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Physics 131
131- Fundamentals of
Physics for Biologists I
Professor: Arpita Upadhyaya
Quiz
Q
i 10
Energy
e gy
1
Physics 131
In many of your science classes you
talk about “energy.”
energy.”
What is it?
Write down:
one word or sentence or picture
one equation
Hold up your whiteboards
Physics 131
Whiteboard,
2
TA & LA
Energy

N2 tells
ll us that
h a force
f
can change
h
an object’
object’s velocity in one of two ways:
– It can change
h
the
th speedd
– It can change the direction
A l i changes
Analyzing
h
in
i speedd
leads us to study energy.
 Analyzing
A l i changes
h
in
i direction
di ti
leads us to study rotations.

Physics 131
3
Kinetic Energy and Work
Consider an object
moving along a line
feeling a single force F
When it moves a distance
Δx how much does its
Δx,
speed change?
Physics 131
aF
net
/m
v F

t
m
v
F net
x 
x
t
m
net
x F x
v

t
m
net
4
x F x

v

m
t
net
F x
v v 
m
net
vi  v f
F x
(v f  vi ) 
2
m
net
F x
2
2
1
2 (v f  vi ) 
m
2
2
net
1
x
2 m(v f  vi )  F
net
Definitions:
Kinetic
1
energy = 2
mv
Work done
by a force F =
2
F x
Result
 ( mv )  F
Work Energy Theorem
1
2
2
net
x
5
Dimensions and Units of Energy and Work
[1/2 mv2] =M-(L/T) 2 = ML2 /T2
 1 kg-m
g 2 /s2 = 1 N-m = 1 Joule
 Other units of energy are common
(and will be discussed later)

– Calorie
– eV (electron Volt)
6
The diagram depicts two pucks on a
ffrictionless
i i l table.
bl Puck
k II iis ffour times
i
as massive as puck I. Starting from
rest, the
h pucks
k are pushed
h d across the
h
table by two equal forces.
Whiteboard,
TA & LA
Which puck will have the greater kinetic
energy upon reaching the finish line?
1. Puck I
2 Puck II
2.
3. Both will have the same.
4. There is not enough
g information to
decide.
7
Physics 131
The diagram depicts two pucks on a
ffrictionless
i i l table.
bl Puck
k II iis ffour times
i
as massive as puck I. Starting from
rest, the
h pucks
k are pushed
h d across the
h
table by two equal forces.
Whiteboard,
TA & LA
Which puck will have the greater velocity
upon reaching the finish line?
1.
2.
3.
4.
Puck I
Puck II
Both will have the same.
There
h iis not enoughh information
i f
i to
decide.
8
Physics 131
The diagram depicts two pucks on a
ffrictionless
i i l table.
bl Puck
k II iis ffour times
i
as massive as puck I. Starting from
rest, the
h pucks
k are pushed
h d across the
h
table by two equal forces.
Which puck will have the greater
momentum upon reaching the finish line?
1.
2.
3.
4.
Puck I
Puck II
Both will have the same.
There
h iis not enoughh information
i f
i to
decide.
9
Whiteboard,
TA & LA
Work in another direction:
The dot product


Suppose we are moving along a line, but the force
we are interested in in pointed in another direction?
(How can this happen?)
Only the part of the force in the direction of the
motion counts to change the speed (energy).
(energy)
 
Work  F|| r  F cos r  F  r
r
Physics 131
10
Dot products in general
 
F|| r  F  r
r
 
F  r
r  F cos r
In general, for any two vectors
that have an angle θ between them,

the dot product is defined to be

a  b  ab cos 
 
a  b  a x bx  a y by
The dot product is a scalar.
Its value does not depend on the
coordinate system we select.
Physics 131
11
Each row in the following table pairs a force vector
with a corresponding displacement resulting in work
W being done.
done
In which of these rows is the work done zero?

F

r
1
1.
2.
3.
4.
5.
5.
6.
None of the above
Whiteboard,
TA & LA
Each row in the following table pairs a force vector
with a corresponding displacement resulting in work
W being done.
done
In which of these rows is the work done positive?

F

r
1.
1.
2.
3.
4.
5
5.
6.
None of the above
Whiteboard,
TA & LA
Foothold ideas:
Kinetic Energy and Work




Newton’’s laws tell us how velocity changes.
Newton
changes The
Work--Energy theorem tells us how speed
Work
(i d
(independent
d t off direction)
di ti ) changes.
h
Kinetic energy =
1
2
mv
2
Work done by a force = Fx x or
(part of force pparallel to displacement)
(p
p
)
Work--energy theorem:
Work
F r
( 12 mv 2 )  F net r
Physics 131
14
Simplest example:
Consider the motion of two objects
j
duringg a short
time interval while they exert forces on each other.
Momentum change?
Impulse-momentum theorem!


pA  FBA t


 B  FAB t
p
A
B
Add and use N3!






pA  pB  FBA t  FAB t  ( FBA  FAB )t  0
Momentum Conservation!
15
15
Simplest example:
Consider the motion of two objects
j
duringg a short
time interval while they exert forces on each other.
KE change?
Work-energy theorem!


KE A  FBA  rA


KE B  FAB  r
B
They
y may
y each be moving
g
so although the times are
the same,the distances
might NOT be!
A
B
Add and use N3!

 

KE A  KE B  FBA  rA  FAB  rB



 FBA   rA  rB   0
??!
16
16
Foothold ideas:
Potential Energy
For some forces between objects
(gravity, electricity, springs)
springs) the work only
depends of the change in relative position of
th objects.
the
bj t Such
S h forces
f
are called
ll d conservative.
conservative
ti .
 For these forces the work done by them
 
can be
b written
itt

F  rrel  U

U is called a potential energy and can be
considered an energy of place belonging to
th two
the
t objects
bj t that
th t can be
b exchanged
h
d with
ith KE.
KE
Physics 131
17
Foothold ideas:
Potential Energy

For some forces work only depends
on the change in position. Then the work done
 
can be written
F  r
r  U
U
U is called a potential energy.
energy.

For gravity,
Ugravity = mgh
For a spring,
Uspring = ½ kx2
F electric
For
l t i force,
f
Uelectric = kCQ1Q2/r
/ 12
Physics 131
18
A young girl wants to select one of the
(frictionless) playground slides illustrated below
to give her the greatest possible speed when she reaches the
bottom of the slide. Which should she choose?
32m
3.2
1.
2.
3.
4.
1
2
3
4
5.
6.
Physics 131
She should jump straight
down
It doesn’t matter. It would
be the same for each.
each.
Whiteboard,
TA &19
LA