Download Chapter 6 Work & Energy

Section 6-3 Gravitational Potential
Energy
Warm-Up #1
 A sailboat is moving at a constant velocity. Is work
being done by a net external force acting on the
boat?
 No work is being done. If work was being done
on the boat, the KE would change, which means
the velocity would change.
Warm-Up #2
 A ball has a speed of 15 m/s. Only one external
force acts on the ball. After this force acts, the
speed of the ball is 7m/s. Has the force done
 A. positive work
 B. zero work
 C. negative work
on the ball?
6.3 Gravitational Potential Energy
 Work done by the Force of Gravity






Wgravity = F * d = mg (ho - hf)
Where:
W = work
m = mass of the object
ho = initial height above a surface
hf = final height above a surface
6.3 Gravitational Potential Energy
 Work done by the Force of Gravity
Wgravity = F * d = mg (ho - hf)
 Notice that W may be positive or negative.
 Also notice that it is the change in height that
determines the Work done. This means that
h0 and hf do not need to be measured from
the earths' surface.

6.3 Gravitational Potential Energy
 Work done by the Force of Gravity
Wgravity = F * d = mg (ho - hf)
 This equation is valid for any path.
 The work depends only on the difference in
vertical distance (ho-hf)

Example 1
 A gymnast springs vertically upward from a
trampoline. She leaves the trampoline at a height of
1.20 m and reaches a maximum height of 4.80 before
falling back down. Ignore air resistance. Determine
the initial speed with which the gymnast leaves the
trampoline.
 Use the ideas that
 Wgravity = mg (ho - hf)
1
 W = KEf - KEo = m(vf2 - v02)
2
Gravitational Potential Energy
 Gravitational PE is the energy than an object has by
virtue of its position. For an object near the surface of
the earth, the gravitational PE is
 PEgravity = m g h
 ∆PE
= m g hf - mgho
 Where:
 h = height above an arbitrary zero level.
Example 2
 A child's mass is 18 kg. She has climbed up into a tree
and is now frightened and cannot get back down. She is
3.7 m above the ground when she calls for help. Find
her gravitational potential energy.
 PE = 652.7 J
Total Work
 The total work done in a system is

1
2
𝑊 = 𝛥𝐾𝐸 + 𝛥𝑃𝐸 = m (vf2 - v02) + mg (hf - ho)
Conservative vs. Non-conservative
Forces
 The gravitational force has an interesting property that
when an object is moved from one place to another, the
work done by gravity is NOT dependent upon the path
it takes; it merely depends upon the change in
height.
Conservative vs. Non-conservative Forces
 A force is called “conservative” when:
 the work it does on a moving object is independent
of the path between the objects initial and final position,
and
 when it does NO net work, 𝑊 = 0 , on an object
moving around a closed path, starting and finishing at
the same point.
Conservative vs. Non-conservative
Forces
 Gravity obeys both of these ‘rules’ and is
therefore a conservative force.
 Examples of non-conservative forces include:
 Kinetic frictional force (more and more
energy is lost if the path increases)
 Air resistance (more and more energy is lost if
the air conditions change = path dependent)
 Thrust
Conservative vs. Non-conservative
Forces
 In normal situations, conservative forces and
non-conservative forces act simultaneously on an
object.
 𝑊 = Wconserv + Wnon-conserv
 𝑊𝑛𝑐 = 𝛥𝐾𝐸 + 𝛥𝑃𝐸 =
1
2
m(vf2- v02)+mg(hf -ho)
Assignment
 p. 187 Focus on Concepts #11
 p. 190 #29, 31-35
 Use Energy to solve these problems, not
kinematics!