B Why higher speeds need more power if backward force is the same?

[gen x]

Power = Force v Speed

Power of my horse = 104kgx9.81m/s^2 x 0.732m/s = 1HP =746W

Force/tension in rope stay the same if horse run at 0.73m/s or at 15m/s, so why then horse need to be more powerfull to pull at higher speed even if backward force at him(rope tension) stay the same?
I understand that if I increase weight, it is hrader for horse to pull at higher speed because now is backward force increased, but don't understand why is harder to pull at higher speed if weight(backward force) is the same.

 

[Lnewqban]

One thing is work performed by the horse, and a different one is the time in which that work is done.
Less time requires greater power.
Olympic games are mainly about that fact.
Your feet excert the same force on the pedals of your bicycle to climb the same hill, either slowly or quickly, but it is only so fast that you can pedal.

 

[gen x]

One thing is work performed by the horse, and a different one is the time in which that work is done.
Less time requires greater power.

Imagine if car travel in different medium so at 100km/ and 200km/h is same drag force at car.
It turns out that car that travel at 200km/h need more power only because it travel at faster speed, even medium drag is the same, isn't that wierd?
That show me, my physics/life intuition is totally wrong.

 

[PeroK]

Imagine if car travel in different medium so at 100km/ and 200km/h is same drag force at car.
It turns out that car that travel at 200km/h need more power only because it travel at faster speed, even medium drag is the same, isn't that wierd?
That show me, my physics/life intuition is totally wrong.

Consider an object falling in vacuum under a constant gravitational force. The rate that kinetic energy is gained by the object increases with time, as the object accelerates.

Constant force, therefore, implies increasing power.

 

[gen x]

Olympic games are mainly about that fact.
Your feet excert the same force on the pedals of your bicycle to climb the same hill, either slowly or quickly, but it is only so fast that you can pedal.

When I decrease F and use higer gears ratio, I can incease my speeed, but my power still remain the same.

Consider an object falling in vacuum under a constant gravitational force. The rate that kinetic energy is gained by the object increases with time, as the object accelerates.

Constant force, therefore, implies increasing power.

Is my example with horse counter intuitive to you as well or not?

 

[PeroK]

Is my example with horse counter intuitive to you as well or not?

There are a lot of people who think that applied force remains constant as speed increases. They see applied force as the fundamental quantity that can be maintained as speed increases. E.g. in pushing an object, or accelerating a vehicle such as a bike or car. They believe that acceleration only becomes more difficult because of increasing resistance forces, which eventually equal the constant accelerating force.

In fact, leaving aside certain complications, it's the available power that is the constant. As speed increases, the same power yields a smaller accelerating force. Even without any resistance forces, acceleration will decrease. And, eventually, the accelerating force reduces to the point where even a small resistance force will equal it.

Also, as speed increases, resistance forces tend to increase, which makes the reduction in acceleration with speed even more dramatic.

I'm not sure whether what I know about forces, energy and power in this context is intuitive (in whatever sense that means). At some point, I learned the physics of acceleration, and that's all I can say.

 

[gen x]

There are a lot of people who think that applied force remains constant as speed increases. They see applied force as the fundamental quantity that can be maintained as speed increases. E.g. in pushing an object, or accelerating a vehicle such as a bike or car. They believe that acceleration only becomes more difficult because of increasing resistance forces, which eventually equal the constant accelerating force.

In case of bike, lets say my foot push on pedals only in half circle, when I am above pedal so my weight ( mg) make force on pedals. How my force on pedals decrease with speed if mg is constant?

 

[Dale]

Walk up some flights of stairs. Then the next time run up the same stairs. Which makes you more sweaty?

 

[gen x]

Walk up some flights of stairs. Then the next time run up the same stairs. Which makes you more sweaty?

When I run is harder, but when I run I use more power , my leg rpm is higher and my force push on each stair is higher.

