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. Fp100N and Ffr50N. 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
  Earths 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 (v0)B)
Calculate the velocity of the marble at B.C)
Calculate the velocity of the marble at C
A
C
10m
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
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 F?x 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