What is the speed as it hits the wheel?

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In summary, the water falling onto the water wheel from a height of 2.0m at a rate of 95kg/s has both potential and kinetic energy. The maximum power output of the water wheel can be determined using the mass flow rate and elevation above a reference point. The speed of the water as it hits the wheel can also be calculated using equations for potential and kinetic energy.
  • #1
engineer2010
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Homework Statement


Water falls onto a water wheell from a height of 2.0m at a rate of 95kg/s (a) If this water wheel is set up to provide electricity output, what is the max power output. (b) What is the speed as it hits the wheel?


Homework Equations



Ep= mgh Ek= 1/2mv^2

The Attempt at a Solution



I know that the water initally has both potential and kinetic energy as it falls but i am unsure as to how i use the rate in these equations and also which power equation(s) I use once i get to that stage.
 
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  • #2
Well the elevation of a mass m in a gravitational field provides for gravitational potential energy (GPE) by virtue of mgh, where h is the elevation above some reference point.

If an object at h is released and it falls through distance h, then GPE decreases by mgh and that GPE is transformed to kinetic energy 1/2 mv2, and neglecting air resistance mgh = 1/2 mv2.

If one has a mass flow rate [itex]\dot{m}[/itex], then the rate at which energy (described above) is delivered is simply [itex]\dot{m}[/itex]gh, and the rate of energy delivery/transformation is power.
 
  • #3


I would approach this problem by first understanding the basic principles involved. The water wheel is being used to convert the potential energy of the falling water into electrical energy. Therefore, the key equations here are those related to energy and power.

To find the maximum power output of the water wheel, we can use the equation P = mgh, where P is power, m is the mass of water per second (95 kg/s), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the water (2.0 m). Plugging in these values, we get a maximum power output of approximately 1,860 watts.

Now, to find the speed of the water as it hits the wheel, we need to use the equations for potential and kinetic energy. Initially, the water only has potential energy given by Ep = mgh. At the bottom of the fall, this potential energy is converted into kinetic energy, given by Ek = 1/2mv^2. We can equate these two equations to solve for the speed, v, which is the speed of the water as it hits the wheel.

mgh = 1/2mv^2
Solving for v, we get v = √(2gh). Plugging in the values, we get a speed of approximately 6.26 m/s.

In conclusion, the speed of the water as it hits the wheel is approximately 6.26 m/s and the maximum power output of the water wheel is 1,860 watts.
 

FAQ: What is the speed as it hits the wheel?

What is the definition of speed?

Speed is the measure of how fast an object is moving, typically expressed in units of distance traveled per unit of time.

How is the speed of an object calculated?

The speed of an object can be calculated by dividing the distance it has traveled by the time it took to travel that distance. The formula for speed is: speed = distance / time.

What is the difference between speed and velocity?

While speed measures the rate of motion, velocity measures the rate of motion in a specific direction. Therefore, velocity takes into account the direction of an object's movement, while speed does not.

How does an object's speed affect its impact on a wheel?

An object's speed directly affects the force of impact on a wheel. The higher the speed of the object, the greater the force of impact on the wheel will be.

Can the speed of an object change as it hits the wheel?

Yes, the speed of an object can change as it hits the wheel. This change in speed is dependent on the type of collision and the forces involved. In an elastic collision, the object's speed will remain the same after impact, while in an inelastic collision, the object's speed may decrease after impact.

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