Transcript Lecture 6 (Jan. 18) - McMaster Physics and Astronomy

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Physics 1D03 - Lecture 8
1
Newton’s Laws (III)
• Blocks, ramps, pulleys and other problems
Physics 1D03 - Lecture 8
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Equilibrium

• A special case : a  0 (object doesn’t move, or moves
at constant velocity)


• Newton’s second law gives  F  ma  0
The vector sum of forces acting
on a body in equilibrium is zero
• This is equivalent to three independent component
equations:  Fx  0,  Fy  0,  Fz  0
• We can solve for 3 unknowns (or 2, in 2-D problems)
Physics 1D03 - Lecture 8
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Block on a ramp
Determine all the forces acting on this block.
Given m, θ and μk, what would the acceleration be
a) without friction
b) with friction
m
θ
Physics 1D03 - Lecture 8
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Example
A block is in equilibrium on a
frictionless ramp. What is the
tension in the rope?
T
m
f
Physics 1D03 - Lecture 8
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Quiz
The block has weight mg and is in equilibrium on
the ramp. If ms = 0.9, what is the frictional force?
A)
B)
C)
D)
0.90 mg
0.72 mg
0.60 mg
0.54 mg
37o
Physics 1D03 - Lecture 8
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Remember, when doing problems with “F=ma”
• Draw the free-body diagram carefully.
• You may need to know the direction of a from
kinematics, before considering forces (for friction).
• Any axes will do, but some choices make the algebra
simpler – set up equations for each direction.
• You need one (scalar) equation for each (scalar)
unknown, in general (the mass will often cancel out).
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Example
Obtain an expression for the stopping distance for a skier
moving down a slope with friction with an initial speed of v1.
d
θ
Find the distance given that μk=0.18, v=20m/s and θ=5.0º.
Physics 1D03 - Lecture 8
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Accelerated motion
Example: A block is pushed with a force FA at an angle to
the horizontal, find the acceleration. Friction is
given by μk.
FA
θ
m
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Question : Can we calculate μs ?
mg
f

n
Increasing  so that    max , the block slips, from
which we get:
m s  tan  max
This is an easy method of measuring ms
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
Physics 1D03 - Lecture 8
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Example
• Find the acceleration of a system of two masses m
and M, where M is the greater mass. Also, find the
tension, T, in the string.
m
M

There are two ways of solving the problem !
Physics 1D03 - Lecture 8
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Example:
m
Frictionless surfaces,
ideal pulleys, etc.
For what angle  is the
system in equilibrium?
M

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