Suppose the kinetic energy of an object moving is 15 J and the potential energy is 25 J at some point in time. Then I measure the potential energy some time later and find it to be 10 J. What is the new kinetic energy?
To find the new kinetic energy, we need to consider the conservation of mechanical energy. According to the principle of conservation of mechanical energy, the total mechanical energy of a system remains constant if only conservative forces are acting on it.
In this case, we have an object with an initial kinetic energy (15 J) and an initial potential energy (25 J). Later, the potential energy is measured to be 10 J. Since the total mechanical energy is conserved, we can calculate the new kinetic energy as follows:
Total Mechanical Energy = Initial Kinetic Energy + Initial Potential Energy
Total Mechanical Energy = Final Kinetic Energy + Final Potential Energy
Initial Kinetic Energy + Initial Potential Energy = Final Kinetic Energy + Final Potential Energy
Substituting the given values:
15 J + 25 J = Final Kinetic Energy + 10 J
Simplifying the equation:
40 J = Final Kinetic Energy + 10 J
Final Kinetic Energy = 40 J - 10 J
Final Kinetic Energy = 30 J
Therefore, the new kinetic energy is 30 J.