserved.

  36. Conservation of Mechanical Energy • If a non-conservative force is acting on the object • Most common non-conservative energy is friction

  37. Example – From our 2nd lecture • A motorcycle stuntman rides over a cliff. Just at the cliff edge his velocity is completely horizontal with magnitude 9.0 m/s. Find the motorcycles speed after 0.50s.

  38. List the given Origin is cliff edge a=-g=-9.80m/s2 At time t=0s At time t=0.50s

  39. Split into components

  40. Calculate components independently

  41. Calculate velocity

  42. Not needed 29o below the horizontal

  43. Alternate Solution

  44. Alternate Solution

  45. Alternate Solution

  46. Problem – Young and Freedman 7.14 • A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swung so that it makes a maximum angle of 45o with the vertical. (a) What is the speed of the rock when it passes the vertical position? (b) What is the tension in the string when it makes an angle 45o with the vertical? (c) What is the tension in the string when it passes through the vertical?

  47. Problem – Serway 7.33 • A crate of mass 10.0 kg is pulled up a rough incline with an initial speed of 1.50 m/s. The pulling force is 100N parallel to the incline, which makes an angle of 20o with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.00m. (a) How much work is done by the gravitational force on the crate? (b) Determine the increase in internal energy of the crate-incline system due to friction. (c) How much work is done by the 100N force on the crate? (d) What is the change in kinetic energy of the crate? (e) What is the speed of the crate after being pulled 5m?

  48. Other types of potential energy • Elastic Potential • For Ideal Springs • If a spring is to be stretched a certain distance x • Where k is the spring constant (the spring’s stiffness) • It’s me again

  49. Potential Energy of Springs • Restoring Force • Hooke’s Law – valid for small x

  50. Potential Energy of Springs • Work done ON the spring (from equilibrium) • NO • Force is not constant • We can still use average force • Luckily F varies linearly with x

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