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AP Physics Chapter 5

Force and Motion – I

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AP Physics
Take Quiz 5 Lecture Q&A

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Force and Acceleration
Acceleration causes ΔV Force What causes acceleration? Force: an interaction that causes acceleration Kinematics: Study of motion without consideration of force (Describe motion) Mechanics: Study of force and motion (Explain motion)
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Newton’s First Law of Motion Law ofInertia
An object with no net force acting on it remains at rest or moves with constant velocity in a straight line.
No net force is needed to keep a constant velocity. A net force is needed to change a velocity.

Net force = 0 Object at Equilibrium. A special case of Second Law of Motion.

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Interpretation of Newton’s First Law
If no net force acts on a body, we can always find areference frame in which that body has no acceleration. Inertial Frame of Reference:
– – –

Fnet = 0 on a body, then a = 0 Inertial Frame Fnet = 0 on the frame The frame moves with constant velocity. Inertia: Resistance to force Inertia ≈ Mass for now

Newton’s First Law: Law of Inertia
– –

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Newton’s Second Law of Motion
The acceleration of a body is directly proportional to the netforce on it and inversely proportional to its mass.

ΣF ⇔ ΣF = ma a= m

∑F or Fnet: net force, total force, resultant force Force is the cause, and acceleration is the effect. Unit of Force:
F = ma
m [F] = [m] [a] = kg × 2 = Newton = N s

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Practice: An experimental rocket sled can be accelerated at a constant rate from rest to 1600 km/h in 1.8 s. What is the magnitude of the requiredaverage force if the sled has a mass of 500 kg.
m km ⎛ 1000m ⎞ ⎛ 1 h ⎞ vi = 0, v f = 1600 ⎟ = 444 , ⎜ ⎟⎜ s h ⎝ km ⎠ ⎝ 3600 s ⎠ Δt = 1.8s, m = 500kg , F = ?

m Δv v f − vi 444. s − 0 m a= = = = 247. 2 Δt 1.8s Δt s

F = ma = 500kg × 247 m / s 2 = 1.24 × 105 N

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ΣFx = + all forces in + x direction

Force
Force is a vector.

− all forces in − x direction

⎧ ΣFx = max ⎪ ΣF = ma ⇒ ⎨ ΣFy =ma y ⎪ ⎩ ΣFz = maz
The acceleration component along a given axis is caused only by the sum of the force components along that same axis and not affected by force components along any other axis.

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Example: 113-62 Three forces act on a particle that moves with unchanging velocity of v = (2 m/s)i – (7 m/s)j. Two of the forces are F1 = (2N)i + (3N)j + (-2N)k and F2 = (-5N)i + (8N)j + (-2N)k.What is the third force?
ˆ ˆ F1 = (2 N )iˆ + (3N ) ˆ + ( −2 N )k , F2 = ( −5N )iˆ + (8 N ) ˆ + ( −2 N )k , j j v = (2m / s )iˆ − (7m / s ) ˆ = constant, F3 = ? j
v = constant ⇒ ΣF = 0 ⇒ F1 + F2 + F3 = 0
⎧ F3 x = − ( F1x + F2 x ) = − [ 2 N + (−5 N )] = 3N ⎪ ⇒ ⎨ F3 y = − ( F1 y + F2 y ) = − ( 3N + 8 N ) = −11N ⇒ F3 = − ( F1 + F2 ) ⎪F = − ( F1z + F2 z ) = − [ −2 N + (−2 N ) ] = 4 N ⎩ 3z

ˆ ˆ ⎡= − ⎣ ( 2 N − 5 N ) i + ( 3 N + 8 N ) ˆ + ( −2 N − 2 N ) k ⎤ j ⎦
ˆ ˆ F3 = (3N )i − (11N ) ˆ + (4 N )k j

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Two kinds of mass
Two methods to measure or use mass
Inertial mass: measure mass by comparing acceleration of this object to acceleration of an object of known mass when the same force applied to both of them.

a0 F = ma = m0 a0 ⇒ m = m0 a
Gravitational mass: measure mass bycomparing gravitational force on this object to gravitational force on an object of known mass at the same location

W W W0 W m0 ⇒ m= W = mg ⇒ g = ⇒ g = = W0 m m0 m

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But what exactly is mass?
mass ≠ weight or size intrinsic characteristic how much a body resist to force a characteristic of a body that relates a force on the body to the resulting acceleration of the body

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Free BodyDiagram
Force Diagram Draw simple diagram Draw all forces acting on the object being considered
– –



Ignore all forces this object acting on other objects Draw forces starting from center of object or at points of action Make sure each force giver can be identified

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Free-Body Diagram Example
v
N: Normal force, force of incline supporting box T: tension, force of person...
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