 

[PeroK]

In case of bike, lets say my foot push on pedals only in half circle, when I am above pedal so my weight ( mg) make force on pedals. How my force on pedals decrease with speed if mg is constant?

A bike is a complicated machine. As the pedals speed up, it becomes harder to maintain the force. Without changing gear, you end up feeling very little resistance from the pedals. It doesn't matter whether you try to stand up on the pedals - that doesn't work if you are already going fast.

Especially if you are on a downhill section, you can hardly generate any force on the pedals at all.

The gears are important in terms of allowing you to generate more force on the road from the force on the pedal. That allows you to keep accelerating when it would be impossible on a simple bicycle without higher gears.

 

[kuruman]

Force/tension in rope stay the same if horse run at 0.73m/s or at 15m/s, so why then horse need to be more powerfull to pull at higher speed even if backward force at him(rope tension) stay the same?

Here is an easy to understand example. There are 20 boxes of books, each of mass 20 kg, that need to be moved to an apartment 10 meters above ground. There is no elevator. A powerful weightlifter might stack 5 boxes on top of each other and finish the job in 4 trips and 20 minutes total. An average college student will probably take one box at a time and finish the same job in 2 hours (with breaks). The work done against gravity is the same in both cases. However, the work done per unit time (power) is higher in the first case because the weightlifter, being more powerful than the college student, can do the same work in less time.

In your example you have a horse lifting a weight against gravity but the idea is the same. If the horse moves at a higher speed, it lifts the weight by a fixed amount, say 2 m, in less time and therefore has to use more power.

 

[Baluncore]

The rate of energy flow, that an engine can convert, is its power rating.
Kinetic Energy; E_k= ½⋅m⋅v²
Velocity; v = √ ( 2 ⋅ E_k / m )
As energy flows at a fixed rate, the velocity can only rise at a reducing rate.

 

[gmax137]

Power of my horse = 104kgx9.81m/s^2 x 0.732m/s = 1HP =746W

Force/tension in rope stay the same if horse run at 0.73m/s or at 15m/s, so why then horse need to be more powerfull to pull at higher speed even if backward force at him(rope tension) stay the same?

EDIT: @gen x , forget about rockets for now. Just think about your horse \EDIT

Let's say the horse pulls for 10 meters. What is the work done?

1020 N * 10 m = 10,200 Nm

if the horse's velocity is 1 m/sec, what is the power?

power is work/time, and time is distance/velocity, so

$$power = \frac {10,200 Nm} {\frac {10 m}{1 m/s}} = 1020 \frac{Nm}{sec}$$

if the horse's velocity is 2 m/sec, what is the power?
$$power = \frac {10,200 Nm} {\frac {10 m}{2 m/s}} = 2040 \frac{Nm}{sec}$$

as @kuruman said,

In your example you have a horse lifting a weight against gravity but the idea is the same. If the horse moves at a higher speed, it lifts the weight by a fixed amount, say 2 m, in less time and therefore has to use more power.

 

[gen x]

This seems wrong.

Car acceleration decrease when speed rise (even if aero/tire drag is zero), because thrust force decrease.
Torque at wheels are smaller and smaller as you shift gears, gear ratios become lower each shift

 

[wrobel]

I do not understand such questions. There is a definition: Power=$W=(\boldsymbol F,\boldsymbol v)$.
There is a theorem:
$$\dot T=W,\quad T=\frac{1}{2}m|\boldsymbol v|^2.$$
What else?

 

[jack action]

Say, your horse needs to eat 1 kg of hay (that's where it gets its energy) every 60 m it pulls the 1000 N weight.

If it goes at 1 m/s, every 1 minute the horse will have to eat its 1 kg of hay. After 1 hour, it will have covered 3600 m and have eaten 60 kg of hay. So 60 kg of hay per hour is required.

And if it goes 2 m/s, the horse will eat its 1 kg of hay every 30 seconds. After 1 hour, it will have covered 7200 m and have eaten 120 kg of hay. So 120 kg of hay per hour is required. For the same period of time, it requires more food (energy).

