Conservation of mechanical energy ?

In summary, the conversation is about the conservation of mechanical energy and calculating the maximum speed of a falling coconut. The equations used are Ep=mgh and Ek= (1/2)mv^2. The maximum speed for a fall from the tree to the ground beneath it is 14.0 m/s, and from the tree to the bottom of the 15m cliff is 22.14 m/s. The conversation also includes a clarification about the negative sign in the Ep equation and a correction for the height in the second part.
  • #1
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Conservation of mechanical energy ?

A 0.80kg coconut is growing 10m above the ground in its palm tree. The tree is just at the edge of a cliff that is 15 meters tall.

a>What would the maximum speed of the coconut be if it fell to theground beneath the tree?
b>What would the maximum speed be if it fell from the tree to the bottom of the cliff?

Equations:
Ep=mgh
Ek= -Ep
Ek= (1/2)mv^2


The Attempt at a Solution



So I've figured out Ep= 78.48J
However,Im not sure how to relate that to Ek so I could later solve for v?
 
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  • #2


The second relation you wrote, relates Ek to Ep. Also notice that Ep would be -78.48 J (why?)
 
  • #3


so for a>
Ep= -78.48J so Ek= 78.48J
Ek= (1/2)(0.80kg)v^2
v= 14.0 m/s

is that right??
 
  • #4


Yes. For second part, the height changes (to?)
 
  • #5


for b>
Ep= (.80)(9.81)(25cm)
Ek= 196.2J
196.2/ 0.4 = v^2
v= 22.14m/s
 
  • #6


That looks good.

Edit : I assumed you meant 25m and not 25 cm.
 
  • #7


Oops yes, I meant 25m.
Thank you! :)
 
  • #8


You are welcome!
 

FAQ: Conservation of mechanical energy ?

What is conservation of mechanical energy?

Conservation of mechanical energy is a fundamental principle in physics that states that the total amount of mechanical energy in a closed system remains constant over time. This means that energy can neither be created nor destroyed, but can only be transferred or transformed from one form to another.

What are the two forms of mechanical energy?

The two forms of mechanical energy are kinetic energy, which is the energy associated with motion, and potential energy, which is the energy stored in an object due to its position or configuration.

How does the law of conservation of energy apply to mechanical systems?

In mechanical systems, the law of conservation of energy states that the total amount of kinetic energy and potential energy remains constant as the system undergoes any changes. This means that the total mechanical energy at the beginning of a process or interaction will be equal to the total mechanical energy at the end.

What factors can affect the conservation of mechanical energy?

The conservation of mechanical energy can be affected by external forces, such as friction or air resistance, which can convert mechanical energy into other forms of energy and decrease the total amount of mechanical energy in a system. Additionally, non-conservative forces, such as those involved in elastic collisions, can also affect the conservation of mechanical energy.

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, electromagnetic energy, or sound energy. This conversion can occur through various processes, such as friction, collisions, or work done by external forces.

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