Solving for Revolutions: Electric-Generator Turbine

In summary, the electric-generator turbine takes 16.0 minutes to coast to a stop with a spin rate of 3600 revolutions per minute. However, the presence of angular acceleration invalidates the formula used to calculate the total number of revolutions. Further analysis of the angular acceleration is needed to determine the correct number of revolutions after 16 minutes.
  • #1
rjimenez
1
0

Homework Statement



An electric-generator turbine spins at 3600rpm . Friction is so small that it takes the turbine 16.0 min to coast to a stop.How many revolutions does it make while stopping?


Homework Equations





The Attempt at a Solution


(3600rev/min)(16.0min)=57600 i tried this and know the answer is wrong
 
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  • #2
You have to remember that in order for the turbine to come to a stop, it has to be slowing down. In other words, the turbine must have some angular acceleration in order to slow down to a stop. The fact that the angular acceleration is not zero makes the formula you used invalid. Do you know what the angular acceleration is? If you do, what relationships involving the angular acceleration can you use to find the total amount of revolutions after 16 minutes?
 
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  • #3


Your attempt at a solution is incorrect because it does not take into account the fact that the turbine is slowing down, not maintaining a constant speed. To solve for the number of revolutions, you need to use the formula:

Number of revolutions = (initial angular velocity * time) - (1/2 * angular acceleration * time squared)

In this case, the initial angular velocity is 3600 rpm, the time is 16 minutes, and the angular acceleration is equal to the negative of the final angular velocity (since the turbine is slowing down).

Therefore, the correct formula would be:

Number of revolutions = (3600 rpm * 16 min) - (1/2 * (-3600 rpm) * (16 min)^2)

Simplifying, you get:

Number of revolutions = 28800 - 460800 = -432000

This means that the turbine makes a total of 432000 revolutions while stopping.
 

Related to Solving for Revolutions: Electric-Generator Turbine

1. What is a turbine and how does it relate to electric generators?

A turbine is a machine that converts the energy of a moving fluid, such as steam or water, into mechanical energy. This mechanical energy is then used to power an electric generator, which converts it into electricity. Turbines are a crucial component of electric generators as they provide the necessary rotation to generate electricity.

2. What is the purpose of solving for revolutions in an electric-generator turbine?

The purpose of solving for revolutions in an electric-generator turbine is to determine the optimal speed at which the turbine should rotate in order to generate the desired amount of electricity. This involves calculating the number of revolutions per minute (RPM) at which the turbine should operate to produce the required amount of power.

3. What factors are involved in determining the number of revolutions per minute in an electric-generator turbine?

The number of revolutions per minute in an electric-generator turbine is affected by several factors, including the size and design of the turbine, the type of fluid used, the amount of pressure and temperature of the fluid, and the desired output of electricity. These factors can be manipulated to find the optimal RPM for the turbine.

4. How do scientists and engineers calculate the number of revolutions per minute in an electric-generator turbine?

To calculate the number of revolutions per minute in an electric-generator turbine, scientists and engineers use mathematical equations and formulas that take into account the various factors involved, such as the turbine's size, speed, and fluid properties. They may also use computer simulations and experiments to test and refine their calculations.

5. What are some common challenges in solving for revolutions in an electric-generator turbine?

Some common challenges in solving for revolutions in an electric-generator turbine include accurately measuring and accounting for all the factors that affect the turbine's RPM, as well as ensuring the turbine is operating at peak efficiency. Additionally, different types of turbines and fluids may require different equations and approaches to solving for revolutions, making the process more complex.

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