Answer :
To determine which of the given formulas are correctly used to calculate potential and kinetic energy, we'll analyze each option in the context of physics principles.
First, let’s recall the standard formulas for kinetic energy (KE) and potential energy (PE):
1. Kinetic Energy (KE):
The kinetic energy of an object is given by the formula:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where [tex]\( m \)[/tex] is mass and [tex]\( v \)[/tex] is velocity.
2. Potential Energy (PE):
The gravitational potential energy of an object at height [tex]\( h \)[/tex] is given by the formula:
[tex]\[ PE = m g h \][/tex]
where [tex]\( m \)[/tex] is mass, [tex]\( g \)[/tex] is the acceleration due to gravity, and [tex]\( h \)[/tex] is the height above the reference point.
Now, let's evaluate each of the given options:
A. [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]:
- This is the correct formula for kinetic energy.
B. [tex]\( PE = m v h \)[/tex]:
- This formula is irrelevant for potential energy. [tex]\( PE \)[/tex] should involve gravitational acceleration [tex]\( g \)[/tex] instead of velocity [tex]\( v \)[/tex].
C. [tex]\( PE = \frac{1}{2} m v^2 \)[/tex]:
- This is actually the formula for kinetic energy, not potential energy. It doesn't match the potential energy expression.
D. [tex]\( KE = \frac{1}{2} m g^2 \)[/tex]:
- This formula is incorrect for kinetic energy, as it should involve velocity [tex]\( v \)[/tex], not gravitational acceleration [tex]\( g \)[/tex].
E. [tex]\( KE = m g h \)[/tex]:
- This is actually the formula for potential energy, not kinetic energy.
F. [tex]\( PE = m q h \)[/tex]:
- This formula is incorrect for potential energy because it uses [tex]\( q \)[/tex] instead of the gravitational acceleration [tex]\( g \)[/tex].
Based on this analysis, the correct formulas for potential and kinetic energy from the provided options are:
- For Kinetic Energy ([tex]\(KE\)[/tex]): Option A: [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]
- None of the given options correctly represent the standard formula for Potential Energy ([tex]\(PE = mg h\)[/tex]).
Thus, the answer identifying the correct formula among the options provided is:
1. A: [tex]\( KE = \frac{1}{2} m v^2 \)[/tex].
First, let’s recall the standard formulas for kinetic energy (KE) and potential energy (PE):
1. Kinetic Energy (KE):
The kinetic energy of an object is given by the formula:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where [tex]\( m \)[/tex] is mass and [tex]\( v \)[/tex] is velocity.
2. Potential Energy (PE):
The gravitational potential energy of an object at height [tex]\( h \)[/tex] is given by the formula:
[tex]\[ PE = m g h \][/tex]
where [tex]\( m \)[/tex] is mass, [tex]\( g \)[/tex] is the acceleration due to gravity, and [tex]\( h \)[/tex] is the height above the reference point.
Now, let's evaluate each of the given options:
A. [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]:
- This is the correct formula for kinetic energy.
B. [tex]\( PE = m v h \)[/tex]:
- This formula is irrelevant for potential energy. [tex]\( PE \)[/tex] should involve gravitational acceleration [tex]\( g \)[/tex] instead of velocity [tex]\( v \)[/tex].
C. [tex]\( PE = \frac{1}{2} m v^2 \)[/tex]:
- This is actually the formula for kinetic energy, not potential energy. It doesn't match the potential energy expression.
D. [tex]\( KE = \frac{1}{2} m g^2 \)[/tex]:
- This formula is incorrect for kinetic energy, as it should involve velocity [tex]\( v \)[/tex], not gravitational acceleration [tex]\( g \)[/tex].
E. [tex]\( KE = m g h \)[/tex]:
- This is actually the formula for potential energy, not kinetic energy.
F. [tex]\( PE = m q h \)[/tex]:
- This formula is incorrect for potential energy because it uses [tex]\( q \)[/tex] instead of the gravitational acceleration [tex]\( g \)[/tex].
Based on this analysis, the correct formulas for potential and kinetic energy from the provided options are:
- For Kinetic Energy ([tex]\(KE\)[/tex]): Option A: [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]
- None of the given options correctly represent the standard formula for Potential Energy ([tex]\(PE = mg h\)[/tex]).
Thus, the answer identifying the correct formula among the options provided is:
1. A: [tex]\( KE = \frac{1}{2} m v^2 \)[/tex].