But if you have only 60 kg of hay available, if the horse goes at 2 m/s, it will still cover 3600 m, but it will take only 30 minutes.

Why the horse doesn't go at 100 m/s and do the same work faster? Because its digestive system couldn't handle converting 1 kg of hay to mechanical energy within 0.6 second. Every machine has its limit, and that is what power measures.

So, it is not harder to pull the 1000 N for a given distance at faster speeds. But you do need a machine capable of delivering the energy required faster. There is usually heat wasted to deal with during energy conversion, and cooling is then harder when it's done faster, thus why the horse will sweat more at a higher power level.

Same difference with a car, where hay is replaced with fuel.

 

[Dale]

When I run is harder, but when I run I use more power , my leg rpm is higher

Yes.

my force push on each stair is higher.

Not on average, no.

 

[Baluncore]

The work done, is the force applied, multiplied by the distance over which the force is applied. If you are moving initially, you will apply the force over a greater distance. For the same force, that will require more energy, but that is limited by your available power. The force must therefor be reduced at higher speeds, to remain within your available power, or maximum energy flow.

 

[Hornbein]

Walk up some flights of stairs. Then the next time run up the same stairs. Which makes you more sweaty?

Actually running up stairs is easier. I learned it when I was a kid and have practiced it my whole life. It appears I am the only person in the world who does this.

It's biomechanics. The human body has poor leverage when going up stairs slowly : you feel it in the thighs. It's better to use momentum to carry oneself up.

 

[Dale]

Actually running up stairs is easier. I learned it when I was a kid and have practiced it my whole life. It appears I am the only person in the world who does this.

It's biomechanics. The human body has poor leverage when going up stairs slowly : you feel it in the thighs. It's better to use momentum to carry oneself up.

That is specifically why I didn't say easier or harder. I said which makes you sweat more. I.e. which heats you up faster.

 

[Baluncore]

The human body has poor leverage when going up stairs slowly : you feel it in the thighs. It's better to use momentum to carry oneself up.

I believe that running or walking makes no difference, unless you exit with a lower horizontal velocity than you entered. By using your legs not to lift you, but as fixed links, you can convert horizontal kinetic energy into potential energy.

 

[Hornbein]

I believe that running or walking makes no difference, unless you exit with a lower horizontal velocity than you entered. By using your legs not to lift you, but as fixed links, you can convert horizontal kinetic energy into potential energy.

Right, it seems to me that the amount of work done is the same. Lately I experimented -- Tokyo Metro has many stairs -- and felt I could get the same effect by making a conscious effort to use calf muscles instead of thighs. It's a strange case where the instinctive method isn't the best.

 

[Baluncore]

To climb 10 ft ≈ 3m up stairs requires PE = m·g·h ;
If you are moving horizontally, you have KE = ½·m·v² ;
If we equate those; ½·m·v² = m·g·h ; then cancel m,
we get; v² = 2·g·h ; or v = √ ( 2·g·h ) ;
For h = 3 metres, v = 7.67 m/s, which is 27.6 km/hr.
But the average human only runs at about 20 km/hr.
So there is still some heavy lifting to be done,
and you will need to invest energy in the run-up.

 

[Hornbein]

That is specifically why I didn't say easier or harder. I said which makes you sweat more. I.e. which heats you up faster.

I don't noticeably sweat or heat up either way. It is true that the time for running is less so theoretically more heat is expended in less time, but I have never felt that.

There is a similar thing in backpacking. Avoid all swaying and bouncing, imagine a straight line coming out of the center of your chest going up the hill and try to keep the center on that line. It makes a definite difference. All that other motion is nothing but waste.

 

[Baluncore]

It makes a definite difference. All that other motion is nothing but waste.

You are assuming the path is straight, without scrub and rocks.
In a rocky landscape, it is easier to run because you do not have to balance with each step, you only have to recover from the start of this fall, by being light on your toes. The quickest path is not a straight line, but a sequence of deviations and corrections, a bit like riding a bicycle.

