Transcript Potential Energy - McMaster University

Test Review: Examples
Chapters on the test:
- momentum
- energy/work
- oscillations
Physics 1D03 - Lecture 34
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Practice Question
• Momentum: Pg 262 # 10,15,19,20,29a,31,51
• Energy: Pg 298 # 3,5,9,15,23,25,29ab,33
Pg 332 # 2,3,7,15,29,31,39
• SHM: Pg 438 # 3,5,9,15,23,25, 43d, 47
# 65 - extra, for fun, not on test
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Momentum
• Remember, momentum is always
conserved, but energy not.
• draw a picture of Before and After, and
write down the momentum equation
• for impulse, remember, J=Δp=FΔt=area
under a F-t graph
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Example
a)
Initially at rest, a block explodes into two pieces of equal
mass. How would the velocities of the two pieces
compare ?
b)
Initially at rest in space, your arm, 1/20 of the mass of
your body, falls off and moves away with seed v. How
would the velocity of the rest of your body compare, and
in what direction would it move ?
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Example
a)
A block of mass m moving with speed v=3m/s hits a
block of mass 4m at rest and sticks to it. What will their
speed after the collision be ?
b)
how does this change if the collision is elastic ?
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Example
A ball falls down with velocity 10m/s, hits the ground and
bounces back with the same speed.
•
•
•
•
what is the change of momentum ?
what is the impulse ?
if the collision lasts 0.1s, what was the average force ?
if the force looks like below, what was the max force ?
F
t
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Energy
• Energy is conserved, but sometimes it gets
converted into a form that is difficult to
quantify, like heat or sound
• Remember kinetic and potential energy
equations: 1/2mv2 and mgh (h depends on
your point of reference).
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Example
a)
you walk up some stairs and end up 5m higher than
when you started. If your mass is 75kg, how much work
was done by gravity?
b)
you walk across a horizontal surface for 5m. How much
work was done by gravity ?
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Example
a)
A 100g bullet is shot into a 10kg block connected to a
spring with k=10N/m on a surface with μ=0.1 with
velocity of 100m/s. How far would the block compress?
b)
how much energy is in the system?
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SHM
• Simple Harmonic Motion is governed by
the equation:
x(t)=Acos(ωt+φ)
where ω comes from the equation of
motion:
a(t)=-ω2x(t)
A is the amplitude of your motion and φ is
the phase factor, or where you start.
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Springs and Pendulum
Newton’s 2nd Law:
F  ma   kx
a
2
d x
k


x
2
dt
m

k
m
F  m a   g sin 
d 2
g
 
2
dt
L

g
L
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Energy
Since we know the total energy of a SHM, we
can calculate the or displacement velocity at
any point in time:
ETot=1/2kA2 = K+U = 1/2mv2 + 1/2kx2
So, if x=0, all E is in kinetic, and v is at max
if x=A, all E is in potential, and v is zero
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Example
a)
What is the total energy of a mass/spring system with
k=20N/m and m=0.1kg if the amplitude of the motion is
2.0cm and the maximum velocity vmax=0.28m/s ?
b)
does it take more time for the mass to move from
equilibrium to A/2, or from A/2 to A ?
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Example
a)
A mass of 1.0kg is swinging on a string connected to the
ceiling of a building with a period of 10s. What is the
height of the building ?
b)
If the mass starts at θ=30o, what is its angular position at
t=4s ?
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