Regarding the question of mechanical energy, what is mechanical energy

The mechanical energy increment is equal to the amount of change in kinetic energy plus the amount of change in potential energy.

According to the functional principle, the amount of change in mechanical energy is equal to the work done by forces other than gravity. (Because the change in gravitational potential energy caused by the work done by gravity is already included in the amount of change in mechanical energy.)

EA=1 2(MV0 2)-MGH This formula is the increment of mechanical energy, because the gravitational potential energy decreases when falling down, EP is negative.

This is due to the fact that the so-called vector direction and the zero point of the potential energy, this problem takes into account that the vertical direction is positive and the starting point is the ground, so when the object falls, its direction is downward, and the sign is negative, so that the kinetic energy increases, and the energy can decrease. At the moment of landing, the total kinetic energy is ek=1 2(mv0 2)-mgh, the object does not move after landing, the potential energy is zero, the kinetic energy is zero, and the EA in the formula refers to the energy change of the whole object.

EA=1 2(MV0 2)-mgH represents the change in energy from gravitational potential energy to kinetic energy.

1 2 (mv0 2) This represents kinetic energy.

This mgh denotes gravitational potential energy.

You're falling from a great place and it's definitely a decrease in gravitational potential energy, so use a minus sign.

1) A: When A turns from the level to the lowest point, gravity does positive work mgr, so the gravitational potential energy decreases EPA minus = mgr

B: The same is to do positive work, the gravitational potential energy reduces EPB minus = 1 2mgr

Mechanical energy is the sum of kinetic energy and potential energy, and is a physical quantity that expresses the state and height of an object's motion.

Mechanical energy is conserved, which is manifested in the fact that the kinetic energy and potential energy of an object can be converted into each other, and in the process of conversion of only kinetic energy and potential energy into each other, the total amount of mechanical energy remains unchanged. Mechanical energy refers to: without considering friction and medium resistance, only the mutual conversion of kinetic energy and potential energy occurs in the object and the total amount of mechanical energy remains unchanged, that is, the increase or decrease of kinetic energy is equal to the decrease or increase of potential energy, that is, the law of conservation of mechanical energy.

Mechanical energy is related to the mechanical motion of the whole object.

When there is friction, part of the mechanical energy is converted into internal energy, which is lost in the air, and the other part is converted into kinetic energy or potential energy. Therefore, there is no conservation of mechanical energy in nature, so the perpetual motion machine proposed by Leonardo da Vinci cannot be manufactured, that is, there is no perpetual motion machine.

The essence from the point of view of energy transformation:

From the perspective of energy conversion, as long as the total amount of mechanical energy of the system remains unchanged in a certain physical process, and there is no mechanical energy converted into other forms of energy in the system or between the system and the outside world, and no other form of energy is converted into the mechanical energy of the system, then the mechanical energy of the system is conserved, and it has nothing to do with whether the mutual conversion of kinetic energy and potential energy must occur in the system. Such as making an object moving in a straight line at a uniform speed on a smooth horizontal plane.

Its mechanical energy is conserved; If there are other forms of energy and mechanical energy conversion within the system or between the system and the outside world. Even if the total amount of mechanical energy of the system remains unchanged, its mechanical energy is not conserved, such as when a bomb is **, assuming that the external force does not do work, but the chemical energy (non-conservative force) in the system does work on the system, although the total amount of mechanical energy remains unchanged, there are other forms of energy (internal energy or electrical energy) in the system that are converted into the mechanical energy of the system, and the system overcomes the external work to convert the mechanical energy into other forms of energy.

Mechanical energy is the sum of kinetic energy and potential energy, and here potential energy is divided into gravitational potential energy and elastic potential energy. Kinetic energy, gravitational potential energy, and elastic potential energy are collectively referred to as mechanical energy. So what is mechanical energy?

1. It is height and mass that determine the gravitational potential energy, and the potential energy here is divided into gravitational potential energy and elastic potential energy.

2. The kinetic energy is determined by mass and velocity, and the mechanical energy is the sum of kinetic energy and part of the potential energy; The elastic potential energy is determined by the stiffness coefficient and the deformation.

3. Mechanical energy is a physical quantity that expresses the state and height of an object.

Mechanical energy is the sum of kinetic energy and potential energy.

Mechanical energy refers to the fact that only kinetic energy and potential energy are converted to each other, and the total amount of mechanical energy remains unchanged, that is, the increase or decrease of kinetic energy is equal to the decrease or increase of potential energy, which is the law of conservation of mechanical energy. Mechanical energy is related to the mechanical motion of the whole object.

