DATA You have one object of each of these shapes, all with mass 0.840 kg: a uniform solid cylinder, a thin-walled hollow cylinder, a uniform solid sphere, and a thin-walled hollow sphere. You release each object from rest at the same vertical height h above the bottom of a long wooden ramp that is inclined at 35.0° from the horizontal. Each object rolls without slipping down the ramp. You measure the time t that it takes each one to reach the bottom of the ramp; Fig. P10.89 shows the results, (a) From the bar graphs, identify objects A through D by shape, (b) Which of objects A through D has the greatest total kinetic energy at the bottom of the ramp, or do all have the same kinetic energy? (c) Which of objects A through D has the greatest rotational kinetic energy 1 2 I ω 2 at the bottom of the ramp, or do all have the same rotational kinetic energy? (d) What minimum coefficient of static friction is required for all four objects to roll without slipping? Figure P10.89
DATA You have one object of each of these shapes, all with mass 0.840 kg: a uniform solid cylinder, a thin-walled hollow cylinder, a uniform solid sphere, and a thin-walled hollow sphere. You release each object from rest at the same vertical height h above the bottom of a long wooden ramp that is inclined at 35.0° from the horizontal. Each object rolls without slipping down the ramp. You measure the time t that it takes each one to reach the bottom of the ramp; Fig. P10.89 shows the results, (a) From the bar graphs, identify objects A through D by shape, (b) Which of objects A through D has the greatest total kinetic energy at the bottom of the ramp, or do all have the same kinetic energy? (c) Which of objects A through D has the greatest rotational kinetic energy 1 2 I ω 2 at the bottom of the ramp, or do all have the same rotational kinetic energy? (d) What minimum coefficient of static friction is required for all four objects to roll without slipping? Figure P10.89
DATA You have one object of each of these shapes, all with mass 0.840 kg: a uniform solid cylinder, a thin-walled hollow cylinder, a uniform solid sphere, and a thin-walled hollow sphere. You release each object from rest at the same vertical height h above the bottom of a long wooden ramp that is inclined at 35.0° from the horizontal. Each object rolls without slipping down the ramp. You measure the time t that it takes each one to reach the bottom of the ramp; Fig. P10.89 shows the results, (a) From the bar graphs, identify objects A through D by shape, (b) Which of objects A through D has the greatest total kinetic energy at the bottom of the ramp, or do all have the same kinetic energy? (c) Which of objects A through D has the greatest rotational kinetic energy
1
2
I
ω
2
at the bottom of the ramp, or do all have the same rotational kinetic energy? (d) What minimum coefficient of static friction is required for all four objects to roll without slipping?
A solid cylinder has a mass of 1 kg and a radius of 0.1 m. Starting from rest, the cylinder rolls down a ramp angled
at 30° from the horizontal. The ramp is 1 m long and the cylinder rolls without slipping. How fast is it traveling
parallel to the ramp at the moment it reaches the bottom? Take g = 10 m/s².
L = 1m
30°
Your grandmother enjoys creating pottery as a hobby. She uses a potter’s wheel, which is a stone disk of radius R = 0.500 m and mass M = 100 kg. In operation, the wheel rotates at 50.0 rev/min. While the wheel is spinning, your grandmother works clay at the center of the wheel with her hands into a pot-shaped object with circular symmetry. When the correct shape is reached, she wants to stop the wheel in as short a time interval as possible, so that the shape of the pot is not further distorted by the rotation. She pushes continuously with a wet rag as hard as she can radially inward on the edge of the wheel and the wheel stops in 6.00 s. (a) You would like to build a brake to stop the wheel in a shorter time interval, but you must determine the coefficient of friction between the rag and the wheel in order to design a better system. You determine that the maximum pressing force your grandmother can sustain for 6.00 s is 70.0 N. (b) What If? If your grandmother instead chooses to press…
Your grandmother enjoys creating pottery as a hobby. She uses a potter's wheel, which is a stone disk of radius
R = 0.430 m and mass M = 100 kg. In operation, the wheel rotates at 45.0 rev/min. While the wheel is spinning, your
grandmother works clay at the center of the wheel with her hands into a pot-shaped object with circular symmetry. When
the correct shape is reached, she wants to stop the wheel in as short a time interval as possible, so that the shape of the
pot is not further distorted by the rotation. She pushes continuously with a wet rag as hard as she can radially inward on
the edge of the wheel and the wheel stops in 6.00 s.
(a) You would like to build a brake to stop the wheel in a shorter time interval, but you must determine the coefficient of
friction between the rag and the wheel in order to design a better system. You determine that the maximum pressing
force your grandmother can sustain for 6.00 s is 60.0 N.
HK
(b) What If? If your grandmother instead chooses to…
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