Conservative forces

1. Lesson 5B
Energy Transformations in the
Presence of Friction
No Reference Pages from Nelson TB
Includes: Conservative andIncludes: Conservative and
Non-Conservative ForcesNon-Conservative Forces

2. Conservation of mechanical energy requires that all work be donerequires that all work be done
byby conservative forces.
 Consider an object that isConsider an object that is starting atat position 1 and movingand moving
towardstowards position 2. The path of the object may be controlled by. The path of the object may be controlled by
aa frictionless track (for the zigzag & curve). The speed of thetrack (for the zigzag & curve). The speed of the
object just before reachingobject just before reaching position 2 (the ground) would be(the ground) would be
equal for all 3 paths taken.equal for all 3 paths taken.
 The force causing the object to move down is theThe force causing the object to move down is the force offorce of
gravitygravity and itand it is a conservative forceis a conservative force. The. The work done by a
conservative force is independent of the path taken (W=FgΔh)
U p
W E
G r o u n d
P a t h T a k e n
P o s i t i o n 1
O b j e c t
P o s i t i o n 2
Height

3.  Consider the same diagram, but now the 3 similarConsider the same diagram, but now the 3 similar
objects are movedobjects are moved from position 2 to position 1..
The same 3 frictionless paths are taken. To moveThe same 3 frictionless paths are taken. To move
the object upwards,the object upwards, work must be done against
the force of gravity (a conservative force) and(a conservative force) and the
amount of work done is equal for all three paths
(this work, again, is equal to(this work, again, is equal to W=FgΔh, where, where Δh
is theis the vertical height fromfrom position 2 toto position 1).).
 Whenever work is done by a conservative force,
or against a conservative force, the amount of
work done is independent of the path taken.
 Other conservative forces include:Other conservative forces include: magnetic
forces, electrostatic forces (elastic forces can be(elastic forces can be
included but are not perfectly conservative).included but are not perfectly conservative).

4. Non-Conservative Forces
 The amount of work done by, or against, a non-
conservative force depends on the path taken..
 Consider a horizontal friction surface. Two identicalConsider a horizontal friction surface. Two identical
objects (objects (A & B) are moved (by sliding) to final) are moved (by sliding) to final
positions which are an equal linear distance apart.positions which are an equal linear distance apart.
The path taken in slidingThe path taken in sliding A is much longer andis much longer and
requiresrequires more work to be done. The path takenwork to be done. The path taken
movingmoving B is shorter and requires muchis shorter and requires much less work to bework to be
done.done.
N
W E
H o r i z o n t a l F r i c t i o n S u r f a c e
Start
Finish
P a t h T a k e n
A
B
A
B

5.  Non-conservative forces include:include:
Air resistance (and other drag forces),(and other drag forces), friction
as well asas well as thrust or push or pull forces..
 ToTo calculate the work done by non-conservative
forces we use the following equation:we use the following equation:
Wnc = ET-FINAL – ET-INITIAL
 In conclusion: Mechanical energy (ET) can only be
conserved if all work is done by conservative
forces. If Wnc is not equal to zero, then ET has not
been conserved.

6. Example:
 AA 50.0 kg skydiver jumps from a plane at askydiver jumps from a plane at a
height ofheight of 150 m. After pulling her. After pulling her
parachute, she falls to the ground at aparachute, she falls to the ground at a
constant 6.00 m/s. Determine the amount. Determine the amount
of work done by non-conservative forcesof work done by non-conservative forces
(perform your analysis starting when she(perform your analysis starting when she
just leaves the plane and ending whenjust leaves the plane and ending when
she is just about to hit the ground).she is just about to hit the ground).
 Ans. -7.27 x 104
J, ( 98.7% initial energy
loss)

7. Practice Problems
Additional Questions from the McGraw-Hill Textbook:
AA 2.0 g bullet initially movingbullet initially moving east with a speed ofwith a speed of 87
m/s passes through a stationary block of wood.passes through a stationary block of wood.
Upon exiting the block, the bullet moves atUpon exiting the block, the bullet moves at 12 m/s
[E]. If the length of the wood block isIf the length of the wood block is 4.0 cm,,
determine the average force that the wood exerteddetermine the average force that the wood exerted
on the bullet. {on the bullet. { Ans. 186 N [W] }
AA copy of the following questions, also from theof the following questions, also from the
McGraw Hill TB, will be, will be handed out..
 Page 251 #41, 43, 44Page 251 #41, 43, 44