Why is the work done double its expected value? (conveyer belt)

[jbriggs444]

Whenever lossy processes exist in converting any energy type to any other energy type at maximal power or energy being transferred, the loss is 50% . (at least)

Say what? Motor generator set efficiencies cap out at near 100%, not near 25%.

Or are you just saying that if one stresses a motor generator set well past design limits in order to maximize transmitted power that the efficiency is sure to take a 75% hit?

 

[TonyStewart]

Say what? Motor generator set efficiencies cap out at near 100%, not near 25%.

Or are you just saying that if one stresses a motor generator set well past design limits in order to maximize transmitted power that the efficiency is sure to take a 75% hit?

Motor generator sets if rigidly coupled are lossless coupling and not lossy. MPT is when impedances are matched and Motor generators are usually much lower impedance (<1%) than their loads. This is performed due to negative feedback which reduces output impedance from loop gain.

Load regulation$= \frac {R_L} {R_L+R_S}= \frac 12 \text{ if } R_S=R_L$

Commercial power Audio amplifiers are usually 0.1% which means Rs= 0.1% of 8 ohm load for example anf that means Damping factor = 1000.

Grid load regulation is about 5 to 10% max of load then they use tap changers to tune to meet regional specs. ( far-eastern global infrastructures e.g. India =do not meet this spec of 10% V error at service entry)

 

[jbriggs444]

Motor generator sets if rigidly coupled are lossless coupling and not lossy.

A motor generator set converts electrical power to mechanical power. That is lossy.
A motor generator set converts mechanical power to electrical power. That is lossy.
The mechanical connection between motor and generator is not the point.

 

[TonyStewart]

A motor generator set converts electrical power to mechanical power. That is lossy.
A motor generator set converts mechanical power to electrical power. That is lossy.
The mechanical connection between motor and generator is not the point.

{ Motor nor Gens nor Motor-Gens } are never operated at MPT or max. power transfer for operation with the load impedance matched to the generator source.

That would be matching the DCR of the coil and would be equivalent to an electronic brake for generators and a mechanical brake for motors to measure brake Hp at any RPM..

 

[haruspex]

We both understand MPT and are saying the same thing.

Except, that is not what you wrote in post #48.
If you wish to apply the MPT result in this dropped crate scenario you need to explain the analogy. What here corresponds to the maximum power requirement?

Consider this arrangement:
The belt and crate have the same mass. The crate slides smoothly on the belt, but after being dropped it is initially stationary in the ground frame, while the belt continues at speed v. A vertical buffer fixed to the belt strikes the crate perfectly elastically. The crate acquires speed v and the belt comes to a halt. The belt's motor then restores the belt to speed v.
Unless you can find a reason that 50% of the motor's work is wasted, this seems to avoid the losses.

 

[hutchphd]

A vertical buffer fixed to the belt strikes the crate perfectly elastically. The crate acquires speed v and the belt comes to a halt. The belt's motor then restores the belt to speed v.

Sorry but I do not follow this. Can you elaborate? How does this buffer work? (If the belt is elastic it will oscillate horizontally)

 

[TonyStewart]

Sorry but I do not follow this. Can you elaborate? How does this buffer work? (If the belt is elastic it will oscillate horizontally)

au contraire, perfect vertical elasticity creates a vertical oscillator or trampoline.
This modulated loss of traction from friction being on/off vertically only affects time to stop skidding which we have stated is lossless and irrelevant given vertical momentum is assumed lossless.

 

[jbriggs444]

au contraire, perfect vertical elasticity creates a vertical oscillator or trampoline.
This modulated loss of traction from friction being on/off vertically only affects time to stop skidding which we have stated is lossless and irrelevant given vertical momentum is assumed lossless.

This does not seem relevant to either the scenario proposed by @haruspex or the incomprehension expressed by @hutchphd.

@haruspex proposes a collision in the horizontal dimension which is perfectly elastic. The box lands on the equally massive belt. We ignore the vertical component of the impact and any vertical oscillation which may ensue. It is irrelevant to the horizontal momentum balance and to the portion of energy which can be attributed to the horizontal component of motion.

The box now sits [horizontally] stationary on the frictionless surface of the moving belt. It collides elastically with a tab standing up vertically from the surface the moving belt. The belt comes to a stop. The box rebounds at the original speed of the belt and slides forward on the frictionless surface.

The motor speeds the belt back up to match the speed of the box.

I agree with @haruspex that this arrangement contrives to avoid all frictional losses.

An elastic collision does not involve an ensuing oscillation. Indeed, no new vibration can result from the collision. In an elastic collision, the total bulk kinetic energy ($\frac{1}{2}m_\text{tot}v_\text{com}^2$ for each colliding object) summed after the collision is the same as that summed prior. If any vibration also results, that would mean an increase in total energy. But we do not consider a collision "elastic" if it involves an increase in total energy.

 

[hutchphd]

Thanks to @jbriggs444 for the description, I now understand the proposal.

I propose a simpler equivalent method:

1. Have the motor slow down the belt to zero (motor does negative work $W$)
2. Drop the box
3. Speed up the belt and box to v. Motor does positive work $W+ \frac {mv^2} 2$
4. Net work by motor is $\frac {mv^2} 2$

So the motor control is the real difference. Of course one can charge a capacitor without loss using active control as well. Maxwell Demon? '