Transcript Chapter 5 - StrikerPhysics

Chapter 5
Work and Energy
Mechanical Energy
 Mechanical Energy is the energy that an
object has due to its motion or its position.
 Two kinds of mechanical energy:
– Kinetic Energy
– Potential Energy
 Energy is measured in [joules] = [N·m]
Work
 Mechanical Work
– A transfer of mechanical energy
– Measured in [Joules]
– In order for mechanical work to be done, a force
must move an object through a displacement
– Only the component of force in the direction of
displacement contributes to work done
Work
 Consider pushing a lawn mower with a force
at an angle:
 Force applied
along handle..
Work = F·dcosθ
Work
 Work is a scalar quantity measured in
[Joules] = [N·m]
 Work can be positive or negative
(depending on cos θ)
 Calculate Work using W = F·d·cosθ
 Net Work on an object may be zero
Examples
 Examples 5.1, 5.3 and 5.3….
When Force depends on
Displacement
 Often force is constant regardless of the
displacement of an object… notice that
Work is the area under a Force vs.
displacement graph.
 Sometimes the force becomes greater (or
weaker) as displacement increases. Then
work can only be calculated by finding the
area under a Force vs. displacement graph.
Springs!
 Fr = -kx where k is the spring constant
measured in [N/m]
Since the force is not constant, work must be
found using the area under the F vs x curve
Work – Energy Theorem for Kinetic
Energy
 K.E. = ½ mv2
 Work is a transfer of mechanical energy.
 Work – Energy Theorem says Work = Δ KE
 If positive work is done to increase an object’s speed, then
the work done is equal to the change in kinetic energy of
the object.
 When negative work is done, an objects speed (kinetic
energy) decreases.
Math Derivation
 Consider a constant horizontal force moving an object
horizontally:
 We know that F = ma
and a = (vf2 – vi2)/2x
So
F = m (vf2 – vi2)/2x
 We calculate Work using Work = F·x·cosθ
W = (m (vf2 – vi2)/2x)·x
W = ½ mvf2 – ½ m vi2
Potential Energy
 Potential Energy is stored energy.
 An object with potential energy has the potential to
do work (potential to apply force).
 Many objects have stored energy due to their
position.
 Work Done = ΔPE = PEf – PEi [Joules]
Gravitational Potential Energy
 Consider doing work on an object by lifting it
within the Earth’s gravitational field:
– Work =
F·d
= mg(yf – yi)
– Work
= mgyf – mgyi
– Work
= PEf – PEi
Potential Energy Formulas
 Gravitational:
PE = mgy
g = 9.8 m/s2
 Spring:
PE = ½kx2
k = spring constant
[N/m2]
x is displacement
Examples
 If a pendulum of mass 1.5kg swings to a
height of 2.0 meters, what is the change in
PE of the pendulum as it swings from its
lowest point to its highest point?
 A spring with a spring constant of 3.45 N/m2
is compressed by 1.5 meters. How much
work has been done on the spring?
Conservative vs. NonConservative Forces
 A force is conservative if the work done by it
in moving an object from one location to
another is independent of the path taken.
Ex. Gravity is conservative
 A force is non-conservative if the work done
by it in moving an object from one location
to another is dependent on the path taken.
Ex. Friction is non-conservative
Conservation of Mechanical
Energy
 In a conservative system (only conservative
forces acting), the Total Energy of the
System remains unchanged!
 KEf + Uf = KE0 + U0
Examples
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5.8 – Calculate Energy
5.9 – Energy Transformations
5.11 – Conservation of Energy
5.12 – Energy of a Spring
5.13 / 5.14 - Non Conservative Forces
Ex 5.9
 A 0.50 kg ball is thrown vertically upward
with an initial velocity of 10m/s. What is the
change in the balls kinetic energy between
the starting point and the maximum height?
What is the change in the balls potential
energy between the starting point and the
maximum height?
 LOOK AT pg. 155 – reference points
Example 5.11
 A painter on a scaffold drops a 1.5 kg can pf
paint from a height of 6.00m. What is the
kinetic energy of the can when the can is at
a height of 4.00m? With what speed will
the can hit the ground?
Example 5.12
 Three balls of equal mass, m, are projected
with the same speed, in different directions,
from a cliff as shown. Neglecting air
resistance, which ball would you expect to
strike the ground with the greatest speed?
Example 5.14
 A skier with a mass of 80kg starts from rest
at the top of a slope and skis down from an
elevation of 110m. The speed of the skier at
the bottom is 20m/s. Show that the system
is non-conservative. How much work is
done by the force of friction?