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I am trying to understand what would be the power difference in watt for making rolling a car of 1000 kg and a bycycle of 80 kg (human + bycycle weight) on a plate road.

My car as around 100 horsepower. But it does not mean that it needs 100 horsespower for rolling at 50 km/h on a plate road.

Does anyone can help me, please?

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3 Answers 3

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You are confusing power with energy.

The power exerted by a rolling vehicle at a given speed is equal to the summation of all drag forces times the velocity of the vehicle; this is the rate of work required to push it down the road at constant velocity. Even at 60MPH, this drag horsepower is a just a fraction of the full power available from the engine when it is running "wide open", screaming along at full throttle and maximum RPM's.

For example, the drag horsepower of my pontiac vibe cruising at 65 MPH on level ground with no headwind is about 18HP. Its maximum available power is about 132HP. Note that the drag horsepower scales as the cube of the velocity, which means that to double the speed of a vehicle requires 8 times the horsepower.

On the other hand, the kinetic energy of a moving vehicle is equal to 1/2 x (mass) x (velocity)^2. This is a measure of how much damage the vehicle can do if it collides with another object.

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  • $\begingroup$ Yeah i totally agree with you ! But how can I know what is the power needed for my car to be at the speed of 50 Km/h ? $\endgroup$
    – Jess
    Commented Jan 17, 2022 at 20:10
  • $\begingroup$ Is there a way to know what is the force applied on the mass ? It seems possible to know the force link to the air ? Suppose we have a simple form ? $\endgroup$
    – Jess
    Commented Jan 17, 2022 at 20:54
  • $\begingroup$ There is a simple test called a coast-down test where you start at some speed, then disconnect the engine, shut it off, and measure the distance from then to the point where you car rolls to a stop. You can then solve for the drag forces knowing the coast-down distance and the initial velocity of the car. that drag force times your speed yields horsepower (watch the units!). $\endgroup$
    – niels nielsen
    Commented Jan 18, 2022 at 5:14
  • $\begingroup$ Thank you I will try to take a look on it ! :D $\endgroup$
    – Jess
    Commented Jan 18, 2022 at 16:59
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Ok its very simple. Energy = 0.5 m V^2 so E=0.5 x 1000kg x 13 X13 = 84500 Joules is needed (forget the wind drag on the car & friction) Now if you want to finish that energy in 30 minutes then time =1800 seconds So Power = E/t = joules / second So Power needed for that 1/2 hour is: P= 84500J/1800s = 46.9 Watts is what you need power wise. Remember to add friction and drag to get a realistic answer.

Also if you want to accelerate 0-50km/h in 2 seconds then you need much more power Power for 0-50 = E/t = 84500J/2seconds = 42250 Watt will now be needed by the engine. This is like a thousand times bigger engine and thats why your Mustang is 200 horses. So we dont need big engines to cruise, but we need them mostly to accelerate. Giel

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If something is said to be operating at 100 horsepower, then that is the power output. If it was more complicated than this for the problem you are solving then more information would, or at least should, be given.

We know instantaneous power $P$ delivered by a force $\mathbf F$ is given by $P=\mathbf F\cdot\mathbf v$, where $\mathbf v$ is the instantaneous velocity of the object the force is acting on. If we want to simply to one-dimensional motion, we have $P=Fv$. At a constant power, this just means that $F$ and $v$ are inversely proportional: $F=P/v$. As the object speeds up, the applied force decreases.

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  • $\begingroup$ But the motor does not have the same power at each speed. We understand that if there is more gazoil to enter in the motor, there is more energy taken from the gazoil and this energy make the motor turning with less or more power. There is probably a relationship between speed and gazoil consumption and indirectly to power, isn't it ? $\endgroup$
    – Jess
    Commented Jan 16, 2022 at 14:38
  • $\begingroup$ @Jess This is an exercise, or you're asking about a specific motor? $\endgroup$
    – BioPhysicist
    Commented Jan 16, 2022 at 14:43
  • $\begingroup$ This not an exercice this a question that I ask myself... I was thinking that it was possible via the weight and the speed of a mass to know what was the power needed to displace this mass. $\endgroup$
    – Jess
    Commented Jan 16, 2022 at 15:05
  • $\begingroup$ @Jess That problem isn't constrained enough to have a unique answer. Power is a rate of work being done. Just asking for displacement doesn't specify a rate, so any power would do. $\endgroup$
    – BioPhysicist
    Commented Jan 16, 2022 at 20:18

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