A ball falls from a shelf. Assuming there is no friction, why is the conservation of mechanical energy independent of mass?(1 point) Responses 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. Mass is eliminated when equating gravitational potential energy with kinetic energy. Mass is eliminated when equating gravitational potential energy with kinetic energy. The displacement of the ball is insignificant compared with Earth's size. The displacement of the ball is insignificant compared with Earth's size. Mass is eliminated when equating elastic potential energy with kinetic energy. Mass is eliminated when equating elastic potential energy with kinetic energy. Skip to navigation page 10 of 10
Mass is eliminated when equating gravitational potential energy with kinetic energy.
Mass is eliminated when equating gravitational potential energy with kinetic energy.
The conservation of mechanical energy is independent of mass in the context of a ball falling from a shelf because mass is eliminated when equating gravitational potential energy with kinetic energy.
To understand why this is the case, let's break it down step by step:
1. The gravitational potential energy (PE) of an object is given by the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the reference point.
2. As the ball falls from the shelf, its potential energy decreases. This decrease in potential energy is converted into kinetic energy (KE), which is the energy of motion. The equation for kinetic energy is KE = 0.5mv^2, where m is the mass of the object and v is its velocity.
3. According to the law of conservation of mechanical energy, the total mechanical energy remains constant throughout the motion of the ball. This means that the initial mechanical energy (sum of potential energy and kinetic energy at the starting point) is equal to the final mechanical energy (sum of potential energy and kinetic energy at a given point).
4. When the ball falls, its potential energy decreases while its kinetic energy increases. This can be expressed as mgh = 0.5mv^2.
5. Notice that mass (m) is present on both sides of the equation. By dividing both sides of the equation by mass, we get gh = 0.5v^2.
6. From this equation, we can see that the mass cancels out. This implies that the conservation of mechanical energy (represented by the equation gh = 0.5v^2) is independent of mass.
Therefore, in the scenario of a ball falling from a shelf without friction, the conservation of mechanical energy remains the same regardless of the mass of the ball.