Transcript Document

Lecture 9
• Newton’s Laws applied to systems with two or
more accelerated bodies.
Serway and Jewett : 5.7, 5.8
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Problems with several accelerated objects:
• Free-body diagram for each object.
• Relate forces by finding action-reaction pairs, etc.
• Look for constraints on the motion to relate accelerations.
• “F=ma” for each diagram, break into components.
• Count unknowns: do you have enough equations?
• Use algebra to solve.
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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
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Atwood’s Machine
Calculate the acceleration of the blocks.
Assume :
- no friction
- massless rope and pulley
- rope doesn’t stretch
Plan: • free-body diagram for each mass
• relate tensions, accelerations
• use Newton’s second Law
m1
Physics 1D03 - Lecture 9
m2
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Constraints on the motion:
Why are the accelerations equal (in magnitude)?
• Because the cord doesn’t stretch! Any downward
motion of m1 requires an equal upward motion of m2.
This is a constraint on the motion, which comes from
the geometry of the apparatus.
• Label directions of a consistently on both diagrams:
if m1 accelerates up, m2 accelerates down.
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Forces on m1
T1
Forces on m2
T2
a2
a1
m2g
m1g
•
•
Tensions are equal (“ideal” pulley, light rope)
Accelerations are equal in magnitude (why?), opposite in
direction
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Concept Quiz
Consider the more elaborate Atwood’s
machine shown.
Assuming the rope and pulleys are
ideal, the relation between the
accelerations will be:
a1
a ) a1  a2
b ) a1  2 a2
c ) a1 
1
2
m1
a2
m2
a2
d ) The ratio
a1
depends on the values of m1 and m2
a2
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A block of mass m1 on a rough horizontal surface is pulled with a
force FA at an angle θ to the horizontal. A ball of mass m2 is
connected to the other side, hanging over a lightweight frictionless
pulley. The coefficient of friction is given by μk.
Determine the acceleration of the system.
FA
θ
m1
m2
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Eg: Given no friction, determine the acceleration of the
system and the tension in the strings.
m2
m3
m1
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Example: How do you calculate the acceleration
of each block:
i) if the upper block doesn’t slide?
ii) if the upper block does slide?
m
M
FP
m = 1.0 kg
M = 2.0 kg
ms = 0.6
mk = 0.4
FP = 15 N
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Suggested Problems Chapter 5:
Problems 17, 25, 29, 43, 44, 62, Questions 19, 21
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