Physics 2111
Unit 8
Today's Concepts:a) Potential Energy
b) Mechanical Energy
Mechanics Lecture 8, Slide 1
Where are we?
Mechanics Lecture 3, Slide 2
Now we’re going to just
“rephrase” it
Work-Energy Thrm
Stuff you asked about:
Mechanics Lecture 8, Slide 3
Please review the Universal Gravity Equation unless we are saving that
for the end of the semester
Understanding what type of work is conservative and and what isn't
conservative and how it effects the equations we were given was kind of
confusing. Going over how to tell if it is conservative or not again would
help. Also, will we need to know universal gravitation energy equation (the
U(t) = (Gm1m2)/r one) for this class?
Me(With Thanos Voice): Everything .-.
The equations confused me on this one and I am confused how the
questions we answered had to do with potential energy. I think I'm missing
something here.
I understand the concepts, remembering all the formulas is the hard part
I dont even totally understand work and kinetic engery for this i more
puzzle
1) Could you go over the derivations for potential energy? 2) What Energy
formulas should we memorize for this Unit? 3) If energy is conserved, can
we set one energy equal to another (ex: mgh = 1/kx^2)? 4) On test/quiz
questions, how will we know Mechanical Energy is conserved?
Conservative Forces
Force conservative if
ׯ Ԧ𝐹 ∙ 𝑑 Ԧ𝑥 = 0
Mechanics Lecture 7, Slide 4
Examples:
Gravity, Springs
Not kinetic friction!
Potential Energy – NOTHING NEW!
Wtot = DKE
WNC + WCON = DKE
WCON = -DPE
WNC -DPE = DKE
WNC =DPE +DKE = DME
Mechanics Lecture 8, Slide 5
Example 8.1 (Box on Spring)
Mechanics Lecture 7, Slide 6
A 20kg box is placed gently on a vertical spring which compresses it 10cm. I then compress the spring an additional 40cm with my hand.
When I release the box and spring, how high will the box fly?
10cm
40cm
WNC = 0
DME = 0
DPE +DKE = 0
Example 8.2 (Skier)
A skier starts from rest and goes down a 10.4m long 25o slope. The coefficient of kinetic friction between the skis and the snow is mk=0.2.
Mechanics Lecture 8, Slide 7
At the end of the slope, he flies off a 3.5m high cliff.
What is his velocity just before he connects with the snow at the bottom of the cliff and skis coolly off for a hot chocolate?
3.5m
25o
Mechanics Lecture 8, Slide 8
Question
You and your friend both solve the problem involving
the skier. The two of you have chosen different
levels for PE = 0 in your calculations. Which of the
following quantities will you and your friend agree
on?
A. skier’s PE
B. skier’s change in PE
C. skier’s final KE
D. (A) and (C)
E. (B) and (C)3.5m
25o
Example 8.3 (Pendulum)
A pendulum consists of a mass at the end of a 3 meter long string. It is held at rest 30o from the vertical. If it is released, what is its velocity when the string is completely vertical?
Mechanics Lecture 7, Slide 9
30o3m
Mechanics Lecture 2, Slide 10
Example 8.4 (Soccer Ball)
A soccer ball is kicked at an initial velocity of 20m/sec at 30o
above the horizontal. What is it’s maximum height?
D
y
x 30o
Mechanics Lecture 8, Slide 11
Which Method to Use (some hints)
Newton’s Second Law
Given or need information in terms of timeForce is constant in direction and magnitude
Wtot = DKE
Force changes in direction or magnitude
WNC = DME (or MEo = MEf)
No non-conservative forces (e.g. no friction)
Mechanics Lecture 7, Slide 12
In which of the following situations is mechanical energy not conserved?
A. a basketball is tossed in the air and returns to its original position
B. a car applies its brakes and comes to a stop
C. a satellite orbits the earth
D. a student lowers a stereo receiver to lower shelf
E. (B) and (D)
Mechanics Lecture 8, Slide 13
A box is picked up 1 meter and not returned to its original starting position. In this case, is gravity still a conservative force?
A. yes
B. no
C. we can’t tell
Mechanics Lecture 8, Slide 14
Question
A) The block’s kinetic energy
B) The spring potential energy
C) Both A) and B)
A block attached to a spring is oscillating between point x1 (fully compressed) and point x2 (fully stretched). The spring is un-stretched at point o. At point o, which of the following quantities is at its maximum value?
o x2x1
Mechanics Lecture 8, Slide 15
Question
A) The block’s kinetic energy
B) The spring potential energy
C) Both A and B
A block attached to a spring is oscillating between point x1 (fully compressed) and point x2 (fully stretched). The spring is un-stretched at point o. At point x1, which of the following quantities is at its maximum value?
x1 o x2
Mechanics Lecture 8, Slide 16
Question
A) At x1
B) At o
C) At x2
D) At both x1 and x2
A block attached to a spring is oscillating between point x1 (fully compressed) and point x2 (fully stretched). The spring is un-stretched at point o. At which point is the acceleration of the block zero?
o x2x1
CheckPoint
x
A box sliding on a horizontal frictionless surface runs into a fixed spring, compressing it a distance x1 from its relaxed position while momentarily coming to rest.