 

[Dale]

I don't noticeably sweat or heat up either way.

Then do more stairs for the experiment.

None of this distraction you are bringing is likely to be helpful for the OP.

 

[PeroK]

Actually running up stairs is easier. I learned it when I was a kid and have practiced it my whole life. It appears I am the only person in the world who does this.

It's biomechanics. The human body has poor leverage when going up stairs slowly : you feel it in the thighs. It's better to use momentum to carry oneself up.

There is such a thing as hill racing, where athletes run up and down mountains. On the uphill, however, only the top athletes do more than fast walking. This is because the body becomes significantly more inefficient as the speed and power output increase. Everyone has a maximum uphill speed that can be sustained for any length of time. Going steeply uphill even at fast walking pace (4-5 km/h) would quickly exhaust even a fit hill walker. About 2-3 km/hr is the maximum that most people could sustain (this equates to 400-600m of ascent per hour on typical mountain terrain.)

In any case, running upstairs uses considerably more energy than walking. You may not notice this for a few steps, but beyond that you should notice your heart rate increasingly rapidly. Momentum cannot simply be sustained against gravity.

 

[Hornbein]

There is such a thing as hill racing, where athletes run up and down mountains. On the uphill, however, only the top athletes do more than fast walking. This is because the body becomes significantly more inefficient as the speed and power output increase. Everyone has a maximum uphill speed that can be sustained for any length of time. Going steeply uphill even at fast walking pace (4-5 km/h) would quickly exhaust even a fit hill walker. About 2-3 km/hr is the maximum that most people could sustain (this equates to 400-600m of ascent per hour on typical mountain terrain.)

In any case, running upstairs uses considerably more energy than walking. You may not notice this for a few steps, but beyond that you should notice your heart rate increasingly rapidly. Momentum cannot simply be sustained against gravity.

Consider wall sits, something that serious skiers do. Lean against a wall as though sitting in a chair, held up only by friction against your back. It's surprisingly hard on the thighs even though no "work" is being done at all. That's what walking up stairs is like, which is why most people stand still on an escalator. Running up avoids this.

All also note that this trick only works on stairs, not on slopes. And the stairs can't be too far from standard. Not too tall, too short, too deep, too steep, not steep enough. Fortunately most staircases meet these criteria.

Not to be boastful but I would do this on the Tokyo Metro for exercise. In particular there is a station where many lines intersect underground. The later lines had to be dug underneath the earlier ones so the last line is way down there. (I don't remember but it's probably the Tsukuba Express at Akihabara station.) There are five long flights of escalators -- escalators are more common than stairs on the Metro -- to the top, about 200 steps. For the challenge I'd run all the way up that. This is possible because in Tokyo all the standees are on the left and the movers on the right. I'm 70 years old and walk about an hour a day but otherwise nothing special. Whenever I get stuck behind a walker it is quite unpleasant on the thighs, even just a few steps.

Here's a video of a Tokyo staircase I have climbed but it's a mere eighty steps. When I got to the shrine at the top there were twenty Tokyo matrons inside dancing the hula in grass skirts. In eastern and southern Asia dance used to be mainly religious/ceremonial, roughly the same function as singing hymns in the West.

 

[gen x]

Not on average, no.

When we talk about average power/torque/force, if I want to find average power under power curve in some rpm interval, I need to calculate area under that part of curve(integral) and divide by interval?

 

[Dale]

if I want to find average power under power curve in some rpm interval, I need to calculate area under that part of curve(integral) and divide by interval?

Yes, but sometimes there are shortcuts.

In the case of running or walking up the stairs, neglecting the initial start and final stop, you run or walk at a steady pace. That means that your average force is equal to your weight.

You “feel” like you are exerting more force in the running case, but you are not. (Except for the start). The feeling of extra force is actually extra power in this case.