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Chapter 4
NEWTONS LAWS
Newton’s 3 Laws
Force Diagrams
Equilibrium
Unbalanced Forces
Terminal Velocity
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Newtons 1st Law: Law of Inertia
A body at rest remains at rest,
A body in motion remains in motion, at a constant velocity, in a straight line
Until an Unbalanced force acts on it.
INERTIA: Tendency to resist changes in motion.
Inertia is a property of matter
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Newtons 2nd LawAn unbalanced force causes acceleration
Acceleration is:
• directly related to force.
• inversely related to mass.
𝑎 = 𝐹𝑚
1 kg * 1m/s2 = 1 Newton
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Newtons 3rd Law
• When one object exerts a force on a second object, the 2nd object exerts an equal Force in the opposite direction on the first object.
• For every action there is an equal and opposite reaction.
• All Forces come in pairs, equal in magnitude, opposite in direction.
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Force Diagrams (Free Body Diagrams)
• Identify the object you will draw a diagram for.
• Identify all the forces acting directly on the object and the object exerting them.
• Draw a dot or line to represent the object of interest.
• Draw a vector from the dot to represent each force. Draw it in the direction the force is being exerted.
• Label it by (a) the type of force, and/or(b) the object exerting the force
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Force Diagrams (Free Body Diagrams)Determine the net Force on each object below,
• If the vectors should graphically add up to zero, the object is stationary or is moving at a constant velocity,
• If the object is accelerating, the sum of the vectors should produce a vector in the same direction as the acceleration.
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Balanced Forces• Equilibrium :
• Net Force = Zero• Object is at rest or moving at a constant velocity
Tacos(10 kg) PIZZA (5kg)
40o 40o
Find the Tension on each chain
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Balanced Forces The ninja has a mass of 50 kg, ϴ =30o
Find the Tension in Each Rope
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Unbalanced ForcesWorker pushes a 100 kg box with a Force of 85N. Friction exerts a Force of 65 N. What is the acceleration of the box?1) Draw Force diagram
2) Determine Net Force
3) Solve the Problem
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Unbalanced ForcesA Rescue Helicopter lifts 2 people with a total mass of 200kg with an acceleration of 3.0m/s2.
What is the Tension on the Rope holding the people?
1) Draw Force diagram2) Determine Net Force3) Solve the Problem
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Riding in an elevator
A 50 kg woman is standing on a scale in an elevator. The scale reads 55kg. What is the acceleration of the elevator?
A 50 kg woman is standing on a scale in an elevator. The scale reads 45kg. What is the acceleration of the elevator?
A 50 kg woman is standing on a scale in an elevator. The scale reads 0 kg. What is happening to the elevator?
1) Draw Force diagram2) Determine Net Force3) Solve the Problem
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Unbalanced Forces
Net Force = ?Net Force = ?Net Force = ?
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TERMINAL VELOCITY
Drag Force – Force exerted by fluid that resist motion
Depends on many factors, most importantly:Properties of FluidSpeed of object in fluidInteraction between object on fluidArea of object
Can be modeled:
Slow speed: 𝐹 = 𝑘𝑣
High speed: 𝐹 = 𝑘𝑣2
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TERMINAL VELOCITY
• Drag Force increases as velocity increases.
• Acceleration Decreases as Velocity increases
• Net Force Decreases as velocity increases
𝐹𝑛𝑒𝑡 = 𝑚𝑔 𝐹𝑛𝑒𝑡 = 𝐹𝑑 −𝑚𝑔 0 = 𝐹𝑑 −𝑚𝑔
𝐹𝑑 = 𝑚𝑔
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TERMINAL VELOCITY
• Occurs when the drag force is equal to the weight of falling object
• Occurs when the net force on a moving object is zero
𝐹 = 𝑘𝑣 = 𝑚𝑔 → 𝑣 =𝑚𝑔
𝑘
Or
𝐹 = 𝑘𝑣2 = 𝑚𝑔 → 𝑣 =𝑚𝑔
𝑘
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TERMINAL VELOCITY• Slow speed: 𝐹 = 𝑘𝑣
• High speed: 𝐹 = 𝑘𝑣2
• Force depends on Velocity → acceleration depends on force →change in velocity depends on velocity Example:
𝐹𝑛𝑒𝑡 = 𝑚𝑔 − 𝐹𝑑
𝑚𝑎 = 𝑚𝑔 − 𝑘𝑣
𝑚𝑑𝑣
𝑑𝑡= 𝑚𝑔 − 𝑘𝑣
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Determine Velocity based on time
• 𝐹𝑛𝑒𝑡 = 𝑚𝑔 − 𝐹𝑑
• 𝑚𝑎 = 𝑚𝑔 − 𝑘𝑣
• 𝑚𝑑𝑣
𝑑𝑡= 𝑚𝑔 − 𝑘𝑣
𝑚𝑑𝑣
𝑑𝑡= 𝑚𝑔 − 𝑘𝑣
න𝑑𝑣
𝑣 − 𝑣𝑡= −
𝑘
𝑚න𝑑𝑡
𝑙𝑛𝑣𝑡 − 𝑣
𝑣𝑡= −
𝑘
𝑚𝑡
1 −𝑣
𝑣𝑡= 𝑒
−
𝑘
𝑚 𝑡
𝑣 = 𝑣𝑡[1 − 𝑒−
𝑘
𝑚 𝑡]
𝑣 = 𝑣𝑡[1 − 𝑒−
𝑘
𝑚 𝑡]
𝑎 = 𝑔𝑒−
𝑘
𝑚 𝑡