How does the mass of an object affect its speed (and kinetic energy)?
The mass of an object affects its speed and kinetic energy in the following ways:
1. Speed: According to Newton's second law of motion, the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. Mathematically, this is represented as F = ma, where F is the force, m is the mass, and a is the acceleration. Rearranging this equation, we have a = F/m. Thus, for a given force, a smaller mass will result in a greater acceleration and, consequently, a higher speed. On the other hand, a larger mass will require more force to achieve the same acceleration, resulting in a lower speed.
2. Kinetic Energy: The kinetic energy of an object is given by the equation KE = 0.5mv², where KE is the kinetic energy, m is the mass, and v is the speed. As per this equation, the kinetic energy is directly proportional to the square of the speed and directly proportional to the mass. Therefore, if the speed of an object doubles, its kinetic energy increases by a factor of four, assuming the mass remains constant. Similarly, if the mass of an object doubles while the speed remains constant, its kinetic energy also doubles.
In summary, a smaller mass results in a higher speed and a greater kinetic energy, while a larger mass leads to a lower speed and a lesser kinetic energy, assuming the force applied remains constant.