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. F p =100N and F fr =50N. A) Find the work done by each force acting on th crate B)Find the net work done on the crate when it is dragged 40m. W net = W g + W n + W py + W px + W fr

5. Mechanical Energy Types of Mechanical Energy Kinetic Energy = ½ mv 2 Potential Energy (gravitational) = mgh Potential Energy (stored in springs) = ½ kx 2

6. 6-3 Kinetic Energy, and the Work-Energy Principle W net = F net d but F net = ma  W net = mad v 2 2 = v 1 2 + 2ad  a = v 2 2 - v 1 2 2d  W net = m (v 2 2 - v 1 2 ) 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: If the net work is positive, the kinetic energy increases. If the net work is negative, the kinetic energy decreases. (6-4)

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: E i = E f = 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 C B 10m 3m

15. Ex. 6-11 Dart Gun m dart = 0.1kg k = 250n/m x = 6cm Find the velocity of the dart when it releases from the spring at x = 0.

16. 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. h

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 = Fv avg 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