physics 7b-1 (a/b) professor cebra
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Physics 7B-1 (A/B) Professor Cebra. Winter 2010 Lecture 9. Kinematics. Newton’s Laws of Motion. 1 st Law : The velocity of an object will not change unless acted upon by a force 2 nd Law : The net force on an object is equal to the rate of change of momentum - PowerPoint PPT PresentationTRANSCRIPT
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Physics 7B-1 (A/B)Professor Cebra
Kinematics
Winter 2010Lecture 9
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• 1st Law: The velocity of an object will not change unless acted upon by a force
• 2nd Law: The net force on an object is equal to the rate of change of momentum
• 3rd Law: For every force there is an equal but opposite force
Newton’s Laws of Motion
0F
0
pJdtF
amdt
LJAngdt
Idt
Ld
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Newton’s First Law -- Statics0F
0
Long Range ForcesAct on the center of gravity1) Gravitational Force2) Electrical Force
Contact ForcesAct the point of contactConsider every point of Contact3) Normal Forces (Perpendicular to Surface)
Can take any value needed4) Frictional Forces (Parallel to surface)
Can take any value up to msNDynamic friction = mDN
No Motion or
Constant Motion
Do sample problems here
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Newton’s First Law -- Statics
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Newton’s Second Law -- Dynamics
pJdtF
amdt
LJAngdt
Idt
Ld
F
RFv
When do we use force/torque? When do we use impulse?
Talk about vectors
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Constant Acceleration
Rotational Motion(a = constant)
Linear Motion(a = constant)
= w w0 + at v = v0 + at
q = (1/2)(w0 + w)t y = (1/2)(v0 + v)t
q = q0 + w0t + (1/2)at2 y = y0 + v0t + (1/2)at2
w2 = w02 + 2aq v2 = v0
2 + 2ay
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Applying the Kinematics Equations1) Make a drawing to represent the system being studied
2) Decide which directions will be called positive and which negative
3) In an organized way, write down the values for any of the kinematic variables (x, y, v , a, t and initial values). Be alert for the implied meaning in the phrasing of the problem. For example, the phrase “starts at rest” implies that v0 = 0.
4) Determine which equation will provide the required answer using the information given.
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Demo: Ball Drop
Independence of Directions
mgmg
Vx
y = y0 + vy0t + (1/2)ayt2
x = x0 + vx0t + (1/2)axt2
x = x0 + vx0t + (1/2)axt2
F = mg = may
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The Monkey HunterThe monkey drops from the tree the moment that the rifle is fired. Where should one aim to hit the monkey as it falls?
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The Monkey Hunter
= q arctan(h/x)
x
h
t = x/(v cos qr)
v
ym = h + vy0t + (1/2)gt2
yb = 0 + v sin qr t + (1/2)gt2
yb = ym h = vt sinqr
sinqr = (h/vt) = (h/x)cosqr
tanqr = h/x
DEMO: Monkey Hunter
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Maximum Trajectory
Demo: Water Rockets
A projectile will follow a parabolic trajectory.Which firing angle will travel the furthest?
Flight time:
y = y0 + vy0t + (1/2)ayt2 0 = 0 + v sinq t – (1/2)gt2 t = (2v/g) sinq
Distance traveled:
x = x0 + vx0t + (1/2)axt2 x = 0 + v cosq t + 0x = v2 2sinqcosq/g x = v2 sin(2q)/g
Maximum range when q=45
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Rolling Bodies
mg
q
Normal Force:FN = mg cosq
Parallel Force:FP = mg sinq
Frictional Force:f < msFN = msmg cosq
Angular Accelerationt= I a t = fR
Linear AccelerationFtot = maFtot = mg sinq – f
a = a/R
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Inclined Planes
Linear motion: s = 0 + v0t – (1/2) ((mg sin q - f)/m) t2
Demo: Inclined Planes
Which will go higher? A hoop or a frictionless puck?
Consider conservation of energy
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Rotating Projectiles
A body can rotate about a fixed pivot point.
A free body rotates about it center of gravity
DEMO: Center of Gravity
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Center of Gravity
The center of gravity (or Center of mass) is the point about which an object will rotate. For a body under goes both linear projectile motion and rotational motion, the location of the center of mass will behave as a free projectile, while the extended body rotates around the c.o.m.
Parabolic trajectory of the center of mass
Extended body rotating with constant angular velocity
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Center of Gravity
Angular impulse
Parabolic trajectory of the center of mass
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Rotating Off Axis
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Pendulum System
θ
Fgravity
Ftension
sintensionX tension FF costensionY tension FF coscos mgFF gravityR gravity
sinsin mgFF gravityT gravity
sinmgFNet
θ
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Announcements
Final Exam Room Last Name Begins With:
198 Young N - Z
1100 Social Sciences C - M
55 Roessler A - B
The final exam will be Wednesday March 17th 3:30 – 5:30
Bring a student ID with picture
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DL Sections
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