Help with conservation of Mechanical Energy

In summary, the conversation includes different questions related to physics problems and their solutions. The first question involves finding the speed of a fish that fell from a bird flying over water, while the second question deals with the speed of a diver jumping into water from a 10m board. The third question involves calculating the vertical displacement of a runner during a hurdle jump, and the fourth question requires finding the initial height of a pendulum bob using the law of conservation of energy. The conversation also includes a discussion about converting joules per kilogram to meters per second and solving for kinetic and potential energies when mass and velocity are not given.
  • #1
austin1250
29
0
Alright I have a few problems here.

1). A bird is flying with a speed of 18 m/s over water when it accidentally drops a 2 kg fish. If the altitude of the bird is 5.40 meters and friction is disregarded, what is the speed of the fish when it hits the water?

My work: I don't know if I did this one right so if you could check that would be great.
I did PE= (2kg)(9.81m/s^2)(5.4m) = 106 PE
So I made KE at the point of the water 106 KE and 0 PE (potential energy.)

Then I did 106 = 1/2 * 2kg * v^2
I got it to equal v = 10.29 m/s is that correct?

2) A 755N Diver drops from a 10 m boarding above the waters surface. Find the divers speed 5 meters above the water. Then find the diver's speed just before it hits the water.

ok here i got 9.9 m/s for the part 5 meters above water is that correct? and then I got 14 m/s when striking the water?

(Part B) If the same diver leaves the board with initial upward speed of 2.0 m/s find the divers speed when striking the water.

I worked it out until here now I don't know what to do next

3) An Olympic runner leaps over a hurdle. If the runners initial vertical speed is 2.2 m/s how much will the runners center mass be raised during the jump?

Work: I am not really sure what to do here but is the answer .5 meters up?
I don't know if this is a correct equation, but I did V^2 = mgh

4) A pendulum bob is released from some initial height such that the speed of the bob at the bottom of the swing is 1.9 m/s. what is the initial height of the bob?

Ok here i don't know what to do really. I think it goes along the lines of one above, but I am not sure if that was right either.
 
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  • #2
Q1 No, Whether before dropped the fish was moving ? If yes was it having kinetic energy ?
 
  • #3
will someone show me that Joule/Kilogram is equivalent to meter/second? and how can I compute the highest and lowest KE and PE there are no mass, and velociy given?
 
  • #4
Welcome to PF.
A joule = kg - m²/s²
http://en.wikipedia.org/wiki/Joule

Take away kg and you have m²/s² not m/s.

As to the highest and lowest KE and PE, what is the problem you are trying to solve?
 
  • #5
Question 1 is incorrect because you set the KEi as 0 when it is actually 324 J.. Okay, so you know that KEi= (1/2)mvi2.. so KEi= (1/2)(2 kg)(182) giving you 324 J.. & due to the law of conservation of energy, energy can be neither created or destroyed so the initial mechanical energy is equal to the final mechanical energy. Subsitute so you know that PEi + KEi = PEf + KEf.. Now subsitute the information you have in... 105.948 + 324 = 0 + (1/2)(2)vf2.. the final answer is 20.73518748 m/s

Question 2 is correct!

Hope that helped!
 
Last edited:
  • #6
On Q5, set KE=PE
1/2mv^2=mgh
The masses on both sides cancel out
1/2v^2=gh
Then plug in your numbers
1/2(1.9m/s)^2=(9.81m/s^2)(h)
1.805=9.81h
Then divide both sides by 9.81 and it gives you h=.184m
 

1. What is conservation of Mechanical Energy?

The conservation of Mechanical Energy is a fundamental principle in physics that states that the total amount of mechanical energy in an isolated system remains constant over time. This means that energy cannot be created or destroyed, but it can be transferred between different forms, such as kinetic energy and potential energy.

2. Why is conservation of Mechanical Energy important?

The conservation of Mechanical Energy is important because it helps us understand and predict the behavior of objects in motion. It allows us to make accurate calculations and predictions about the motion of objects without having to consider the complex factors of energy transfer and transformation.

3. How does friction affect conservation of Mechanical Energy?

Friction is a force that acts in the opposite direction of an object's motion, causing it to lose mechanical energy. This means that in real-world situations, the total amount of mechanical energy may decrease due to the presence of friction. However, the principle of conservation of Mechanical Energy still applies, as the lost energy is transferred to other forms, such as heat energy.

4. Can Mechanical Energy be converted into other forms of energy?

Yes, Mechanical Energy can be converted into other forms of energy, such as thermal energy, electrical energy, or sound energy. This is because energy is always conserved, and it can be transformed from one form to another.

5. How can we apply conservation of Mechanical Energy in real-life situations?

Conservation of Mechanical Energy can be applied in various real-life situations, such as designing roller coasters, calculating the efficiency of machines, or understanding the movement of objects in sports. It also helps us to make more sustainable choices by considering energy conservation in our daily activities.

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