Does the mass of the skater affect the magnitude of the kinetic and potential energy ?
The correct answer and explanation is:
Yes, the mass of the skater affects the magnitude of both kinetic energy and potential energy.
Kinetic energy (KE) is given by the formula KE = 1/2 m v², where m is the mass of the skater and v is the velocity. Since kinetic energy is directly proportional to the mass, if the mass increases while velocity remains constant, the kinetic energy increases proportionally. For example, a heavier skater moving at the same speed as a lighter skater will have more kinetic energy.
Potential energy (PE), specifically gravitational potential energy near the Earth’s surface, is calculated by PE = m g h, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height above a reference point. Because potential energy is directly proportional to mass, a skater with greater mass will have more potential energy at the same height compared to a skater with less mass.
In summary, mass is a key factor influencing both types of energy. The heavier the skater, the greater the kinetic energy at a given velocity and the greater the potential energy at a given height. The velocity and height are also important variables, but mass directly scales the energy values.
Understanding this relationship is important in contexts such as skating or any physical system involving motion and elevation. For example, when a skater goes down a ramp, the potential energy they have at the top due to their height converts into kinetic energy as they move downward. The greater the mass, the greater the energy involved in this conversion, which can affect speed and force during movement.
Therefore, the mass of the skater is directly proportional to both kinetic and potential energy magnitudes.