Question
What will be the velocity by which a body is moving when pe=ke
Answers
GPT-4o mini
In physics, when the potential energy (PE) of an object is equal to its kinetic energy (KE), you can use the relationship between these forms of energy to determine the velocity of the object.
The potential energy \( PE \) of an object near the Earth’s surface can be described by the formula:
\[
PE = mgh
\]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height above some reference point.
The kinetic energy \( KE \) of an object in motion is given by the formula:
\[
KE = \frac{1}{2}mv^2
\]
where:
- \( v \) is the velocity of the object.
If we set the potential energy equal to the kinetic energy, we have:
\[
mgh = \frac{1}{2}mv^2
\]
Assuming \( m \) (the mass) is not zero, we can divide both sides by \( m \):
\[
gh = \frac{1}{2}v^2
\]
Next, we can rearrange this equation to solve for \( v \):
\[
v^2 = 2gh
\]
Taking the square root of both sides gives:
\[
v = \sqrt{2gh}
\]
Thus, the velocity of the body when its potential energy is equal to its kinetic energy is \( v = \sqrt{2gh} \). This shows the relationship between the height of the object and its velocity when the energies are equal. You would need to know the height \( h \) in order to calculate the actual velocity.
The potential energy \( PE \) of an object near the Earth’s surface can be described by the formula:
\[
PE = mgh
\]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height above some reference point.
The kinetic energy \( KE \) of an object in motion is given by the formula:
\[
KE = \frac{1}{2}mv^2
\]
where:
- \( v \) is the velocity of the object.
If we set the potential energy equal to the kinetic energy, we have:
\[
mgh = \frac{1}{2}mv^2
\]
Assuming \( m \) (the mass) is not zero, we can divide both sides by \( m \):
\[
gh = \frac{1}{2}v^2
\]
Next, we can rearrange this equation to solve for \( v \):
\[
v^2 = 2gh
\]
Taking the square root of both sides gives:
\[
v = \sqrt{2gh}
\]
Thus, the velocity of the body when its potential energy is equal to its kinetic energy is \( v = \sqrt{2gh} \). This shows the relationship between the height of the object and its velocity when the energies are equal. You would need to know the height \( h \) in order to calculate the actual velocity.