# Using energy conservation to find speed

• vu10758
In summary, when a stone of mass m is thrown straight up with initial speed v_o, it experiences a force of air resistance of magnitude f during its flight. To determine the speed of the stone when it hits the ground, energy conservation equations must be combined for the upward and downward parts of the motion. The correct equation for the downward part is mgh - Fh = (1/2)m(v_f)^2, where v_f is the final speed of the stone. To find the maximum height, the first equation (1/2)m(v_o)^2 - F(h) = (1/2)(m)(v_f)^2 + mgh can be used, with v_f as zero. The speed when the stone
vu10758
A stone of mass m is thrown straight up into the air with speed v_o. While the flight it feels a force of air resistance of magnitude f. Determine the speed of the stone when it hits the ground. You will need to combine energy conservation equations for the upward and downward parts of the motion.

This is what I did...

upward

(1/2)m(v_o)^2 - F = (1/2)(m)(v_f)^2 + mgh

downward

mgh - F = (1/2)m(v_o)^2

Am I correct so far? How do I combine them?

The correct answer is v = (v_o) SQRT(mg-f/mg+f). How do I get there?

You cannot add or subtract force and energy. You have to either equate forces with forces or energies with energies (work is like energy in that it is the mechanism by which energies are changed)

Thanks for pointing that out
Now I have ...

upward

(1/2)m(v_o)^2 - F(h) = (1/2)(m)(v_f)^2 + mgh

downward

mgh - Fh = (1/2)m(v_o)^2

Is this correct?

vu10758 said:
Thanks for pointing that out
Now I have ...

upward

(1/2)m(v_o)^2 - F(h) = (1/2)(m)(v_f)^2 + mgh

downward

mgh - Fh = (1/2)m(v_o)^2

Is this correct?
That last term in the last equation...where you have v_o...that's not correct. You are trying to find its speed as it hits ground...

vu10758 said:
Thanks for pointing that out
Now I have ...

upward

(1/2)m(v_o)^2 - F(h) = (1/2)(m)(v_f)^2 + mgh

downward

mgh - Fh = (1/2)m(v_o)^2

Is this correct?
You need your first equation to find the maximum height. In that equation v_f is zero. Then use that h in the second equation, making the correction Jay noted.

vu10758 said:
I have a quick question. Wouldn't the v that the hitting the ground be the same as the v_o? Wouldn't the speed going up equals to the speed going down at ever position?
That would be true without the resistance, but not when the motion is constantly being opposed.

-Johnson

## 1. How does energy conservation help find speed?

Energy conservation is a fundamental principle in physics which states that energy cannot be created or destroyed, but only transferred from one form to another. This principle allows us to use the conservation of energy equation to find the speed of an object. By equating the initial kinetic energy (KE) of the object to its final potential energy (PE), we can solve for the speed using the equation KE = 1/2 * mv^2, where m is the mass of the object and v is its speed.

## 2. Can energy conservation be used for all types of motion?

Yes, energy conservation can be used for all types of motion as long as there is no external force acting on the object. This is because in the absence of external forces, the total energy of the system remains constant. Therefore, the initial kinetic energy of the object will be equal to its final potential energy, regardless of the type of motion.

## 3. Are there any limitations to using energy conservation to find speed?

Yes, there are some limitations to using energy conservation to find speed. This method can only be used for objects that are in motion and have a known mass. Additionally, it assumes that there are no external forces acting on the object, which may not always be the case in real-world scenarios.

## 4. How accurate is using energy conservation to find speed?

Using energy conservation to find speed can be very accurate if all the necessary factors are known and accounted for. However, as mentioned before, there may be external forces acting on the object that can affect its speed and accuracy of the calculation. It is also important to note that this method is based on the assumption that the object is moving at a constant velocity, which may not always be the case.

## 5. Can energy conservation be used to find the speed of an object in a vacuum?

Yes, energy conservation can still be used to find the speed of an object in a vacuum. In a vacuum, there is no air resistance or other external forces acting on the object, so the total energy of the system remains constant. Therefore, the initial kinetic energy of the object will be equal to its final potential energy, allowing us to use the conservation of energy equation to find the speed.

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