If the initial speed of the box were doubled, how far x2 would the spring compress?
2 12x x 2 12x x2 14x xA) B) C)
Mechanics Lecture 8, Slide 17
Mechanics Lecture 8, Slide 18
Question
A box is sliding back and forth on a frictionless surface while attached to a spring. How many conservatives forces are doing work on the object?
a) 0b) 1c) 2d) 3
Mechanics Lecture 8, Slide 19
Question
A box is moving up and down while attached to a spring. How many conservatives forces are doing work on the object?
a) 0b) 1c) 2d) 3
Example 8.5 (vertical spring)
Mechanics Lecture 8, Slide 20
A 5kg box is gently hung from a vertical spring which stretches out 20cm. You then stretch the spring an additional 10cm with your hand. When you release the box, you give it an upwards shove so it has an initial velocity of 2m/sec.
How high will be box go before coming to rest?
Big point of confusion in the past!!!!
Mechanics Lecture 8, Slide 21
IMPORTANT POINT – Works every time!!!
a) define PE = 0 at the relaxed position of the spring
b) include all conservative forces doing work on the object in the PE (1 for horizontal or 2 for vertical)
Both vertical or horizontal springs
REMEMBER THIS ONE?
Mechanics Lecture 7, Slide 22
A 20kg box is placed gently on a vertical spring which compresses it 10cm. I then compress the spring an additional 40cm with my hand.
10cm
40cm
Where is we define PE=0?
How did we find the spring constant?
When I release the box and spring, how high will the box fly?
Question
(b) Bottom of
relaxed spring
(c) equilibrium
position with
mass attached
A box is gently hung from a vertical spring and it sags down from position (b) to position (c). What is it that defines position (c)? It is when
A) ½ kx2 = mghB) kx = mghC) kx = mgD) ½ kx2 = mgE) Both (A) and (C)
Mechanics Lecture 8, Slide 24
Question
(a) Top of relaxed
spring
(b) Bottom of
relaxed spring
(c) equilibrium
position with
mass attached
(d) lowest point of
oscillation
A box is hung from a vertical spring and oscillates up and down. Where is the box’s velocity maximum?
Mechanics Lecture 8, Slide 25
Question
(c) equilibrium
position with
mass attached
a) Zerob) Positivec) negative
When we solved our previous problem, what the potential energy of the box/spring system when the velocity was maximum?
A short cut of limited cases
Mechanics Lecture 8, Slide 26
Works only when the spring is vertical and the box is attached the spring
Worked out in detail in the prelecture
Trick that works some times
Mechanics Lecture 8, Slide 27
Vertical Spring with box attached
a) define PE = 0 at the equilibrium position of the spring
b) include only the force of the spring in PE.
Gravity term in PE canceled out when you moved the PE= 0 point.
Example 8.5 (vertical spring)
Mechanics Lecture 8, Slide 28
A 5kg box is gently hung from a vertical spring which stretches out 20cm. You then stretch the spring an additional 10cm with your hand. When you release the box, you give it an upwards shove so it has an initial velocity of 2m/sec.
How high will be box go before coming to rest?
When we did this problem using our previous method, the answer was H = 10.2cm. What should the answer be with our current method?
a) H’ = 10.2cmb) H’ = 20cmc) H’ = -20cmd) H’ = 8.8cme) H’ = 30.2cm
REMEMBER THIS ONE?
Mechanics Lecture 7, Slide 29
A 20kg box is placed gently on a vertical spring which compresses it 10cm. I then compress the spring an additional 40cm with my hand.
10cm
40cm
Would this trick have worked in Example 8.1?
When I release the box and spring, how high will the box fly?
Big point of confusion in the past!!!!
Mechanics Lecture 8, Slide 30
Want the one that always works?a) define PE = 0 at the relaxed position
of the springb) include both conservative forces
doing work on the object in the PE (gravity and spring)
Save yourself time for special cases?a) define PE = 0 at the equilibrium
position of the box/springb) include only spring in the PE of
the object
Good?
Mechanics Lecture 8, Slide 31
IF YOU DIDN’T UNDERSTAND THE PREVIOUS SLIDE, ASK ME NOW
OR
SEE ME LATER