Transcript Potential Energy - McMaster University

Energy Examples
Serway and Jewett 8.1 – 8.3
Physics 1D03 - Lecture 22
Conservative Forces
path 1
A force is called “conservative”
if the work done (in going from
some point A to B) is the same
for all paths from A to B.
B
A
path 2
W1 = W2
An equivalent definition:
For a conservative force, the
work done on any closed path
is zero. Later you’ll see this
written as:
Total work is zero.
Physics 1D03 - Lecture 22
Conservation of mechanical energy
If only conservative forces do work,
potential energy is converted into kinetic
energy or vice versa, leaving the total
constant. Define the mechanical energy E
as the sum of kinetic and potential energy:
E  K + U = K + Ug + Us + ...
Conservative forces only: W = -DU
Work-energy theorem:
W = DK
So:
DK+DU = 0
Physics 1D03 - Lecture 22
Concept Quiz
You drop two rocks from top of a building. One has mass m
and the other mass 2m. When they hit the ground
A) they have the same speed and same kinetic energy
B) they have the same speed but the first rock has more kinetic
energy
C) they have the same speed but the second rock has more
kinetic energy
D) the second rock has a higher speed and more kinetic
energy
Physics 1D03 - Lecture 22
Concept Quiz
A particle is acted upon by only two forces, one
conservative and one non conservative, as it moves from
point A to point B. The kinetic energies of the particle at
points A and B are equal if:
A) The sum of the works done by the two forces is zero.
B) The work done by the conservative force is equal to
the work done by the non conservative force.
C) The work done by the conservative force is zero.
D) The work done by the non conservative force is zero.
Physics 1D03 - Lecture 22
Concept Quiz
If the total mechanical energy of a particle decreases,
then it is necessarily true that:
A) the kinetic energy decreases
B) the work done by the conservative forces is negative
C) the work done by non-conservative forces is negative
D) the net work done by all forces is negative
Physics 1D03 - Lecture 22
Example 1
A 10kg block on a horizontal surface is attached to a spring
with k=0.8 kN/m. The block is initially at rest at it’s
equilibrium position when a constant force P=80 N acts
parallel to the surface and is applied to the block. What is
the speed of the block when it has moved 13 cm from its
equilibrium position?
Physics 1D03 - Lecture 22
Example 2
A 6 kg block initially at rest is pulled to the right along a
horizontal surface by a constant force of P=12 N. Find
the speed of the block after it has moved d=3 m if the
surface has a coefficient of kinetic friction of 0.15.
Physics 1D03 - Lecture 22
Example 3
A block initially at rest is pulled to the right along a
horizontal surface that has μk = 0.15 by a constant force F,
which acts at an angle of θ above the horizontal.
Find the angle that will achieve the maximum possible
speed after the block has been pulled a distance d.
Physics 1D03 - Lecture 22
Solution
Physics 1D03 - Lecture 22
Example 4
A 2.0-kg block situated on a frictionless incline (angle 37o to
the horizontal) is connected to a light spring (k = 100 N/m),
as shown. The block is released from rest when the spring
is unstretched. The pulley is frictionless and has negligible
mass. What is the speed of the block when it has moved
0.20 m down the plane?
Physics 1D03 - Lecture 22
Solution
Physics 1D03 - Lecture 22