Chapter 5 Work and Energy

1. Chapter 5 Work and Energy

2. 6-1 Work Done by a Constant Force The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement: (6-1)

3. 6-1 Work Done by a Constant Force In the SI system, the units of work are joules: • For person walking at constant velocity: • Force and displacement are orthogonal, therefore the person does no work on the grocery bag • Is this true if the person begins to accelerate?

4. Example 6-1. A 50-kg crate is pulled along a floor. Fp=100N and Ffr=50N. A) Find the work done by each force acting on th crateB)Find the net work done on the crate when it is dragged 40m. Wnet = Wg + Wn + Wpy + Wpx + Wfr

5. Mechanical Energy • Types of Mechanical Energy • Kinetic Energy = ½ mv2 • Potential Energy (gravitational) = mgh • Potential Energy (stored in springs) = ½ kx2

6. 6-3 Kinetic Energy, and the Work-Energy Principle • Wnet = Fnetd • but Fnet = ma • Wnet = mad • v22 = v12 + 2ad • a = v22 - v12 • 2d • Wnet = m (v22 - v12) • 2 We define the kinetic energy:

7. 6-3 Kinetic Energy, and the Work-Energy Principle The work done on an object is equal to the change in the kinetic energy: (6-4) • If the net work is positive, the kinetic energy increases. • If the net work is negative, the kinetic energy decreases.

8. Example: A 145g baseball is accelrated from rest to 25m/s.A) What is its KE when released?B) What is the work done on the ball?

9. Potential Energy • Potential energy is associated with the position of the object within some system • Gravitational Potential Energy is the energy associated with the position of an object to the Earth’s surface

10. 6-4 Potential Energy In raising a mass m to a height h, the work done by the external force is We therefore define the gravitational potential energy: (6-5a) (6-6)

11. 6-4 Potential Energy Potential energy can also be stored in a spring when it is compressed; the figure below shows potential energy yielding kinetic energy.

12. 6-4 Potential Energy The force required to compress or stretch a spring is: where k is called the spring constant, and needs to be measured for each spring. k is measured in N/m. (6-8)

13. Conservation of Energy • Energy cannot be created or destroyed • In the absence of non-conservative forces such as friction and air resistance: Ei = Ef = constant • E is the total mechanical energy

14. Example: A marble having a mass of 0.15 kg rolls along the path shown below. A) Calculate the Potential Energy of the marble at A (v=0)B) Calculate the velocity of the marble at B.C) Calculate the velocity of the marble at C A 10m C B 3m

15. Ex. 6-11 Dart Gunmdart = 0.1kgk = 250n/mx = 6cmFind the velocity of the dart when it releases from the spring at x = 0.

16. h A marble having a mass of 0.2 kg is placed against a compressed spring as shown below. The spring is initially compressed 0.1m and has a spring constant of 200N/m. The spring is released. Calculate the height that the marble rises above its starting point. Assume the ramp is frictionless.

17. Nonconservative Forces • A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points. • Examples of nonconservative forces • kinetic friction, air drag, propulsive forces • Examples of conservative forces • Gravitational, elastic, electric

18. Power • Often also interested in the rate at which the energy transfer takes place • Power is defined as this rate of energy transfer • SI units are Watts (W) P = W = FΔx = Fvavg t t

19. Power, cont. • US Customary units are generally hp • need a conversion factor • Can define units of work or energy in terms of units of power: • kilowatt hours (kWh) are often used in electric bills