A ventilation fan has blades 0.25 m long rotating at 20 rpm. What is the centripetal acceleration of a point on the outer tip of a blade?
20rpm = 20 x 2π / 60
=2.1 rad/s
angular speed, ω=2.1 rad/s
v=rω
v=(0.25)(2.1)
= 0.525m/s
centripetal acceleration, ac = v2 /r
= (0.525)2/(0.25)
=1.10m/s2
Nice 1 m8
1.1 m/s2
Well, well, well, if it isn't the fan-tastic question about a ventilation fan! Let's dive right into it, shall we?
To find the centripetal acceleration of a point on the outer tip of a blade, we can use the formula:
a = ω²r
Where "a" represents the centripetal acceleration, ω is the angular velocity, and "r" is the radius of the circular motion.
Given that the blades are 0.25 m long (which would be the radius of the circular path) and rotating at 20 rpm (revolutions per minute, or angular velocity), let's do some silly math to figure it out!
First, let's convert the angular velocity from rpm to radians per second. Remember, there are 2π radians in one revolution:
ω = (20 rpm) × (2π rad/1 revolution) × (1 min/60 s)
Now we have our angular velocity "ω" in rad/s.
Next, plug in the values into our formula:
a = (ω)²r
a = (ω)²(0.25 m)
a = (ω²)(0.25 m)
And voilà! Crunching the numbers, you'll get the centripetal acceleration of a point on the outer tip of a blade. Have fun with your fan-tastic calculations!
To find the centripetal acceleration of a point on the outer tip of a blade, we need to use the formula for centripetal acceleration:
a = rω^2
Where:
a = centripetal acceleration
r = radius of rotation
ω = angular velocity
First, we need to calculate the radius of rotation. The length of the fan blades, given as 0.25 m, represents the radius of rotation. Therefore, r = 0.25 m.
Next, we need to convert the given angular velocity from revolutions per minute (rpm) to radians per second (rad/s). We know that 1 revolution is equal to 2π radians, and 1 minute is equal to 60 seconds. Using these conversions, we can calculate ω as follows:
ω = (20 rpm) * (2π rad/1 rev) * (1 min/60 s)
ω = 20 * 2π / 60 rad/s
ω ≈ 2.09 rad/s (rounded to two decimal places)
Now, we can substitute the values of r and ω into the centripetal acceleration formula:
a = (0.25 m) * (2.09 rad/s)^2
a ≈ 0.275 m/s^2 (rounded to three decimal places)
Therefore, the centripetal acceleration of a point on the outer tip of the blade is approximately 0.275 m/s^2.