Question
Question
A ball falls from a shelf. Assuming there is no friction, why is the conservation of mechanical energy independent of mass?(1 point)
Responses
Mass is eliminated when equating gravitational potential energy with kinetic energy.
Mass is eliminated when equating gravitational potential energy with kinetic energy.
Mass is eliminated when equating elastic potential energy with kinetic energy.
Mass is eliminated when equating elastic potential energy with kinetic energy.
The mass of the ball is insignificant compared with the mass of Earth.
The mass of the ball is insignificant compared with the mass of Earth.
The displacement of the ball is insignificant compared with Earth's size.
A ball falls from a shelf. Assuming there is no friction, why is the conservation of mechanical energy independent of mass?(1 point)
Responses
Mass is eliminated when equating gravitational potential energy with kinetic energy.
Mass is eliminated when equating gravitational potential energy with kinetic energy.
Mass is eliminated when equating elastic potential energy with kinetic energy.
Mass is eliminated when equating elastic potential energy with kinetic energy.
The mass of the ball is insignificant compared with the mass of Earth.
The mass of the ball is insignificant compared with the mass of Earth.
The displacement of the ball is insignificant compared with Earth's size.
Answers
GPT-4o mini
The correct response is:
**Mass is eliminated when equating gravitational potential energy with kinetic energy.**
This is because the gravitational potential energy (PE) of the ball is given by the formula \( PE = mgh \), and the kinetic energy (KE) is given by \( KE = \frac{1}{2} mv^2 \). When applying the conservation of mechanical energy, we can set these two equations equal to each other during the fall, leading to \( mgh = \frac{1}{2} mv^2 \). The mass \( m \) appears on both sides of the equation and can be canceled out, showing that the conservation of mechanical energy does not depend on the mass of the object.
**Mass is eliminated when equating gravitational potential energy with kinetic energy.**
This is because the gravitational potential energy (PE) of the ball is given by the formula \( PE = mgh \), and the kinetic energy (KE) is given by \( KE = \frac{1}{2} mv^2 \). When applying the conservation of mechanical energy, we can set these two equations equal to each other during the fall, leading to \( mgh = \frac{1}{2} mv^2 \). The mass \( m \) appears on both sides of the equation and can be canceled out, showing that the conservation of mechanical energy does not depend on the mass of the object.