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Work and Energy

Work and Energy. Chapter 6. Work. What is work? Work done on an object is defined as a constant force that makes an object move a displacement. W = Fd The unit for work is the Joule (J). A Joule is also a Nm. Now let’s imagine pushing on a box at an angle…

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Work and Energy

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  1. Work and Energy Chapter 6

  2. Work • What is work? • Work done on an object is defined as a constant force that makes an object move a displacement. • W = Fd • The unit for work is the Joule (J). • A Joule is also a Nm.

  3. Now let’s imagine pushing on a box at an angle… • Work is only done by the components parallel to the displacement.

  4. Work at an Angle • If you resolve the force into its components, what is the parallel component? • It’s the cosine of the angle! • This means that the equation for work can be changed: • W = Fnetd(cos Θ) • When a force is applied at an angle, only the parallel component of the force applies to the work done on the object. • The perpendicular component does not do any work on the object.

  5. More Work? • Let’s consider carrying a book from the front of the room to the back of the room. Was work done? • NO!!!! No work was done because the force was applied in the vertical direction and did not make the object move horizontally.

  6. Work is Scalar • Work is a scalar quantity. • What was a scalar again? • Work has only a magnitude and no direction, however we can have positive and negative work. • Positive work means that the force contributes to the displacement. Negative work means that the force opposes the displacement. • Can you think of a force that acts against the direction of the displacement?

  7. Net Work • What happens to the work if you have more than one force applied to the object? • The total work is the sum of all the individual works. • Example: pyramid building • Wnet = FnetΔx

  8. By vs On • When talking about work, make sure that you distinguish between work done on and object and work done by an object. • What does that mean? • Example of work done on: pushing a box • Example of work done by: crane lifting a box

  9. Problem 1 • A 50 kg crate is pulled 40 m along a horizontal floor by a constant force of 100 N at an angle of 37o above the horizontal. The floor exerts a frictional force of 50 N. Determine the work done by each force and the net work done on the crate.

  10. Problem 2 • Determine the work a hiker must do on a 15 kg backpack to carry it up a hill of height 10.0 m. Also determine the work done by gravity on the backpack and the net work done on the backpack.

  11. Work Done by a Constant Force Centripetal forces do no work, as they are always perpendicular to the direction of motion.

  12. Force vs Displacement Graphs • When the force is constant, we can also find the amount of work done by looking at the Force vs Displacement graph.

  13. Problem 3 • What is the work done on the graph below?

  14. Work Done by a Varying Force • The definition of work stated earlier only applies to constant forces. • If the force varies, we have to calculate work a little differently. • For example, how do we calculate the work done by a rubber band?

  15. x F F m x Hooke’s Law • When a spring or a rubber band are stretched, there is a restoring force present that can be calculated using the following: • Work done ONthe spring is positive. • Work BY the spring is negative. • Work done will still be the area of the graph F = -kx Work = ½ kx2

  16. Problem 4 • A 4-kg mass suspended from a spring produces a displacement of 20 cm. What is the spring constant? How much work is done when the spring is stretched from 0 cm to 30 cm?

  17. Force vs Displacement Graphs • For a force that varies, the work can be approximated by dividing the distance up into small pieces, finding the work done during each, and adding them up. As the pieces become very narrow, the work done is the area under the force vs. distance curve.

  18. Energy

  19. Energy • Energy is defined as the ability to do work. • We also refer to energy for motion as mechanical energy. • There are two kinds of energy: • Kinetic Energy • Potential Energy

  20. Kinetic Energy • What does kinetic mean? • Kinetic means moving. Kinetic energy is the energy of motion. • In this chapter, we will only be dealing with translational motion. • KE = ½ mv2 • What is the unit for energy?

  21. Facts About KE • Kinetic energy depends on the mass as well as the velocity. • This means that an object moving more slowly can have more kinetic energy than a fast moving energy if it is more massive.

  22. Work-Energy Principle • The work done is equal to the change in the kinetic energy • If the net work is positive, the kinetic energy increases. • If the net work is negative, the kinetic energy decreases.

  23. Problem 5 • A 20-g projectile strikes a mud bank, penetrating a distance of 6 cm before stopping. Find the stopping force F if the entrance velocity is 80 m/s.

  24. Problem 6 • On a flat frozen pond, Bob kicks a 10 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.1?

  25. Potential Energy • Potential energy is the energy that is stored due to the position of the object. • Potential energy is energy that is present because of its position relative to some other location. • Potential energy relies on not only the properties of the object but also how it will interact with its environment.

  26. Gravitational Potential Energy • Let’s think about a pen balanced on the edge of a desk… • It has potential energy based on the fact that gravity will pull it down. Energy associated with a gravitational pull is called gravitational potential energy. • Ug = mgh • The unit for PE is still the Joule.

