• Last Time:
Dynamics: Forces
Newton’s Laws of Motion Gravitation WeightNewton s Laws of Motion, Gravitation, Weight
• Today:y
Applications of Newton’s Laws of Motion
Free Body Diagrams Free Body Diagrams
HW #3 due Tuesday Sept 21 11:59 p mHW #3 due Tuesday, Sept 21, 11:59 p.m.
(Last HW before Exam #1)
Exam #1 on Thursday, Sept 23
Formula sheet will be posted by Monday night1
Formula sheet will be posted by Monday night
Tension in a Rope• The tension in a rope is the magnitude of the force exerted
along the rope.g p
section of rope with mass m
x
TT’
maTT
• Neglecting friction and the mass of the rope (m = 0):
0TT TT
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The tension is the SAME at all points along the rope.
Free‐Body Diagram• If we want to analyze the motion of an object subject to
forces we must identify ALL of the forces acting on itforces, we must identify ALL of the forces acting on it.
• A “free‐body diagram” is used to identify all of the forces that would act on an otherwise free body.ou d ac o a o e se ee body
S d / l d i i di tiSuppose dogs/sled moving in x‐directionAssuming friction is negligible …
sledn
y
Tx
3Fg
Free‐Body Diagram
sledn
sled
Tx
y
Fg
x
Fg
• Important point: Only the “action forces” are included in theImportant point: Only the action forces are included in the free‐body diagram. The reaction forces:
Force exerted by rope on dogy p g
Gravitational force exerted by sled on the Earth
Force exerted by the sled on the ground
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y g
all act on different objects (NOT on the sled!).
Free‐Body Diagram
sledn
sled
Tx
y
Fg
x
Fg
x‐direction : y‐direction :
mTamaT xx 0 mgnmay
(constant)
If sled starts from rest :
T
mgn 1 T
5
tmTtav xx 2
21 t
mTx
Objects in Equilibrium
Key Point :
Objects that are either at rest, or moving with constant velocity, are said to be in equilibrium. These objects have
l ti f 0an acceleration of a = 0.
Recall Newton’s Second Law :Recall Newton s Second Law :
amF
Since the acceleration a = 0 for an object in equilibrium :
0F 0xF The sum of the x‐components
of all the forces is 0.
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0F 0yF The sum of the y‐components
of all the forces is 0.
Example 4.5 (p. 96)
A traffic light weighing 100 N hangs f ti l bl ti d t t thfrom a vertical cable tied to two other cables, that are fastened to supports. Find the tension in each of the threeFind the tension in each of the three cables.
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Example 4.5 (p. 96)
A traffic light weighing 100 N hangs f ti l bl ti d t t thfrom a vertical cable tied to two other cables, that are fastened to supports. Find the tension in each of the threeFind the tension in each of the three cables.
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Example
An object with mass m slides down an inclined plane with an angle of θ. Assuming the plane is frictionless, what is the object’s acceleration? What is the magnitude of the normal ?
θ
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Example
An object with mass m slides down an inclined plane with an angle of θ. Assuming the plane is frictionless, what is the object’s acceleration? What is the magnitude of the normal ?
y
nx
mg cosθ θ
θi θ
10mg
mg sinθ
Example: 4.28
Two crates are connected by a light string that passes over a frictionless pulley. Find the acceleration of the 5 kg crate d th t i i th t iand the tension in the string.
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Example: 4.28
xy
T
n
T
5 0 kg
mg cosθ θ
5.0 kgT
θ
mg cosθ θ
10.0 kg
mg−mg sinθ
12mg
“Atwood’s Machine”
Two objects with m2 > m1 are connected by a light, inextensible cord, and hung over a frictionless pulley. The cord and pulley have negligible mass.
Find the magnitude of the acceleration of the system and the tensionof the system and the tension.
mm 13
12 mm
“Atwood’s Machine”
mm 14
12 mm
Example: 4.33
An 80‐kg stuntman jumps from a window of a buildingAn 80‐kg stuntman jumps from a window of a building situated 30 m above a catching net.
Assuming air resistance exerts a 100‐N force on him as he falls, determine his velocity just before he hits the net.
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Reading Assignment
• Next class: 4.6
Friction
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