Ceiling Fan Velocity
March 11, 2011
|
Posted by admin
tough physics question?
An electric ceiling fan is rotating about a fixed axis with an initial angular velocity of 0.220 rev/s. The angular acceleration is 0.905 rev/s^2. Its blades form a circle of diameter 0.770 m.
Part A) Compute the angular velocity of the fan after time 0.192 s has passed?
Part B) Through how many revolutions has the blade turned in the time interval 0.192 s from Part A?
Part C) What is the tangential speed v_tan(t) of a point on the tip of the blade at time t = 0.192 s?
Part D) What is the magnitude of the resultant acceleration (a) of a point on the tip of the blade at time t = 0.192 s?
A) ω_f = ω_i + αt
ω_f = final angular velocity
ω_i = initial angular velocity = 0.220 rev/s
α = angular acceleration = 0.905 rev/s²
t = time = 0.192s
ω_f = (0.220 rev/s) + (0.905 rev/s²)(0.192s)
ω_f = 0.394 rev/s
B) Δθ = ωt + (1/2)αt²
Δθ = change in angle
Δθ = (0.220 rev/s)(0.192 s) + (1/2)(0.905 rev/s²)(0.192 s)²
Δθ = 0.059 rev
C) v = rω
v = velocity
r = radius = 0.77/2 = 0.385m
We already have ω from part A, but for the formula to work it has to be in rad/s instead of rev/s. To do that just multiply by 2π.
v = (0.385 m)(0.394 rev/s)(2π rad/rev)
v = 0.953 m/s
D) a_t = rα
a_t = tangential acceleration
a_n = rω²
a_n = normal acceleration
First find tangential acceleration. Again, it has to be in rad/s² so multiply by 2π:
a_t = (0.385m)(0.905 rev/s²)(2π rad/rev)
a_t = 2.189 m/s²
Then find normal (with the same rev→rad deal):
a_n = (0.385 m)[(0.394 rev/s)(2π rad/rev)]²
a_n = 2.359 m/s²
Finally, use the pythagorean theorem to find the resultant:
a = √[(a_n)² + (a_t)²]
a = √(2.359 m/s²)² + (2.189 m/s²)²]
a = 3.22 m/s²
Hunter 14 High-Velocity Garage Fan Model #: 90220
|
|
Craftmade VE58SS Velocity 58″ Nickel Ceiling Fan $162.00 |
|
|
Craftmade VE5 56in. Velocity Ceiling Fan $162.00 |
|
|
Craftmade Velocity 58″ Ceiling Fan in Stainless Steel VE58SS $154.80 |
|
|
Suncourt HC500-B Flush Mount Heating and Air Conditioning Booster Fan, $36.50 Depending on the season, lowering or raising your thermostat just 4° can cost an additional 5 to 0 per month. Running the Heating and Air Conditioning Booster over the same period only costs about 60 cents! Unlike a traditional booster that simply mou… |
|
|
Optimus Industrial Grade 3-Speed High-Velocity Fan, 18 Inches, Black/Chrome, F-4182 $46.05 Product Features. 18 inch industrial grade high velocity fan. Three speed high-torque motor. Reinforced wire grill for added safety. OSHA approved three prong grounded plug. Head tilts for use as air circulator. . Product Description. Optimus brings you the finest in fans and heaters. The F-4182 is an 18 Inch industrial grade high-velocity fan. Three speed high-torque motor, reinforced wire grill … |
|
|
MAXXAIR BF24TF YEL 24-Inch High Velocity Air Movement Two Speed Portable Air Circulator, Yellow $113.41 Use this versatile fan in the workshop, the patio or the basement to provide 2800 or 4000 CFM of circulation with a heavy-duty 2-speed 1/4 HP thermally protected PSC motor. Not to be used with an extension cord or any speed control device, in an unprotected, outdoor, or wet area, or to exhaust hazardous fumes or chemicals. Fan Diameter (in.): 24, Air Delivery (CFM): 2,800 / 4,000, HP: 1/4, Speeds … |
|
|
Maxxair 00-965001 Turbo/Maxx 3 Speed Fan with Thermostat $226.45 Now any roof vent can become a powerful ceiling fan ventilator! Setting up your RV for a power vent has never been easier. This drop-in unit fits right into your existing vent hole to deliver powerful 3-speed circulation for your rig. Screened cover lets you vent without worry of rain, bugs or debris getting inside your RV. Quiet, variable speed fan allows intake or exhaust operation. Powerful 4-a… |
Categories: Fans And Home Accessories
| 
Tags: ceiling fan velocity, ceiling_fans, fan, fans, floor, home
|
No Comments
