# What speed v(t) enables constant power by solenoid pull?

• cairoliu
In summary, the conversation discusses the dynamics of a solenoid and plunger system with different boundary conditions and a given magnetic force. The speaker wishes to find the dynamic position and velocity of the system and is considering using constant power to avoid a big crash noise. However, this approach may still result in a lot of energy needing to be dispersed rapidly, so an alternative solution of using a damping force or spring is suggested.
cairoliu
Assuming the position x = 0 if no air gap, max stroke of plunger is L.
Bordery conditions: x(t=0) = L, x(t=T)= 0.
Given magnetic force F(x) = kx(t)^-2, here k is constant.
If uncontrolled, there is big crash noise afer solenoid actuated, so I wish it pull plunger at constant power.
Help me find the dynamic position x(t), then I can get velocity.
I know Wolfram software may resolve it, but I have no money to buy it.

cairoliu said:
Bordery conditions: x(t=0) = L, x(t=T)= 0.
Given magnetic force F(x) = kx(t)^-2, here k is constant.
If uncontrolled, there is big crash noise afer solenoid actuated, so I wish it pull plunger at constant power.
If x(t=T)= 0, then F(x(t=T)) = kx(t=T)^-2 = k(0)^-2 = ##\infty##. How do you expect not having a big crash noise at t=T ?

jack action said:
If x(t=T)= 0, then F(x(t=T)) = kx(t=T)^-2 = k(0)^-2 = ##\infty##. How do you expect not having a big crash noise at t=T ?
Now that noise not good, I can reserve a minimal air gap 𝛿, then x(t=T)= 𝛿, and still ask for the solution of constant power.

How is constant power helping you? If you have power ##P## at the end of the stroke, then if ##F = 0##, ##v## must be infinite, or if ##v = 0##, then ##F## must be infinite. Any way you choose, you will have a lot of energy to disperse rapidly when the plunger suddenly stops.

To avoid the big crash noise, you would normally remove the energy - with a damping force - before it reaches the end. Which means power would gradually go to zero.

Lnewqban
Or a spring, depending upon duration.

## What is a solenoid pull?

A solenoid pull is a type of electromagnetic force where a coil of wire is used to generate a magnetic field, which then pulls on a ferromagnetic material such as iron or steel.

## What is constant power?

Constant power is a measure of the rate at which energy is transferred or converted, and it remains the same over time. In the case of a solenoid pull, it refers to the amount of power needed to maintain a steady pull force on the ferromagnetic material.

## How does the speed of v(t) affect the solenoid pull?

The speed of v(t) refers to the velocity or rate of change of the solenoid pull. The higher the speed, the greater the force generated by the solenoid. However, there is an optimal speed at which the solenoid can maintain a constant power without overheating or losing efficiency.

## What factors determine the optimal speed for constant power in a solenoid pull?

The optimal speed for constant power in a solenoid pull depends on various factors such as the size and strength of the solenoid, the material and weight of the object being pulled, and the amount of power being supplied to the solenoid. It also depends on external factors such as temperature and friction.

## How can the optimal speed for constant power in a solenoid pull be calculated?

The optimal speed for constant power in a solenoid pull can be calculated using mathematical equations that take into account the factors mentioned above. These equations can be derived from the laws of electromagnetism and can vary depending on the specific parameters of the solenoid and the object being pulled.

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