department of physics and applied physics 95.141, f2010 lecture 9 physics i 95.141 lecture 10...
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Department of Physics and Applied Physics95.141, F2010 Lecture 9
Physics I95.141
LECTURE 1010/6/10
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Exam Prep Problem
• Two blocks are connected by a cord/pulley system, as shown below. mB=5kg. The surface under block B has μS=0.6 and μS=0.4.
• A) (5pts) Draw the free body diagram for the blocks. Show coordinates for each.
• B) (10pts) The mass of mA is slowly increased from zero, at what mass mA will the system start to move? What will its acceleration be for this value of mA?
• C) (10pts) What is the acceleration of the system if mA is 10kg?
A
B
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Exam Prep Problem
• Two blocks are connected by a cord/pulley system, as shown below. mB=5kg. The surface under block B has μS=0.6 and μS=0.4.
• A) (5pts) Draw the free body diagram for the blocks. Show coordinates for each.
A
B
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Exam Prep Problem
• Two blocks are connected by a cord/pulley system, as shown below. mB=5kg. The surface under block B has μS=0.6 and μK=0.4.
• B) (10pts) The mass of mA is slowly increased from zero, at what mass mA will the system start to move?
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Exam Prep Problem
• Two blocks are connected by a cord/pulley system, as shown below. mB=5kg. The surface under block B has μS=0.6 and μK=0.4.
• B) (10pts) The mass of mA is slowly increased from zero, at what mass mA will the system start to move? What will its acceleration be for this value of mA?
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Exam Prep Problem
• C) (10pts) What is the tension in the cord if mA is 10kg?
Department of Physics and Applied Physics95.141, F2010 Lecture 9
EXAM 1 Results
• Results from exam were pretty good!• However, you were given problems ahead of
time, and there were only 3 problems.• Future exams will be harder!!• In order to do well, you need to put the time in to
study• If your grade is <50, you NEED to take
advantage of the resources we offer!!
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
# S
tud
en
ts
Score
Mean: 62STDEV: 20
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Outline
• Velocity Dependent Forces• Uniform Circular Motion• Highway curves (banked/unbanked)
• What do we know?– Units– Kinematic equations– Freely falling objects– Vectors– Kinematics + Vectors = Vector Kinematics– Relative motion– Projectile motion– Uniform circular motion– Newton’s Laws– Force of Gravity/Normal Force– Free Body Diagrams– Problem solving
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Drag Forces
• Force acting on an object as it moves through a Fluid or Gas.– Boat in water– Any motion in air
• Cars• Skydivers• Projectile motion
• Mathematics of velocity dependent Forces is tricky, but a good approximations are:
bvFD 2bvFD
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Terminal Velocity
• If we assume drag force is:• What is terminal velocity of a skydiver?
bvFD
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Uniform Circular Motion (Ch. 5.2-5.4)
• It might seem counterintuitive, but another type of constant acceleration problem comes from uniform circular motion moving at constant speed in a circular path. y
x
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Uniform Circular Motion (Ch. 5.2-5.4)
• It might seem counterintuitive, but another type of constant acceleration problem comes from uniform circular motion.
y
x
R
• It is easiest to describe circular motion in polar coordinates
Rarclength
,R
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Uniform Circular Motion
• To find tangential speed:
y
x
R dd
Rdd
Tv
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Uniform circular motion
• Example– A record spins at 45rpm– A) Do you know what a record is?– B) What is the record’s angular velocity?– C) What is the tangential speed of a bug sitting 4cm away from the
center of the record?
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Uniform Circular Motion
• Period of rotation– Angular velocity tells us the radians/s– Period is the time it takes to make one rotation
– Frequency f is #rev/s or Hertz (Hz)
TvR T2
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Uniform Circular Motion (acceleration)
• Tangential speed is constant, but velocity is not!
)(tr
)( dttr
)( dttvT )(tvT
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Uniform Circular Motion (acceleration)
)( dttvT
)(tvT
dt
tvdttv
dt
vda
)()(
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Uniform Circular Motion (acceleration)
• What about somewhere else on the circle?
)(tr
)( dttr
)( dttvT
)(tvT
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Acceleration (mathematically)
)(tr
)( dttr
)( dttvT
)(tvT
T
T
v
v
r
r
rr
va ˆ
2
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Uniform circular motion
• Example– A record spins at 45rpm and the bug is still sitting 4cm away from the
center of the record– A) What is the frequency and period of the bug’s rotation?– B) What is the acceleration of bug?
sm
Tv 19.0
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Circular Motion Review
• Angular velocity [rad/s]
• Period [s]
• Frequency [1/s, Hz]
• Centripetal acceleration. Always towards center of circle!
2
T
f
r
var
2
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Centripetal Force
• Centripetal Force is the name we assign to a Force which results in uniform circular motion.
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Example IV (Conical Pendulum)
• A small mass (m) suspended on a cord revolves in a circle of radius r. – A) What direction is acceleration and what causes it?– B) Calculate speed and period of the ball.
m
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Example IV (Conical Pendulum)• A small mass (m) suspended on a cord revolves in a circle of radius
r. – B) Calculate speed and period of the ball.
m
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Loop-de-loops
• Imagine you want to do a loop-de-loop at constant speed v…
• Where are the centripetal forces coming from?
x
y
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Circular Motion Problem
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Simpson’s Circular Motion
• In order to make the loop-de-loop at a constant speed, how fast must Homer be going?
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Highway Curves
• In order for the car to make a curve without slipping/skidding, need sufficient Force from friction.
• This force is a static friction, even though the car is moving!!
• Coordinate system!!!
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Flat Curves (unbanked)
• What is the coefficient of static friction required to make an unbanked curve with radius R, for a car traveling with a speed v?
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Banked Curves
• Can a car make a turn on a banked frictionless surface without skidding? For speed v, radius R, what angle is required?
• Coordinate system!!
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Example Problem
• A car goes around an unbanked curve (R=100m) at a speed of 50m/s. The concrete/tire interface has a coefficient of static friction of 1. Can the car make this turn?
Department of Physics and Applied Physics95.141, F2010 Lecture 9
Example Problem
• A car goes around an banked curve (R=100m) at a speed of 50m/s. Ignoring friction, what angle should the curve be banked at to allow the car to make the curve?