Define mechanical energy.

Mechanical energy is the sum of kinetic and potential energy in a system of objects.

Mechanical energy is a form of energy that is associated with the motion and position of an object or a system of objects. It is the sum of kinetic energy, which is the energy of motion, and potential energy, which is the energy of position. Kinetic energy is given by the formula KE = 1/2mv^2, where m is the mass of the object and v is its velocity. Potential energy is given by the formula 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 a reference point.

Mechanical energy is conserved in a closed system, meaning that the total mechanical energy of the system remains constant. This is known as the law of conservation of mechanical energy. For example, if a ball is thrown into the air, its kinetic energy is converted into potential energy as it rises, and then back into kinetic energy as it falls. At all times, the total mechanical energy of the ball remains constant.

Mechanical energy can be used to do work, which is the transfer of energy from one object to another. For example, a roller coaster uses mechanical energy to move the cars along the track and to lift them to the top of a hill. As the cars move down the hill, their potential energy is converted into kinetic energy, which is used to power the rest of the ride.

In summary, mechanical energy is the sum of kinetic and potential energy in a system of objects. It is conserved in a closed system and can be used to do work.