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PHYS 11: Chap. 5, Pg 2
1. Choice One 2. Choice Two 3. Choice Three 4. Choice Four 5. Choice Five
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ConcepTest 5.3.a Barrel of Fun
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PHYS 11: Chap. 5, Pg 3
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PHYS 11: Chap. 5, Pg 4
Suppose the x- and y-components of acceleration are independent of each other. That is, ax does not depend on y or vy, and ay does not depend on x or vx. Your problem-solving strategy is to
1. Draw a pictorial representation and a FBD. 2. Choose the appropriate coordinate system 3. Use Newton’s second law in component form.
The force components (including proper signs) are found from the free-body diagram.
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PHYS 11: Chap. 5, Pg 5
4. Solve for the acceleration. If the acceleration is constant, use the two-dimensional kinematic equations of Chapter 4 to find velocities and positions.
PHYS 11: Chap. 5, Pg 6 New Topic
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PHYS 11: Chap. 5, Pg 7
R
v
x
y
Some circular motion terms:
Recall that 1 revolution = 360° = 2π radians » frequency ( f ) = revolutions / second » period ( P ) = seconds / revolution
f = 1/ P
PHYS 11: Chap. 5, Pg 8
a v2 R =
m v2 R
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PHYS 11: Chap. 5, Pg 9
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W
T
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W T
W
T
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A stunt plane does a series of vertical loop-the-loops. At what point in the circle does the pilot feel the heaviest? Explain. Include a free-body diagram with your explanation.
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PHYS 1021: Chap. 8, Pg 15
A conical pendulum is formed by attaching a 600 g ball to a 1.0 m long string, then allowing the mass to move in a horizontal circle. Tension in string equals 8.3 N. What is the angular velocity.
T = mω2L ω2 = 13.8 (rad/s)2 = 13.8 s-2
What angle does the string make with the vertical?
cos(θ) = mg/T = θ = 44.9o
Tie a large washer to a string and (carefully) whirl it in a vertical circle. When the washer is at its lowest point, is the tension in the string greater than, less than, or equal to the ball’s weight? Explain.
(You may want to include a free-body diagram as part of your explanation.)
What is the tension in the string when the speed is slow enough for the washer to just basely make it over the top?
Calculate the minimum speed needed to just get over the top. At that same speed, what is the tension on the string at the bottom?
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What does it do? It opposes motion!
How do we characterize this? Drag results in a force in a direction opposite to the
direction of motion! Drag force is proportional to v (small, slow objects)
or v2 (large, fast objects)
For microscopic, spherical objects (paramecium, e.coli).
η = viscosity, r = radius, v = velocity
(spherical fish approximation, r = (abc)1/3, a,b,c are elliptical axes The “faster” something goes …the greater the drag will be….
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FD = 6πηrv
Beyond the spherical fish: Spherical fish accounts for the drag along
the fish body by assuming that the entire volume of the fish is packed into a spherical shape (hence r ~ (abc)1/3)
Can expand in terms of elliptical integrals and use a correction factor, K’
Then, if β = b/a (a=c, see figure)
If β >> 1, 4 or more is sufficient
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FD = K '6πηav
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K '= 23
βln2β −1
See (http://web2.clarkson.edu/projects/crcd/me637/downloads/1_2Drag.pdf)
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A steel ball is dropped in a lake. As it moves faster and faster, the viscous drag will increase. Use an fbd to show that eventually, the viscous drag force will be equal and opposite to the gravitational force and the velocity will then no longer increase. This is called the terminal velocity.
Sketch a plot of the velocity as a function of time from when the ball begins to drop in the water until it reaches terminal velocity.
Show that the terminal velocity is given by the expression:
Now rewrite this in terms of the density to show that
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vt =mg
K '6πηrv
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vt =2r2g9K 'ηv
In this exercise, we will measure the terminal velocity of steel balls dropped into fluids (corn syrup – dark and light, maple syrup, safflower oil, motor oil, and 96% glycerin
Gather the following materials: Computer (or use yours if equipped with logger pro) Labpro unit + USB and power cable Track + leveling feet + level Simple cart Photogate + pulley + post + cable Magnet + string + 3/4” ball + 5/8” ball
Start the computer and plug the labpro unit into the usb port Assemble the cart, track, and hook everything up – we will do this
together While things are starting up, roll the cart back and forth and brain
storm about how to measure the coefficient of friction of the cart (hint draw fbd of cart moving one way and then the other way under the influence of the 5/8” ball.
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Now measure the frictional force on the cart by rolling the cart with a gently push up the ramp (in direction to raise the weight)
Measure the acceleration as the cart goes up and then down the ramp Is there a difference? What is the acceleration of the ball, is this what you would calculate
it to be? Now measure the viscosity
1. Take one of the 6 1-liter graduated cylinders of fluid and set it on the floor beneath the ball hanging from the string.
2. After positioning the ball just below the surface, actuate data collection (press the space bar) and when ready, let go of the cart.
3. Save the data [cmd]L or ⌘L 4. Repeat once 5. Get another cylinder and repeat 1-4, carefully noting in your
notebook the color and run number corresponding to each fluid 6. Cycle through all 6 liquids
Save your loggerpro file to the desktop. Email your loggerpro file to [email protected] with your group
number and computer number in the subject line Take pictures of any whiteboard work and post to fb
******very important******
Write the file name and computer number in your notebook – Put everything away!!!
