Download Chapter 8b

Chapter 8: Potential Energy and
Conservation of Energy part 2
Reading assignment: Chapter 9.1-9.4
Homework : (due Wednesday, Oct. 5, 2005):
Problems: Q2, 3, 6, 15, 20, 22
• One form of energy can be converted
into another form of energy.
• Conservative and non-conservative
forces
• CONSERVATION OF ENERGY
Work due to friction
If friction is involved in moving objects, work has to be
done against the kinetic frictional force.
This work is:
Wf  fk  d
Work done by non-conservative forces
1. Work done by an applied force.
(System is not _____________)
An applied force can _________ energy into or out of the system.
Example. Applying a ____________ to an object and lifting
increases the energy of the object.
 
W  F  d  F  d  cos
Black board example 7.4
Angus is pulling a 10,000 kg truck with all his
might (2000N) on a frictionless surface
for 10.0 m.
(a) How much work is the man doing?
(b) What is the speed of the truck after 10 m.
(c) What is the speed of the truck after 10 m
if there is friction?
(friction coefficient: 0.0153)
Power
Power is the
done:
Average power:
(work done per time
interval Dt)
at which work is
dW
P
dt
W
P
Dt
The power can also be expressed as:

dW  ds  
P
F
 F v
dt
dt
(Dot product)
The units of power are __________ (__/__) = watt (W)
Black board example 7.7
An elevator having a total mass of
3000 kg moves upward against
the gravitational force at a
constant speed of 9.13 m/s.
(a) What is the power delivered by
the motor?
Review Important energy formulas:
Work:
 
W  F d
 F  d  cos 
xf
W   F  x dx
 Fx  d x  Fy  d y  Fz  d z
xi
Forms of energy:
Kinetic energy :
1
K  m  v2
2
Gravitatio nal potential energy :
Ug  m g  y
1 2
Elastic potential energy : U e  kx
2
Black board example 8.2
A mass m is bobbing up and down on a
spring.
Describe the various forms of energy
of this system.
(a) At the highest point
(b) At the point where the kinetic
energy is highest
(c) At the lowest point
Black board example 8.3
Three balls are thrown from the
top of a building, all with
the same initial speed.
The first is thrown horizontally,
the second with some angle
above the horizontal and the
third with some angle below
the horizontal.
(a) Describe the motion of the balls.
(b) Rank the speed of the balls as they hit the ground.
Black board example 8.5
Nose crusher?
A bowling ball of mass m
is suspended from the
ceiling by a cord of
length L. The ball is
released from rest
when the cord makes
an angle A with the
vertical.
(a) Find the speed of the ball at the lowest point B.
(b) Assume a cord length L = 5m and an angle A = 20°.
(c) The ball swings back. Will it crush the operator’s nose?
Reading potential energy curves
Remember:
dU
____  
dx
E  ___ ____
Black board example 8.6
During a rock slide, a 520 kg rock slides from rest down a hillside that is
500 m long and 300 m high. The coefficient of friction between the
rock and the hillside is 0.25.
(a) What is the gravitational potential energy of the rock before the
slide?
(b) How much energy is transferred into thermal energy during the slide?
(c) What is the kinetic energy of the rock as it reaches the bottom of the
hill?