On the question of conservation of mechanical energy of a conical pendulum

Is the centripetal force the resultant force of pull and gravity? This sentence is not true, the direction of the resultant force of the pulling force and the gravitational force is always the direction of the object swinging, that is, the direction perpendicular to the centripetal force. The centripetal force is what the pulling force provides, not the resultant force.

The pull force does not do work. Because it is always perpendicular to the direction of velocity.

Yes, the centripetal force of all uniform circular motion is the resultant force, and the centripetal force is an effect force, that is, an effect produced by other forces or the resultant force of other forces, and this effect is the effect of making the object move in a circular motion. The centripetal force of the conical pendulum is the resultant force of the two forces of the rope, the pulling force and the gravitational force, and since the centripetal force is always perpendicular to the direction of motion of the object, all the centripetal forces do not do work, or to be precise: the combined work done by all the centripetal forces is equal to zero!

Gravity does the work, so that the kinetic energy of the object and the gravitational potential energy are converted into each other; The centripetal force does not do work, the centripetal force is the resultant force of the pull force and the gravitational force Its direction always points to the center of the circle, perpendicular and velocity. The cone pendulum has no displacement component in the direction of the centripetal force at any moment, so the centripetal force does not do work.

The centripetal force is a qualitative force, it is the factor that maintains the motion of the object to do a curvilinear motion, it does not actually exist, the centripetal force is provided by other forces, it never does work.

Your question is not clear, the cone does not do work by gravity, nor does the pulling force do work, and the centripetal force is not a force in the real sense, but the combined force of the pulling force and gravity.

Tie a small object with a mass of m at the lower end of the rope with length L, shout Hu and fix the upper end of the rope, try to make the small object rotate at a constant speed of size on the horizontal circumference, and the string will sweep over the surface of the cone, which is the cone pendulum. It can be seen that the center of the circle of the ball to do circular motion is O, the radius of the circular motion is LSIN, and the centripetal force required by the ball is actually the resultant force of the rope tension f and gravity g. And there is f-synthesis=mg tg=m2lsin.

It can be obtained by doing this pose.

cosθ=g/(ω2l)

This shows that the angle between the cycloid and the vertical direction of the ball in conical motion has nothing to do with the quality of the pendulum, but with the length and angular velocity of the cycloid. When the pendulum length is constant, the angular velocity is greater and the greater it is. Due to the tensile force of the rope f=mg cos = mg (g 2l) = m 2l.

It can be seen that the tensile force of the rope increases with the increase of angular velocity. The periodic formula for the conical pendulum.

t=2π√(lcosθ/g)

At the same place on the earth's surface, the period of the cone Zheng trace pendulum is the same.

lcosθ)

is proportional and has nothing to do with the mass of the pellet. If the cycloid l is of fixed length, then the larger, the larger, the smaller the period.

According to the above, you can judge that you should work harder.

Not conserved, the kinetic energy of the pendulum ball of the conical pendulum ball in a uniform circular motion in the plane does not change, but its gravitational potential energy changes, so the mechanical energy is not conserved.

1 How to tell if mechanical energy is conserved.

1) For an object, if only gravity does the work, and the other forces do not do the work, then the mechanical energy of the object is conserved.

2) For a system composed of two or more objects (including springs), if the system only does the work done by gravity or elastic force, there is only the mutual conversion between kinetic energy, gravitational potential energy and elastic potential energy between the objects, there is no transfer of mechanical energy between the system and the outside world, and there is no conservation of mechanical energy in the system with other forms of energy conversion system mechanical energy.

3) If the object or system has other forces to do work besides gravity or elasticity, then the mechanical energy is to change.

4) What is the difference between the so-called object only subject to gravity and only gravity doing work?

In the first case, the object is subject only to gravity and not to other forces. The second case: the object is subjected to other forces besides gravity, but the other forces do not do work.

5) What are the so-called only elastic work, including what kinds of situations?

In the first case, the object is only subjected to elastic force and is not subject to other forces; The second case: the object is subjected to other forces in addition to the elastic force, but the other forces do not do work.

I don't know what your foundation is, so it's difficult to communicate in a targeted and efficient way.

The basic principle is that as long as there is no sliding friction, then the whole system is conserved in mechanical energy, and there is no need to even consider whether it is circular motion or uniform circular motion. From the perspective of mechanical energy, only the magnitude of the velocity, the height (corresponding to the gravitational work and the gravitational potential energy), and the elastic potential energy (corresponding to the elastic force to do the work, if the work is not done, such as a rope or rod pulling an object to do circular motion, etc.).

Taking a closer look at your question, it is advisable to downplay the "circular" motion, which is not related to mechanical energy, when dealing with curvilinear motion.

Specific questions can be practiced through daily practice, pay attention to the above points, do not think too complicated, knead all kinds of relevant and irrelevant factors together, for beginners, it will be maddening.

This can't be one-sidedly just talked about in a circular motion, what if someone else comes up with another topic?

A good application of the conservation law is based on an understanding of the theorem itself. For the conservation of mechanical energy, then there are two key words, one is mechanical energy, the other is conservation, in a system, the mechanical energy of the object is the sum of the kinetic energy and potential energy of each object, the typical circular motion in the vertical plane, is the mutual transformation of gravitational potential energy and kinetic energy, this transformation is no energy loss, so it is conserved, you remember one thing, for a certain research object you identify, such as a small ball, its gravitational potential energy changes, so where does this energy go? Of course, it becomes its kinetic energy, and the amount of change is equal.

To be more specific, how much the gravitational potential energy decreases, then how much his kinetic energy will increase, and this is how the equation comes out!

There are so many such questions that they are usually found in workbooks!

The most typical one is a rope with a ball hanging from it. Give the length of the rope l, the mass of the ball m (the size of the ball is ignored). The questions are often about how fast the ball can reach the lowest or highest point, or whether it can pass the highest point or something like that!

This kind of problem requires the knowledge of the binding force, the centripetal force (is a key, generally considering the relationship between the centripetal force and the gravitational force experienced by the ball, which can be considered through the highest point!) ）

As for the conservation of mechanical energy, it is nothing more than the kinetic energy and potential energy at the beginning are equal to the sum of kinetic energy and potential energy in a certain state after that! This is easy to solve by calculating the height difference h before and after according to the mathematical skills! (The increased potential energy is equal to the decreasing kinetic energy).

The kinetic energy of the conic pendulum e= mv

v Linear velocity of the conical pendulum.

v=ωr=ωlsinα

Kinetic energy e= m(lsin).

Let the angle between the cycloid and the vertical direction of the blind is a, the ball is subject to gravity and tension, and the resultant force of the two forces provides centripetal force, and the direction points to the center of the circle, so a is wrong

b. The ball moves in a uniform circular motion, the size of the linear velocity remains the same, and the direction changes at all times, so B is wrong;

c. The centripetal acceleration always points to the center of the circle, the size does not change, and the direction changes, so C is wrong;

d. The centripetal force provided according to the resultant force is: mgtan = ma, the solution is a = gtan, and the magnitude of the centripetal acceleration of the ball is determined by the angle at which the cycloid deviates from the vertical direction of the vertical limb, so d is correct

Therefore, the side is empty: d