Physics- Mechanical Energy

In summary, the conversation is discussing the calculation of the maximum height reached by an arrow shot at a speed of 46m/s, neglecting any friction. The correct equations for the total initial and final energies are given, and it is pointed out that the mistake of double counting kinetic energy has been made in the calculations. The correct method is to equate the two energies and solve for the maximum height.
  • #1
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An arrow is shot from ground (height=0) at a speed of 46m/s and travels in an archy line and at the maximum height has a speed of 42m/s. Arrows mass is, m...what is the maximum height that the arrow reaches? **IGNORE ANY FRICTION**

Thanks for any help guys


What I did was:

Et1=Mechanical energy before arrow was shot
Et2=Mechanical Energy after arrow was shot
Vf2=Final velocity squared
Vf1=Initial velocity squared



Et1=Et2

m(vf2)/2 - m(vi2)/2 = mgh + m(vf2)/2 - m(vi2)/2

...it doesn't work out though...why?
 
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  • #2
Originally posted by PiRsq
Et1=Mechanical energy before arrow was shot
Et2=Mechanical Energy after arrow was shot
Vf2=Final velocity squared
Vf1=Initial velocity squared

Et1=Et2

You've got the right idea.

m(vf2)/2 - m(vi2)/2 = mgh + m(vf2)/2 - m(vi2)/2

...it doesn't work out though...why?

You've double-counted the kinetic energies. Each one should only appear once.

The total initial energy is Ei=(1/2)mvi2

The total final energy is Ef=(1/2)mvf2+mgh

Just equate and solve.
 
  • #3
But why though, I don't get it?
 
  • #4
What don't you get? The expressions for the total energies, or the mistake of double counting kinetic energy?
 
  • #5
Double counting the Kinetic energy thing...
 
  • #6


Continuing with what I wrote earlier:

Originally posted by Tom
The total initial energy is Ei=(1/2)mvi2

The total final energy is Ef=(1/2)mvf2+mgh

Just equate and solve.

Equate the energies Ei=Ef

(1/2)mvi2=(1/2)mvf2+mgh

See? You put in an extra -(1/2)mvi2 on the RHS and an extra -(1/2)mvf2 on the LHS.
 

1. What is mechanical energy?

Mechanical energy is a type of energy that an object possesses due to its motion or position. It is the sum of an object's kinetic energy (energy of motion) and potential energy (energy of position).

2. What are the two types of mechanical energy?

The two types of mechanical energy are kinetic energy and potential energy. Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object possesses due to its position or stored energy.

3. How is mechanical energy calculated?

The total mechanical energy of an object is calculated by adding its kinetic energy and potential energy together. The formula for mechanical energy is E = KE + PE, where E is mechanical energy, KE is kinetic energy, and PE is potential energy.

4. What are some examples of mechanical energy?

Some examples of mechanical energy include a roller coaster at the top of a hill (potential energy), a moving car (kinetic energy), a stretched rubber band (potential energy), and a swinging pendulum (alternating between kinetic and potential energy).

5. Is mechanical energy conserved?

According to the law of conservation of energy, mechanical energy is conserved. This means that the total amount of mechanical energy in a closed system remains constant, even as it changes between potential and kinetic energy. However, mechanical energy can be converted into other forms of energy, such as thermal energy, through processes like friction.

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