Transcript Potential Energy - McMaster University

Review
Physics 1D03 - Lecture 35
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Topics to study
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basic kinematics
forces & free-body diagrams
circular motion
center of mass
energy + conservation + conservative forces




0
,
F
statics 
 0
linear + angular momentum, impulse + conservation
rotational energy, rolling objects
torque, power, work
SHM, x=Acos(ωt+φ), know the graphs (signs of x,v,a)
No integrals or integration !
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MC1) Two cars are traveling down a straight road. The
statement that one car passes the other car can be tested by
solving for:
A) The time t, at which one car has a velocity greater than the
other
B) The position x, at which one car has a velocity greater than
the other
C) The time t, at which both cars have the some position x
D) The position x, at which one car has a greater acceleration
than the other.
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MC2) Four particles, each of mass m, are placed at the corners of a square of side
a. They are joined by massless and rigid rods. The square is rotated about an
axis through one corner, and perpendicular to the page. The moment of inertia
about this axis will be:
A) 5ma2
B) 4ma2
C) 3ma2
D) 2ma2
E) 1ma2
Axis of rotation
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Dynamics
The incline has an angle θ=30o and coefficient of kinetic friction
μk=0.1. If m=1kg and M=5kg, draw a FBD and determine the
acceleration of the system, and its speed when it moves 0.5m.
m
θ
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Dynamics
A block of mass M is pushed up an incline with a horizontal force
of P. If the incline has an angle of θ, determine the normal force.
P
θ
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Momentum (Linear):
Momentum, p=mv, is conserved in all collisions
(energy does not have to be conserved).
So: pi=pf
You can use a diagram and geometry to help you
decide on the sign, or simply use equations.
Momentum can be broken up into components.
v1i
m2
m1
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Momentum – Impulse
High-speed stroboscopic photographs show that the head of a golf club of
mass 200 grams is traveling at 55 m/s just before it strikes a 46-gram golf ball
at rest on a tee. After the collision, the club head travels (in the same
direction) at 40 m/s.
a) Find the speed of the golf ball just after impact.
b) If the collision lasted 0.03 second, what average force did the ball
experience?
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Angular Momentum
A particle of mass 0.4kg is attached to the 100 cm mark of a meter stick of
mass 0.1kg. The meter stick rotates on a horizontal frictionless table with
ω=4rad/s. Calculate the angular momentum of the system if the stick is
pivoted about an axis:
a) perpendicular to the table and through the 50 cm mark
b) perpendicular to the table and through the 0 cm mark
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Center of Mass
A uniform piece of sheet metal is shaped as shown below. Compute the
x and y coords of the center of mass.
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Statics
A 10,000 N shark is supported by a cable attached to a 4.0 m rod that
can pivot around the base. Calculate the cable tension needed to hold
the system in position as shown. Find the horizontal and vertical forces
exerted on the base of the rod.
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Rigid Bodies/Work
A 4m length of nylon cord is wound around a solid cylinder of radius 0.5m and
1.0kg mass. The cylinder is mounted on a frictionless axle and is initially at
rest. The cord is pulled with a=2.5m/s2.
a) how much work has been done on the cylinder if it reaches
ω=8 rad/s
b) how long will it take the spool to reach ω=8 rad/s?
c) Is there enough cord on the cylinder to reach this ω?
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Rotational Energy & Conservation of E
Determine the velocity of an object with a moment of inertia I and
mass m and radius R rolling down an incline for a distance d.
I,m
d
θ
* Know how mass distribution affects inertia
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SHM:
Remember,
2

 2f
T

k
m

in radians/sec !
g
l
* Know how to convert revolutions to radians (2π/rev)
* Know how to determine the phase constant, or use
* x,v,a equations to solve for A, phase, or ω.
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SHM
A 0.5 kg mass attached to a spring of k=8 N/m oscillates with SHM with an
amplitude of 10 cm, starting at x=0. Calculate:
a) the maximum value for the speed and acceleration
b) the speed and acceleration when the mass is at x=6cm from equilibrium
c) the time it takes the mass to move from x=0 cm to x=8 cm
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