In the process of starting up the car plant, a turbine accelerates from rest at 0.49 rad/s^2 .How long does it take to reach its 4400 rpm operating speed?
How many revolutions does it make during this time?
I got 940 s for the first part, but for the second part Do i use the formula theta=w^2/2(.49/2pi)
I am very lost on the second part.
I am very lost please help. I determined that
on the second...
revolutions= wi*t+ 1/2 alpha*t^2
wi is zero
alpha is ang acceleration in rpm
alpha= .49rad/s^2 * 3600sec^2/min^2*1rev/2pi rad
That ought to do it.
To answer the first part of the question, we can use the formula for angular acceleration:
ω = ω₀ + αt
Where:
ω is the final angular velocity (in rad/s)
ω₀ is the initial angular velocity (in rad/s)
α is the angular acceleration (in rad/s²)
t is the time taken (in seconds)
In this case, ω₀ is 0 (since the turbine starts from rest), ω is the operating speed of 4400 rpm, and α is given as 0.49 rad/s².
The first step is to convert the operating speed from rpm to rad/s. Since 1 revolution is equal to 2π radians, we can use the conversion factor:
1 revolution = 2π radians
4400 revolutions = (4400 * 2π) radians
Next, we can plug in the values into the formula and solve for t:
4400 rpm = (ω₀) + (0.49 rad/s²)(t)
Converting 4400 rpm to rad/s:
(4400 * 2π) radians/s = 0 + (0.49 rad/s²)(t)
Now we can solve for t:
(4400 * 2π) radians/s = 0.49 rad/s² * t
Dividing both sides by 0.49 rad/s²:
t = [(4400 * 2π) radians/s] / (0.49 rad/s²)
Now, calculate this expression to find the value of t. This should give you the time it takes for the turbine to reach its operating speed.
Now, moving on to the second part of the question, it seems like you're trying to use the formula:
θ = (ω² - ω₀²) / (2α)
Where θ is the angle in radians, ω is the final angular velocity, ω₀ is the initial angular velocity, and α is the angular acceleration. However, this formula is used to calculate the angle traveled, not the number of revolutions.
To find the number of revolutions, you can use the relationship between angular displacement (θ) and the number of revolutions (N):
θ = 2πN
Rearranging this formula, we have:
N = θ / (2π)
Now, we need to find the angle traveled (θ) during the time it takes to reach the operating speed. Using the formula:
θ = ω₀t + 0.5αt²
Where θ is the angle in radians, ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time taken.
You should already have the values for ω₀, α, and t from the first part of the question. Plug these values into the formula and calculate the angle traveled (θ).
Finally, use the formula N = θ / (2π) to find the number of revolutions.