Physics 211 (Fall 2015) (4 Credit Hours General Physics II ...
Welcome back to Physics 211 - Syracuse University · 2020. 8. 25. · Physics 211– Fall 2014...
Transcript of Welcome back to Physics 211 - Syracuse University · 2020. 8. 25. · Physics 211– Fall 2014...
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Physics 211– Fall 2014 Lecture 06-2 1
Welcome back to Physics 211
Today’s agenda: • Newton’s Third Law • Free Body Diagrams
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Physics 211– Fall 2014 Lecture 06-2 2
First Law: In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with constant velocity.
Second Law: Fnet = ∑Fon object = m a
Third Law: FAB = - FBA (“action = reaction”) [regardless of type of force and of motion of objects in question]
Newton’s Laws
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Physics 211– Fall 2014 Lecture 06-2 3
1. the net force on the person must be zero
2. the two forces form a Newton’s third-law pair
3. neither of the above explanations
4. both of the above explanations
6-2.1 Consider a person sitting on a chair. We can conclude that the downward weight force on the person (by the Earth) and the upward normal force on the person (by the chair) are equal and in opposite directions, because
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Physics 211– Fall 2014 Lecture 06-2 4
1. Cart A doesn’t move and Cart B moves backwards
2. Cart B doesn’t move and Cart A moves backwards
3. Both carts move in opposite directions 4. Neither cart moves
6-2.2 There are two people facing each other, each on a separate cart. If person A pushes on person B, while person B does nothing, what will be the resulting motion of the carts?
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Physics 211– Fall 2014 Lecture 06-2 5
1. greater than 2. less than 3. equal to the force that cart B exerts on
cart A 4. Need to know how fast cart A is moving.
6-2.3 Two carts collide on a level track. Cart A has twice the mass of cart B and is initially moving, while cart B is initially at rest.
The force that cart A exerts on cart B is
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Physics 211– Fall 2014 Lecture 06-2 6
A force P is applied by a hand to two blocks which are in contact on a frictionless, horizontal table as shown in the figure. The blocks accelerate together to the right. Block A has a smaller mass than block B. (a) Draw free body diagrams for each block. (b) Which block experiences the larger net force? (c) Suppose that initially the mass of block A were half that of block B. If in a subsequent experiment the mass of block A were doubled, by what factor would the acceleration change assuming the
pushing force remained constant?
A B
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Physics 211– Fall 2014 Lecture 06-2 7
1. zero 2. straight down 3. down and to the left
(along the incline) 4. not zero, but neither
2 nor 3
6-2.4 A block is held in place on a friction-less incline by a massless string, as shown. The acceleration of the block is
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Physics 211– Fall 2014 Lecture 06-2 8
1. a normal force given by vector A.
2. a normal force given by vector B.
A block is held in place on a frictionless incline by a massless string, as shown. The force on the block by the incline is
A B
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Physics 211– Fall 2014 Lecture 06-2 9
Normal force
• Always perpendicular to the surface of contact
• Generic name given to contact force between 2 objects
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Physics 211– Fall 2014 Lecture 06-2 10
Other forces
Besides normal force what other forces are present for block on inclined plane?
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Physics 211– Fall 2014 Lecture 06-2 11
Free-body diagram: Block on frictionless incline
• Show all forces exerted on the block. • Do not show forces exerted by the block on anything else.
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Physics 211– Fall 2014 Lecture 06-2 12
Geometry…
θ
θ
N
W
T x
y
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Physics 211– Fall 2014 Lecture 06-2 13
Triangle for Normal force on this inclined plane problem:
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Physics 211– Fall 2014 Lecture 06-2 14
Triangle for Tension force on this inclined plane problem:
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Physics 211– Fall 2014 Lecture 06-2 15
Force components: Block on frictionless incline
F = 0 implies all components of F are zero! Horizontal and vertical
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Physics 211– Fall 2014 Lecture 06-2 16
Solving system • Vertical equilibrium: NBPcos(θ) + WBE + TBRsin(θ) = 0
• Horizontal equilibrium: -NBPsin(θ) + TBRcos(θ) = 0
2 equations solve for NBP and TBR in terms of WBE and θ (Example in a minute)
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Physics 211– Fall 2014 Lecture 06-2 17
What have we learned? • If at rest – net force = 0, since a = 0 !
• Write down FBD – identify all forces present
• Take force components in 2 (in 2D) directions to find unknowns
• Don’t plug in numbers until end
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Physics 211– Fall 2014 Lecture 06-2 18
Sample Problem: The block has mass 577g, and the angle is 30 degrees, how much tension T1 is required to keep the block from moving?
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Physics 211– Fall 2014 Lecture 06-2 19
Solving system • Vertical equilibrium: NBPcos(θ) + WBE + TBRsin(θ) = 0
• Horizontal equilibrium: - NBPsin(θ) + TBRcos(θ) = 0
2 equations solve for NBP and TBR in terms of WBE and θ
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Physics 211– Fall 2014 Lecture 06-2 20
6-2.5: What happens if the tension is higher than this value?