  27. Elastic Potential Energy • Potential energy can also be stored in a spring or an elastic that can be stretched or compressed. This type of potential energy is called Elastic Potential Energy. • Ue = ½ kx2 • k= the spring constant (N/m) • x= distance compressed or stretched

  28. Problem 7 • A 70 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally stops, the cord has stretched to a length of 44.0 m. Assuming the spring constant is 71.8 N/m, what is the total potential energy relative to the water when the man stops falling?

  29. Conservation of Energy

  30. Conservation of Energy • When the pen was dropped off of the table, the pen’s velocity increases as it falls. • What is happening is that the pen’s potential energy is being converted into kinetic energy. • When the pen hits the ground, all of the potential energy it had while it was on the table has been converted into kinetic energy.

  31. Conservative Forces vsNonconservative Forces • Gravitational potential energy is independent of the path that the object takes. The potential is based off of the height, not how you got it there. It is a conserved force. • If friction is present, the work done depends not only on the starting and ending points, but also on the path taken. Friction is called a nonconservative force. • Work done by nonconservative forces cannot be restored. Energy is lost and cannot be regained.

  32. Conservative Forces vs Nonconservative Forces • Potential energy can only be defined for conservative forces.

  33. Conservative and NonconservativeForces • Therefore, we distinguish between the work done by conservative forces and the work done by nonconservative forces. • We find that the work done by nonconservative forces is equal to the total change in kinetic and potential energies: (U + K)o = (U + K)f + Losses

  34. Mechanical Energy and Its Conservation • If there are no nonconservative forces, the sum of the changes in the kinetic energy and in the potential energy is zero – the kinetic and potential energy changes are equal but opposite in sign. • This allows us to define the total mechanical energy:

  35. Mechanical Energy • Let’s think about a grandfather clock… • As the pendulum swings back and forth, it has both potential energy and kinetic energy. • Mechanical energy is the sum of both the kinetic energy and all forms of the potential energy. • ME= KE + Ug + Ue

  36. Conservation of Energy • When we say that energy is neither created nor destroyed, we mean that whatever you start out with, you end up with. • MEi = MEf • This can also be written this way:

  37. Problem 8 • A ball is released from a height of 20 m. What is its velocity when its height has decreased to 5 m?

  38. s h 30o Problem 9 • How far up the 30o incline will a 2-kg block move after being released? The spring constant is 2000 N/m and it is compressed by 8 cm.

  39. A L vc B d r U = 0 Problem 10 • A mass m is connected to a cord of length L and held horizontally as shown. What will be the velocity at point B? (d = 12 m, L = 20 m)

  40. Roller Coasters and Energy • It is important to note that energy is conserved regardless of the path it takes when we have conserved forces. • Let’s consider a rollercoaster…

  41. Other Types of Energy • Some other forms of energy: • Electric energy, nuclear energy, thermal energy, chemical energy. • Work is done when energy is transferred from one object to another. • Accounting for all forms of energy, we find that the total energy neither increases nor decreases. Energy as a whole is still conserved.

  42. Energy Conservation with Dissipative Processes • If there is a nonconservative force such as friction, where do the kinetic and potential energies go? • They become heat; the actual temperature rise of the materials involved can be calculated.

  43. Power

  44. What is Power? • Power is the rate at which work is done. • More simply translated, P= Work/time • What are the units for Power? • The units for Power are watts (W). One watt is a J/s. • Another unit for power is horsepower. • 1 hp = 746 watts

  45. The Alternative • W = Fd so if we substitute this for W in the power equation, we can get an alternative equation for power. • P = Fv • Power is equal to the force times the speed.

  46. Problem 11 • A 70 kg jogger runs up a long flight of stairs in 4.0 s. The vertical height of the stairs is 4.5 m. Estimate the jogger’s power output in watts and horsepower. How much energy is required?

  47. Problem 12 • A 100-kg cheetah moves from rest to 30 m/s in 4 s. What is the power dissipated by the cheetah?

  48. Working Hard for the Money… • Something to keep in mind… • Who has more power, the muscle man that lifts 500 lbs 2 meters in 1 minute or the little dude who lifts 50 lbs 2 meters in 6 s? • Two things can have the same power rating. It has to do with the time involved and the work done.

  49. Turn off the Lights! • We are usually more familiar with the term power when it comes to electricity. • We pay for kWh. The going rate of electricity is about $0.126 per kWh. • What is a kWh? • If you turn on your outside light that is 60 w for 8 hours a day for a month (31 days), how much would it cost? • $1.87!

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