Transcript Document

Newton’s Laws (IV)
• Blocks, ramps, pulleys and other problems
Physics 1D03 - Lecture 8
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To be handed in for marks on Friday !!!
A block of mass m=5kg is pulled with a force FA = 10N at
an angle θ=45o to the horizontal, find the acceleration.
Friction is given by μk=0.1.
FA
θ
m
Include you NAME and Student #
Physics 1D03 - Lecture 8
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Two blocks connected by a rope are being pulled by a horizontal
force FA. Given that F=60 N, m1=12kg and m2=18kg, and that
μk=0.1, find the tension in the rope between them and the
acceleration of the system.
T
m1
m2
FA
Physics 1D03 - Lecture 8
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Elevator go up, elevator go down
• A person of mass 70kg is standing on a scale in an
elevator at rest. What is her weight ?
• What is her weight when the elevator is accelerating
up at 5m/s2 ???
• What is her weight when the elevator is accelerating
down at 5m/s2 ???
Physics 1D03 - Lecture 8
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Pulleys
• To solve pulley problems, we assume that:
1) the pulley is frictionless
2) the pulley is massless
• Hence, the force of tension on both sides of the
pulley is the same
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Example
• Find the acceleration of a system of two masses
m=5kg and M=10kg. The angle θ=30o. No friction!
• Also, find the tension, T, in the string.
M
m
q
There are two ways of solving the problem !
Physics 1D03 - Lecture 8
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Kinematics in Two Dimensions
• Position, velocity, acceleration vectors
• Constant acceleration in 2-D
• Free fall in 2-D
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
The Position vector r
points from the origin to
the particle.
y
yj
path
(x,y)

r
xi
x

The components
of r are the coordinates (x,y) of the

particle: r  x i  y j

For a moving particle, r (t ), x(t), y(t) are functions of
time.
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Components: Each vector relation implies 2
separate relations for the 2 Cartesian components.

r  xi y j
(i, j are unit vectors)
We get velocity components by differentiation:

 dr
v
dt
 dx   dy 
 i  j
 dt   dt 
 vx i  v y j
the unit vectors are
constants
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Constant Acceleration + Projectile Motion

If a is constant (magnitude and direction), then:

 
v (t )  vo  a t


 2
1
r (t )  vo t  2 a t

Where vo
is the initial value at t = 0.
In 2-D, each vector equation is equivalent to a pair of
component equations:
x(t )  vox t  1 2 a x t 2
y (t )  voy t  1 2 a y t 2
 
2
Example: Free fall : a  g  9.8 m/s [down]
Physics 1D03 - Lecture 8
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Shooting the Gorilla
Tarzan has a new slingshot. George the gorilla hangs
from a tree, and bets that Tarzan can’t hit him. Tarzan
aims at George, and is sorry that he didn’t pay more
attention in physics class. Where should he aim?
Physics 1D03 - Lecture 8
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Example Problem
A stone is thrown upwards from the top of a 45.0 m high
building with a 30º angle above the horizontal. If the
initial velocity of the stone is 20.0 m/s, how long is the
stone in the air, and how far from the base of the
building does it land ?
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