Transcript Today`s Powerpoint

Physics 151 Week 12 Day 1
Topics: Energy, Power, Hooke’s Law, and
Oscillations (Chs. 8, 10, & 14)
Energy
Work-Energy Theorem
Similar to Constant a equation without time
Example Problems
Power
Springs
Hooke’s Law
Applications
Oscillations
Period & Frequency
Work Energy Theorem
Wnet = 
ma*Delta x * cos()= 1/2 mvf2 - 1/2 mvi2
2 * ma*Delta x = 2 * (1/2 mvf2 - 1/2 mvi2)
vf2 - vi2 = 2a*Delta x
vf2 = vi2 + 2a*Delta x
Look familiar?
Slide 10-23
Work Energy Problem 2
2. A 1000 kg car is rolling slowly across a level surface at 1
m/s, heading towards a group of small children. The doors are
locked so you can't get inside and use the brake. Instead, you
run in front of the car and push on the hood at an angle 30
degrees below the horizontal. How hard must you push to stop
the car in a distance of 1 m?
Slide 10-23
Work Energy Problem 1
A 1 kg block moves along the x-axis. It passes x = 0 with a
velocity v = 2 m/s. It is then subjected to the force shown in
the graph below.
a. Which of the following is true: The block gets to x = 5 m
with a speed greater than, less than, or equal to 2 m/s.
State explicitly if the block never reaches x = 5 m.
b. Calculate the block speed at x = 5 m.
Slide 10-23
Example Problem
A typical human head has a mass of 5.0 kg. If the head is moving
at some speed and strikes a fixed surface, it will come to rest. A
helmet can help protect against injury; the foam in the helmet
allows the head to come to rest over a longer distance, reducing
the force on the head. The foam in helmets is generally designed
to fail at a certain large force below the threshold of damage to
the head. If this force is exceeded, the foam begins to compress.
If the foam in a helmet compresses by 1.5 cm under a force of
2500 N (below the threshold for damage to the head), what is the
maximum speed the head could have on impact?
Use energy concepts to solve this problem.
Slide 10-46
Power
•
•
Same mass...
Both reach 60 mph...
Same final kinetic
energy, but
different times mean
different powers.
Slide 10-40
Power
Instantaneous Power
r r
P  F gv
Slide 10-39
Checking Understanding
Four toy cars accelerate from rest to their top speed in a certain
amount of time. The masses of the cars, the final speeds, and the
time to reach this speed are noted in the table. Which car has the
greatest power?
Car
Mass (g)
Speed (m/s)
Time (s)
A
100
3
2
B
200
2
2
C
200
2
3
D
300
2
3
E
300
1
4
Slide 10-41
Answer
Four toy cars accelerate from rest to their top speed in a certain
amount of time. The masses of the cars, the final speeds, and the
time to reach this speed are noted in the table. Which car has the
greatest power?
Car
Mass (g)
Speed (m/s)
Time (s)
A
100
3
2
B
200
2
2
C
200
2
3
D
300
2
3
E
300
1
4
Slide 10-42
Example Problem
Data for one stage of the 2004 Tour de France show that Lance
Armstrong’s average speed was 15 m/s, and that keeping Lance
and his bike moving at this zippy pace required a power of 450 W.
A. What was the average forward force keeping Lance and
his bike moving forward?
B. To put this in perspective, compute what mass would
have this weight.
Slide 10-47
The Spring Force
The magnitude of the spring force is proportional to the
displacement of its end:
Fsp = k ∆l
Slide 8-21
Hooke’s Law
The spring force is directed oppositely to the displacement. We
can then write Hooke’s law as
(Fsp)x = –k ∆x
Slide 8-22
Equilibrium and Oscillation
Slide 14-12
Frequency and Period
Period
The time t for the oscillator to make
one complete cycle
Frequency
The number of cycles in a given
amount of time.
For example: the number of cycles
per second (units => Hertz - Hz )
Linear Restoring Forces and Simple Harmonic
Motion
Slide 14-13
Sinusoidal Relationships
Slide 14-21