When there is friction, a part of the mechanical energy is converted into heat energy, which is lost in the air, while the other part is converted into kinetic or potential energy. Therefore, if there is no conservation of mechanical energy in nature, then the perpetual motion machine proposed by Leonardo da Vinci cannot be manufactured, that is, there is no perpetual motion machine.

From the point of view of energy conversion, as long as the total amount of mechanical energy of the system remains constant in a certain physical process, and there is no mechanical energy converted into other forms of energy within the system or between the system and the outside world.

And there is no other form of energy converted into the mechanical energy of the system, then the mechanical energy of the system bond is conserved, and it has nothing to do with whether the mutual conversion of kinetic energy and potential energy must occur within the system. For example, an object moving in a straight line at a uniform speed on a smooth horizontal plane.

The formulation of the law of conservation of mechanical energy is

When only gravity does the work, the kinetic energy and potential energy of the object are converted into each other, but the total amount of mechanical energy remains the same. This is the most common case of the law of conservation of mechanical energy (i.e., in the mutual conversion of gravitational potential energy and kinetic energy, only gravity comes into play).

In fact, in the mutual conversion of gravitational potential energy with elastic potential energy and kinetic energy, when only gravity and spring elasticity do the work, the sum of the kinetic energy of the object and the potential energy of the system remains constant, and the mechanical energy of the system is conserved), which is also a special case of the more general law of conservation of mass.

Mechanical energy is the sum of kinetic energy and potential energy, and the potential energy here is divided into gravitational potential energy and elastic potential energy. We refer to kinetic energy, gravitational potential energy, and elastic potential energy collectively as mechanical energy. It is mass and velocity that determine kinetic energy; It is the mass and height that determine the gravitational potential energy; The elastic potential energy is determined by the stiffness coefficient and the deformation.

Mechanical energy is simply the sum of kinetic energy and potential energy. Mechanical energy is a physical quantity that represents the state of motion of an object. There is a conversion between the kinetic energy and the potential energy of an object.

In the process where only kinetic energy and potential energy are converted into each other, the total amount of mechanical energy remains the same, i.e., mechanical energy is conserved.

For example, if a car moving on the ground has only kinetic energy, and the potential energy is zero (with the ground as the reference plane), then the mechanical energy is equal to the kinetic energy; An airplane flying in the sky, that is, it has kinetic energy and gravitational potential energy, then the mechanical energy is kinetic energy and aggravating force potential energy; The kinetic energy of an object suspended by a spring is zero, there is gravitational potential energy and elastic potential energy, then the mechanical energy is gravitational potential energy plus elastic potential energy.

Mechanical energy. It is divided into kinetic energy and potential energy. Potential energy is further divided into gravitational potential energy.

and elastic potential energy.

The factors that affect kinetic energy are the mass and velocity of the object.

The factors that affect the gravitational potential energy are the height and mass of the object.

The factors influencing the elastic potential energy are the stiffness coefficient of the elastic object and the degree of defection before the elastic shape.

Orthogonal decomposition along the rod direction:

The rod is vertical, and the elastic force is n=|mgcos30°-fsina|

Horizontal balance of the rod:

mgsin30°-fcosa|=un=u|mgcos30°-fsina|

To minimize the work done by the tensile force, even if the FCOSA is minimal.

Category Discussion:1 mgsin30°-fcosa>0, mgcos30°-fsina>0

mgsin30°-fcosa=u(mgcos30°-fsina)

If fcosa is the smallest, then the fsina is the smallest, and the minimum is 0, a=0

f=mg(sin30°-ucos30°)

2. mgsin30°-fcosa<0, mgcos30°-fsina>0

fcosa-mgsin30°=u(mgcos30°-fsina)

If FCOSA is the smallest, then MGCOS30°-FSINA is the smallest, and the minimum is 0:

fcosa-mgsin30°=0，mgcos30°-fsina=0

It can be obtained: f=mg, a=60°

3. mgsin30°-fcosa>0, mgcos30°-fsina<0

mgsin30°-fcosa=u(fsina-mgcos30°)

If the FCOSA is the smallest, the FSINA should be the largest, and when the FSOSA is the largest, A=90°

Mgsin30°=U(F-MgCoS30°), and F=Mg(Sin30° U+CoS30°)

However, in this case, it is impossible for the ball to automatically move from the low end to the top along the rod at a uniform speed, which does not meet the topic and must be discarded!

4. mgsin30°-fcosa<0, mgcos30°-fsina<0

fcosa-mgsin30°=u(fsina-mgcos30°)

If FCOSA is the smallest, FSINA-MGCOS30° is the smallest, and the minimum is 0

This is the same as the second case!

It can be seen that in the first case, the FCOSA is the smallest, and the tensile work is the smallest.

So: the angle between the tensile force f and the rod = 0, and the tensile force magnitude f = mg (sin30°-ucos30°).