Phy 2053 Announcements
Exam 1
Feb 17 Wednesday, 8:20 – 10:10 pm
Please get there at least 10 minutes early
Covers Chapters 1 - 5 (includes Lecture on Feb 11 Th)
Room assignments
If your last name begins with A through O, you
should go to Carleton 100
If your last name begins with P through Z, you
should go to McCarty C 100
You will be allowed one handwritten formula sheet
(both sides)
Sample exam from last year posted on website.
Previous exams & solutions available at Target copy.
Review: Energy and Work
Work done by a force F on an object:
W ≡ (F cos θ)∆x
Can Be Positive
or Negative
Kinetic Energy:
1
2
KE = mv
2
Gravitational
potential Energy:
PE = mgy
Conservation of Mechanical Energy
In any isolated system of objects interacting
only through conservative forces, the total
mechanical energy of the system remains
constant.
Ei = E f
KEi + PEi = KE f + PE f
Problem 5.46 (modified) A child of mass m starts
from rest and slides without friction from a height
h along a curved waterslide. She is launched
from a height h/5 into the pool. Find the max
height y after she leaves the waterslide.
Force is a vector:
When applying Newton’s law, we write the
x and y components separately:
∑F
x
= ma x
∑F
y
= ma y
Energy is a scalar: do NOT write energy
conservation separately in x and y components
KEi + PEi = KE f + PE f
Non-conservative forces and
mechanical energy
If nonconservative forces are present, then the
full Work-Energy Theorem must be used instead
of the equation for Conservation of Energy
Wnc = (KEf- KEi) + (PEf-PEi)
Wnc = (KEf+PEf) - (KEi+PEi)
Total final mechanical energy
Total initial mechanical energy
Example: work-energy theorem
The pendulum (mass 2 kg,
length 4 m) is released
from rest, at an angle of 30
degrees from the vertical.
When the pendulum comes
back, it only reached 28
degrees to the vertical.
Find the work done by nonconservative forces (friction
and air resistance) on the
mass.
Wnc = (KEf+PEf) - (KEi+PEi)
Spring Force
Hooke’s Law gives the
force
F=-kx
F is the restoring force
F is in the opposite
direction of x
k is spring constant
k is larger for a stiffer
spring
x = 0 is the
equilibrium position
F
Slope = -k
x
Work done by a Spring
only valid for a
W ≡ (F cos θ)∆x
constant force F
In a spring F varies linearly with x: F = - k x
To calculate work done by the spring, we need
to use the average force:
Faverage
F0 + F1 0 + (−kx)
kx
=
=
=−
2
2
2
1 2
 kx 
Work done by the spring = Ws = Faverage x =  −
( x) = − kx
2
 2
Potential Energy in a Spring
1 2
PE s = kx
2
Spring + Gravity
Wnc = (KEf – KEi) + (PEgf – PEgi) +
(PEsf – PEsi)
PEg is the gravitational potential energy
PEs is the elastic potential energy
associated with a spring
PE will now be used to denote the total
potential energy of the system
Conservation of Energy: Spring +
Gravity
The PE of the spring is added to
both sides of the conservation of
energy equation
(KE + PE g + PE s )i = (KE + PE g + PE s )f
Assuming that there is no nonconservative forces such as friction
Example #5-39
The launching mechanism of a
toy gun consists of a spring of
unknown spring constant. If
the spring is compressed by x
= 0.120 m and the gun fired
vertically as shown, the gun
can launch a 20.0 g projectile
from rest to a maximum height
of 20.0 m above the starting
point of the projectile (x=0).
(a) Find the spring constant,
and (b) find the speed of the
projectile as it moves through
the equilibrium position of the
spring.