Physics 114B Mechanics Lecture 15 Walker: Ch' 6'24 Strings

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Physics 114B - MechanicsLecture 15 (Walker
Ch. 6.2-4)Strings SpringsApril 27, 2009

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

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Announcements

• HW4 is due at 1159 PM on Thursday, April 30.
  Homework up to 24 hours late will receive 70
  credit. I note that some students in Physics
  114B have been doing the Physics 114A Homework by
  mistake. I will give credit for this up to HW3,
  but no credit will be given after that.
• Physics 114B now has a UW GoPost discussion board
  at https//catalysttools.washington.edu/gopost/bo
  ard/jcramer/11164/
• As of today 92/96 clickers are registered.
  Clicker numbers and cumulative clicker scores (26
  max) as of Friday are currently posted on Tycho
  under Lecture Score items 1 and 2.
• If you want to request a regrade on a part of
  Exam 1, first check the solutions on the web,
  then write on a separate piece of paper a
  statement of your question or complaint, attach
  it to your graded paper. For the MC questions
  turn them in me. For the Tycho and qualitative
  questions, turn them in to Susan Hong, room C136
  PAB, by 400 PM Monday, April 27 (today).

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Lecture Schedule (Part 2)
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Strings
When you pull on a string or rope, it
becomes taut. We say that there is tension in the
string.
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Strings
The tension in a real rope will vary along
its length, due to the weight of the rope.
Here, we will assume that all ropes, strings,
wires, etc. are massless unless otherwise stated.
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The Massless String Approximation
Isolate the string and consider the forces
on it (Fnet)x TA on STB on S mSa,so TA on
S TB on S mSa ¹TB on S
A horizontal force F acts on a block that is
connected to another block by a string.
Consider the constraints and the forces.
Massless String ApproximationAssume that mS0
so that TA on S TB on S
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Pulleys and Ropes
An ideal pulley is one that simply changes
the direction of the tension
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Pulleys
Massless String Approximation
Strings and ropes often pass over pulleys
that change the direction of the tension. In
principle, the friction and inertia in the pulley
could modify the transmitted tension.
Therefore, it is conventional to assume that such
pulleys are massless and frictionless.
Massless and Frictionless Pulley Approximation
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Springs
Spring Force A stretched or compressed
spring exerts one of the most common contact
forces. A spring can either push (when
compressed) or pull (when stretched). In either
case, the tail of the vector force is attached to
the contact point. There is no special symbol for
the spring force, but we can use Fsp.
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Hookes Law for Springs
Hookes law for springs states that the
force increases linearly with the amount the
spring is stretched or compressed
The constant k is called the spring
constant. In the SI system, k has units of N/m
or kg/s2.
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Spring Forces
Hookes law for springs states that the
force increases linearly with the amount the
spring is stretched or compressed. The force is
negative because it always opposes the
compression or extension of the spring.
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Translational Equilibrium
When an object is in translational
equilibrium, the net force on it is zero
This allows the calculation of unknown or
unmeasured forces.
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Translational Equilibrium
A person lifts a bucket of water from the
bottom of a well with a constant speed v.
Because the speed is constant, the acceleration
must be zero, and the net force on the bucket is
zero, so T1 W.
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Clicker Question 1
A
B
In which situation is the tension on the
rope larger?
a. A b. B c. Both tensions are the
same d. Need to know the mass of the bucket
water.
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Example Mountain Climbing (1)
A 90 kg mountain climber is suspended from
ropes as shown. Rope 3 can sustain a maximum
tension of 1500 N before breaking. What is
the smallest that angle q can become before the
rope breaks?
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Example Mountain Climbing (2)
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Connected Objects
When forces are exerted on connected
objects, their accelerations are the same.
If there are two objects connected by a string,
and we know the force and the masses, we can find
the acceleration and the tension
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Connected Objects
We treat each box as a separate system. We
write separate equations for each and solve them
together.
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Connected Objects
If there is a pulley, it is easiest to have
the coordinate system follow the string
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Example Connected Masses
A block of mass m1 slides on a frictionless
tabletop. It is connected by a string and pulley
to a hanging mass m2. Find the acceleration
a and string tension T.
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Example Atwoods Machine
Atwoods Machine consists of two masses
connected by a string and pulley. Find the
acceleration a.
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Example Stagecraft (1)
A 200 kg set S used in a play is stored in a
loft above the stage. The rope holding the set
passes up and over a pulley, then is tied
backstage. The director tells a 100 kg stagehand
to lower the set. He unties the set, holds on to
the rope, and is hoisted into the loft. What
is his acceleration? (Assume a massless
rope and a massless frictionless pulley.)
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Example Stagecraft (2)
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Example A Bank Robbery (1)
Bank robbers have pushed a 1,000 kg safe to
a second-story floor-to-ceiling window. The plan
to break the window and lower the safe 3.0 m to
their truck. They stack up 500 kg of furniture,
tie a rope between the safe and the furniture,
place the rope over a pulley, and push the safe
out the window. What is the safes speed
when it hits the truck bed? (Assume mk0.5
between the furniture and the floor.)
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Example A Bank Robbery (2)
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End of Lecture 15

• Before Tuesday, read Walker Chapter 6.5
• Homework Assignments 4 should be submitted
  using the Tycho system by1159 PM on Thursday,
  April 30.(24 hours late Þ 70 credit)
• Register your clicker, using the Clicker link
  on the Physics 114B Syllabus page.