1. The bus moves down the incline. 2. The bus moves up the incline. 3. The bus doesn’t move 4. The bus is lifted up into the air 5. None of the above
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Physics 211– Fall 2014 Lecture 06-2 21
6-2.6 The string that holds the block breaks, so there is no more tension force exerted on the block.
Will the magnitudes of either of the other two forces on the block (i.e., the weight and the normal force) change?
1. Both weight and normal force will change. 2. Only the weight force will change. 3. Only the normal force will change. 4. Neither one of the two forces will change.
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Physics 211– Fall 2014 Lecture 06-2 22
Geometry (2)
θ
θ
N
W θ
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Physics 211– Fall 2014 Lecture 06-2 23
Force components: Block on frictionless incline
• The string that holds the block breaks. • What does happen? • Take components now along and
perpendicular to incline
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Physics 211– Fall 2014 Lecture 06-2 24
Solving for second case • Since acceleration is down incline,
component of net force at 90 degrees to slope is zero.
NBP - WBEcos(θ) = 0 • Using second law applied to components
along incline:
a = -WBEsin(θ)/mblock
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Physics 211– Fall 2014 Lecture 06-2 25
Demo: bus on an inclined plane
T1 T2
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Physics 211– Fall 2014 Lecture 06-2 26
6-2.7 What is the smallest tension T2 that will make the bus lift up into the air?
1. The bus will be lifted if any tension T2 is applied (T2 > 0)
2. T2 > weight of the bus due to earth = WBE
3. T2 > WBE cosθ 4. T2 > WBE sinθ
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Physics 211– Fall 2014 Lecture 06-2 27
6-2.8 What will happen to the bus if the incline suddenly collapses if T=W cosθ?
1. The bus will stay in exactly the same spot
2. The bus will fall straight down 3. The bus will move a little bit down
and to the left 4. The bus will move a little bit up and to
the right
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Physics 211– Fall 2014 Lecture 06-2 28
Conclusion
• Normal forces can change when small changes are made to the situation.
• Can choose any 2 directions to find force components, but it pays to pick ones that simplify equations
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Physics 211– Fall 2014 Lecture 06-2 29
Summary • To solve problems in mechanics, identify all
forces and draw free body diagrams for all objects
• If more than one object, use Newton’s Third law to reduce number of independent forces
• Use Newton’s Second law for all components of net force on each object
• Choose component directions to simplify equations
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Physics 211– Fall 2014 Lecture 06-2 30
Weight, mass, and acceleration
• What does a bathroom scale ``weigh’’?
• Does it depend on your frame of reference?
• Consider elevators….
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Physics 211– Fall 2014 Lecture 06-2 31
Thinking about elevators…
• Y-axis: up is positive • If an elevator is moving upward, then
– if it speeds up the acceleration is _______ – If it slows down the acceleration is ______
• If an elevator is moving downward – Speeding up: a 0 – Slowing down: a 0
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Physics 211– Fall 2014 Lecture 06-2 32
6-2.6 A person is standing on a bathroom scale while riding an express elevator upwards (towards the top) in a tall office building. When the elevator is at rest, the scale reads about 160 lbs.
While the elevator is moving, the reading is frequently changing, with values ranging anywhere from about 120 lbs to about 200 lbs.
At a moment when the scale shows the maximum reading (i.e., 200 lbs) the elevator
1. Must be slowing down 2. Must be speeding up 3. could be slowing down or speeding up 4. I’m not sure.
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Physics 211– Fall 2014 Lecture 06-2 33
Sample problem: What is the force that the scale must exert on the person in the elevator? If that force is 200 lbs for a person who weighs
160 lbs at rest, how fast is the elevator accelerating?
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Physics 211– Fall 2014 Lecture 06-2 34
Conclusions
• Scale reads magnitude of normal force |NPS|
• Reading on scale does not depend on velocity (principle of relativity again!)
• Depends on acceleration only * a > 0 → normal force bigger * a < 0 → normal force smaller
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Physics 211– Fall 2014 Lecture 06-2 35
“Weight”: WOE
• Free fall: only force acting is gravity – a = g
• From Newton’s 2nd law, a = F/m – But F = WOE ( gravitational force on object
due to earth)
– So g = a = • In this class, when we say “weight” we
usually mean “force due to gravity” = “force on a scale when at rest”: WOE = mg
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Physics 211– Fall 2014 Lecture 06-2 36
Forces of friction • There are two types of situations in which
frictional forces occur: – Two objects “stick to each other” while at rest
relative to one another (static friction).
– Two objects “rub against each other” while moving relative to each other (kinetic friction).
• We will use a macroscopic description of friction that was obtained by experiment.
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Physics 211– Fall 2014 Lecture 06-2 37
Friction demo
• Static friction: depends on surface and normal force for pulled block
• Kinetic friction: generally less than maximal static friction
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Physics 211– Fall 2014 Lecture 06-2 38
The maximum magnitude of the force of static friction between two objects
The actual magnitude of the force of static friction is generally less than the maximum value.
• depends on the type of surfaces of the objects • depends on the normal force that the objects exert on
each other • does not depend on the surface area where the two
objects are touching