Energy

1
Chapter 5

• Energy

2
Forms of Energy

• Mechanical
• May be kinetic (associated with motion) or
  potential (associated with position)
• Chemical
• Electromagnetic
• Nuclear

3
Work - Energy and Force

• F is the magnitude of the force
• ?x is the magnitude of the objects displacement
• q is the angle between

4
Notes on Work

• Gives no information about
• time it took for the displacement to occur
• the velocity or acceleration of the object
• Work is a scalar quantity
• Work done by a force is zero when force and
  displacement are perpendicular
• cos 90 0
• For multiple forces, the total work done is the
  algebraic sum of the amount of work done by each
  force

5
More Notes on Work

• SI
• Newton meter Joule
• N m J kg m2 / s2
• US Customary
• foot pound
• ft lb
• Work can be positive or negative
• Positive if the force and the displacement are in
  the same direction
• Negative if the force and the displacement are in
  the opposite direction

6
Example of Sign for Work

• Work is positive when lifting the box
• Work would be negative if lowering the box
• The force would still be upward, but the
  displacement would be downward

7
Exmaple Problem

• An eskimo pulls a sled of salmon. A force of 120
  N is exerted on the sled via the rope to pull the
  sled 5 m
• Find the work if q0o
• Find the work if q30o
• Does it seem odd that less work is required in
  the second case?!

8
Work and Dissipative Forces

• Work can be done by friction
• The energy lost to friction by an object goes
  into heating both the object and its environment
• Some energy may be converted into sound
• For now, the phrase Work done by friction will
  denote the effect of the friction processes on
  mechanical energy alone

9
Example 5.2, and a Lesson in Graphical Display

• Consider the eskimo pulling the sled again. The
  loaded sled has a total mass of 50.0 kg
• Find the net work done for the previous two cases
• Consider the figure at right for the normalized
  net work as a function of m and q

10
Kinetic Energy

• Energy associated with the motion of an object
• Scalar quantity with the same units as work
• Work-Kinetic Energy Theorem
• Speed will increase if work is positive
• Speed will decrease if work is negative

11
Work and Kinetic Energy

• An objects kinetic energy can be likened to the
  work that could be done if object were brought to
  rest (so, the K.E. is like potential work
  content)
• The moving hammer has kinetic energy and can do
  work on the nail

12
Example

• Find the minimum stopping distance for a car
  traveling at 35.0 m/s (about 80 mph) with a mass
  of 1000 kg to avoid backending the SUV. Assume
  that braking is a constant frictional force of
  8000 N.

13
Types of Forces

• There are two general classes of forces
• Conservative
• Work and energy associated with the force can be
  recovered
• Nonconservative
• The forces are generally dissipative and work
  done against it cannot easily be recovered

14
Friction Depends on Path

• The blue path is shorter than the red path
• The work required is less on the blue path than
  on the red path
• Friction depends on the path and so is a
  non-conservative force

15
Potential Energy

• Potential energy is associated with the position
  of the object within some system
• Potential energy is a property of the system, not
  the object
• A system is a collection of objects interacting
  via forces or processes that are internal to the
  system

16
Work and Potential Energy

• For every conservative force a potential energy
  (PE) function can be found
• Evaluating the difference of the function at any
  two points in an objects path gives the negative
  of the work done by the force between those two
  points

17
Work and Gravitational Potential Energy

• PE mgy

18
Work-Energy Theorem, Extended

• The work-energy theorem can be extended to
  include potential energy
• If other conservative forces are present,
  potential energy functions can be developed for
  them and their change in that potential energy
  added to the right side of the equation

19
Conservation of Energy

• Total mechanical energy is the sum of the kinetic
  and potential energies in the system
• Other types of potential energy functions can be
  added to modify this equation

20
Quick Quiz

• Three balls are cast from the same point with
  the same speed, but different trajectories. Rank
  their speeds (from fast to slow) when they hit
  the ground.

21
Example

• A grasshopper makes a leap as shown at right,
  and achieves a maximum height of 1.00 m. What
  was its initial speed vi?

22
Non-Conservative Forces

• This young woman (at m60 kg) zips down a
  waterslide and is clocked at the bottom at 18.0
  m/s. If conservative, she should have been
  moving at 20.7 m/s.
• How much energy was lost to friction, both as an
  amount and as a percentage?

23
Springs

• Involves the spring constant, k
• Hookes Law gives the force
• F - k x
• F is the restoring force
• F is in the opposite direction of x
• k depends on how the spring was formed, the
  material it is made from, thickness of the wire,
  etc.
• The force is conservative for ideal springs, so
  there is an associated PE function

24
Spring Potential Energy

• Elastic Potential Energy
• related to the work required to compress a spring
  from its equilibrium position to some final,
  arbitrary, position x

25
Work-Energy Theorem Including a Spring

• Wnc (KEf KEi) (PEgf PEgi) (PEsf PEsi)
  
• PEg is the gravitational potential energy
• PEs is the elastic potential energy associated
  with a spring

26
Classic Spring Problem

• A block has mass m 0.500 kg. The spring has k
  625 N/m and is compressed 10 cm.
• Find the distance d traveled if q 30o.
• How fast is the block moving at halfway up?

27
Nonconservative Forces with Energy Considerations

• When nonconservative forces are present, the
  total mechanical energy of the system is not
  constant
• The work done by all nonconservative forces
  acting on parts of a system equals the change in
  the mechanical energy of the system

28
Nonconservative Forces and Energy

• In equation form
• The energy can either cross a boundary or the
  energy is transformed into a form of
  non-mechanical energy such as thermal energy (so
  the total energy is still conserved, just not the
  sum of KE and PE)

29
Power - Energy Transfer

• Often interested in the rate at which energy
  transfer takes place
• Power is defined as this rate of energy transfer
• SI units are Watts (W, but not Work)

30
Center of Mass

• The point in the body at which all the mass may
  be considered to be concentrated
• When using mechanical energy, the change in
  potential energy is related to the change in
  height of the center of mass

31
Work Done by Varying Forces

• The work done by a variable force acting on an
  object that undergoes a displacement is equal to
  the area under the graph of F versus x

32
Recall Spring Example

• Spring is slowly stretched from 0 to xmax
• W 1/2 kx2

33
Spring Energy

• The work is also equal to the area under the
  curve
• In this case, the curve is a triangle
• Area 1/2 X Base X height
• gives W 1/2 k x2