Power and Velocity: Can You Help Me Understand Better?

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In summary, the conversation discusses the relationship between power (P), force (F), and velocity (v) in terms of a car's acceleration. It is noted that the power delivered by an engine is dependent on the engine's RPM, and as the RPM increases, the power eventually peaks and then starts to drop off. This is illustrated through diagrams and equations. The conversation also mentions the concept of mass decreasing as a rocket accelerates, leading to a faster acceleration.
  • #1
kishtik
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I cannot imagine P=F v cosa alhough I know its mathematical derivation.

Think a car speeding up from 0 to 30. It cannot have the same acceleration when it continues to 60 km/h. It seems nonsense.

Can you help me understand this better?

Any help is appreciated.
 
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  • #2
Originally posted by kishtik
Think a car speeding up from 0 to 30. It cannot have the same acceleration when it continues to 60 km/h. It seems nonsense.
Why? It seems perfectly sensible to me. Maybe you are confused by the fact that with an internal combustion engine, power does not come on till you are at a sufficiently high engine speed. Try this: With a gear chosen so that you are near maximum power output for your car at so 50km/h, hit the throttle suddenly and note how hard it presses you back into your seat. That's a measure of acceleration. Now do the same at 100km/h. You will notice considerably less force pressing you into your seat at the higher speed.
 
  • #3
Its much easier to think about it with an electric motor as it has a much flatter torque curve as krab implied.
 
  • #4
Just a comment, but I think of it this way:
If 30 to 60 mph acceleration only required the same energy as 0 to 30 mph, than space travel would be far, far easier, and anyone could do it in their own backyard.
 
  • #5
Originally posted by kishtik
I cannot imagine P=F v cosa alhough I know its mathematical derivation.

Think a car speeding up from 0 to 30. It cannot have the same acceleration when it continues to 60 km/h. It seems nonsense.

Can you help me understand this better?

Any help is appreciated.

The torque delivered by the engine is a function of R.P.M. As the RPM increases there is a power peak range where there is a maximum power being delivered by the engine. As the rpm increases past that point the power starts to drop off.

There are some nice diagrams which illustrate this concept for model engines --

http://www.mh-aerotools.de/airfoils/engingeperformance.htm

As for the relationship P = Fv this applies in this case by noting what the force is. The torque on the wheels is being delivered the engine which exerting a torque by applying a force to the crankshaft through a lever arm. It can then be shown the relationship is


P = T*omega

where T = torque and omega = angular frequency.

Why the power/rpm curve has the shape that it does is a whole different and very interesting question. I've never looked into this myself. Perhaps someone has a good answer.
 
  • #6
Originally posted by pallidin
If 30 to 60 mph acceleration only required the same energy as 0 to 30 mph, than space travel would be far, far easier, and anyone could do it in their own backyard.

LOL. Still, that doesn't stop some of us from trying!
 
  • #7
Originally posted by pallidin
Just a comment, but I think of it this way:
If 30 to 60 mph acceleration only required the same energy as 0 to 30 mph, than space travel would be far, far easier, and anyone could do it in their own backyard.
Not really. For low speed travel, a=f/m. A rocket actually accelerates FASTER the faster it gets because its mass is decreasing.
 
  • #8
Originally posted by russ_watters
Not really. For low speed travel, a=f/m. A rocket actually accelerates FASTER the faster it gets because its mass is decreasing.
In which case one uses dp/dt = d(mv)/dt = m*dv/dt + v*dm/dt
 
  • #9
Lots of thanks.
 

1. What is the difference between power and velocity?

Power and velocity are both measures of movement, but they measure different aspects. Power is the rate at which work is done or energy is transferred, while velocity is the rate of change of an object's position with respect to time. In simpler terms, power is the ability to do work, while velocity is the speed at which an object is moving.

2. How are power and velocity related?

Power and velocity are related in that an increase in velocity can result in an increase in power. This is because power is calculated by multiplying force and velocity, so if the velocity increases, the power will also increase. However, it is important to note that power and velocity are not directly proportional, as there are other factors such as mass and friction that can affect power.

3. How is power measured?

Power is measured in watts (W) or horsepower (hp). One watt is equal to one joule per second, meaning that one watt of power is equal to one joule of work being done in one second. One horsepower is equal to 746 watts. Power can also be measured in other units such as kilowatts (kW) or BTUs per hour (BTU/h).

4. How is velocity measured?

Velocity is measured in meters per second (m/s) in the metric system, or feet per second (ft/s) in the imperial system. It can also be measured in other units such as kilometers per hour (km/h) or miles per hour (mph). Velocity is typically measured using tools such as speedometers or radar guns.

5. How can understanding power and velocity be useful?

Understanding power and velocity can be useful in various fields, including physics, engineering, and sports. In physics and engineering, these concepts are important for understanding the movement and energy of objects. In sports, understanding power and velocity can help athletes improve their performance and optimize their training methods.

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