# Mechanical energy- how to solve for v

• Woopa
In summary, the conversation is about solving a mechanical energy question. The solution involves factoring out the mass term and then getting rid of the factors of 1/2. To do this, one can simply multiply the equation by 2 and then take the square root. The final answer is VA=√ v^2-gh.
Woopa
Homework Statement
Mechanical energy. Solve for v
Relevant Equations
1/2mv^2 + mgh
Hi there,

I am doing a mechanical energy question. I think the solution is simple but I'm stuck on an algebra step.

This is the solution but I am really not sure how they have simplified down to Va.

For example I tried to factor out the m resulting in

1/2mv^2=m(1/2va^2+gh)

Then I cancel the m

1/2v^2= 1/2va^2+gh

From here I am not really sure what they did to arrive at the final answer

Woopa said:
Homework Statement:: Mechanical energy. Solve for v
Relevant Equations:: 1/2mv^2 + mgh

Hi there,

I am doing a mechanical energy question. I think the solution is simple but I'm stuck on an algebra step.

View attachment 279825
This is the solution but I am really not sure how they have simplified down to Va.

For example I tried to factor out the m resulting in

1/2mv^2=m(1/2va^2+gh)

Then I cancel the m

1/2v^2= 1/2va^2+gh

From here I am not really sure what they did to arrive at the final answer
You can see they got rid of the factors of 1/2. How would you do that?
They also got vA on one side of the equation and everything else on the other , so do that.

haruspex said:
You can see they got rid of the factors of 1/2. How would you do that?
They also got vA on one side of the equation and everything else on the other , so do that.
I'm really not sure how they got rid of the factors of 1/2. Can you help me?

Getting VA to one side is easy enough for me. Starting with ½v^2=½VA^2+gh after factoring out m, I would then just subtract gh resulting in 1/2 v^2-gh= 1/2 VA^2.

Still really not sure how they got rid of the halfs. My first thought is to multiply by 2 but that doesn't give me the answer

Woopa said:
My first thought is to multiply by 2
It gets rid of the halves, so do it.
With vA alone on one side, what is your equation now?

haruspex said:
It gets rid of the halves, so do it.
With vA alone on one side, what is your equation now?

If I multiply by 2 and then sqrt I end up with

VA=√ v^2-gh

I'm just missing the 2gh

Woopa said:
If I multiply by 2 and then sqrt I end up with

VA=√ v^2-gh

I'm just missing the 2gh
Then you did not get rid of the halves correctly. Retry that step.

haruspex said:
Then you did not get rid of the halves correctly. Retry that step.
It's just clicked! Thank you for the prompts I've got it

## 1. What is mechanical energy?

Mechanical energy is the sum of potential energy and kinetic energy in a system. Potential energy is the energy stored in an object due to its position or configuration, while kinetic energy is the energy an object possesses due to its motion.

## 2. How is mechanical energy related to velocity?

The kinetic energy of an object is directly proportional to its velocity. This means that as the velocity of an object increases, its kinetic energy also increases.

## 3. How can I calculate the velocity using mechanical energy?

The formula for mechanical energy is ME = PE + KE. To solve for velocity, you can use the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is the velocity. Rearranging the formula, v = √(2 * KE/m).

## 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 known as the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted.

## 5. How is mechanical energy used in everyday life?

Mechanical energy is used in various everyday activities, such as riding a bike, playing sports, or using a machine. It is also used in larger-scale applications, such as generating electricity from wind turbines or hydroelectric dams.

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