An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disk’s center, as in Figure P8.41. The disk has mass 2.50 kg and radius 0.200 m. Each rod has mass 0.850 kg and is 0.750 m long, (a) Find the ceiling fan’s moment of inertia about a vertical axis through the disk’s center, (b) Friction exerts a constant torque of magnitude 0.115 N · m on the fan as it rotates. Find the magnitude of the constant torque provided by the fan’s motor if the fan starts from rest and takes 15.0 s and 18.5 full revolutions to reach its maximum speed. Figure P8.41
An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disk’s center, as in Figure P8.41. The disk has mass 2.50 kg and radius 0.200 m. Each rod has mass 0.850 kg and is 0.750 m long, (a) Find the ceiling fan’s moment of inertia about a vertical axis through the disk’s center, (b) Friction exerts a constant torque of magnitude 0.115 N · m on the fan as it rotates. Find the magnitude of the constant torque provided by the fan’s motor if the fan starts from rest and takes 15.0 s and 18.5 full revolutions to reach its maximum speed. Figure P8.41
Solution Summary: The author explains the ceiling fan's moment of inertia about vertical axis through the disk’s center.
An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disk’s center, as in Figure P8.41. The disk has mass 2.50 kg and radius 0.200 m. Each rod has mass 0.850 kg and is 0.750 m long, (a) Find the ceiling fan’s moment of inertia about a vertical axis through the disk’s center, (b) Friction exerts a constant torque of magnitude 0.115 N · m on the fan as it rotates. Find the magnitude of the constant torque provided by the fan’s motor if the fan starts from rest and takes 15.0 s and 18.5 full revolutions to reach its maximum speed.
You are working with a team that is designing a new roller coaster-type amusement park ride for a major theme park. You are present for the testing of the ride, in which an empty 150 kg car is sent along the entire ride. Near the end of the ride, the car is at near rest at the top of a 100 m
tall track. It then enters a final section, rolling down an undulating hill to ground level. The total length of track for this final section from the top to the ground is 250 m. For the first 230 m, a constant friction force of 370 N acts from computer-controlled brakes. For the last 20 m, which is
horizontal at ground level, the computer increases the friction force to a value required for the speed to be reduced to zero just as the car arrives at the point on the track at which the passengers exit.
(a) Determine the required constant friction force (in N) for the last 20 m for the empty test car.
Write AK + AU + AE int
= W+Q + TMW
+
TMT + TET + TER for the car-track-Earth system and solve for…
=
12 kg, and m3
Three objects with masses m₁ = 3.8 kg, m₂
find the speed of m3 after it moves down 4.0 m.
m/s
19 kg, respectively, are attached by strings over frictionless pulleys as indicated in the figure below. The horizontal surface exerts a force of friction of 30 N on m2. If the system is released from rest, use energy concepts to
m
m2
m3
i
Three objects with masses m₁ = 3.8 kg, m₂ = 12 kg, and m 19 kg, respectively, are attached by strings over frictionless pulleys as indicated in the figure below. The horizontal surface exerts a force of friction of 30 N on m2. If the system is released from rest, use energy concepts to
find the speed of m¸ after it moves down 4.0 m.
m/s
m
m2
mg
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