# Force, Horsepower and Acceleration logic?

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1. Mar 30, 2015

### lgoptimus

hi guys,
Im not a science student but wanted help in understanding a few fundamentals.
Here is where i have learnt till please correct me if i am wrong.

is it correct if i state, "If you can lift 74.6kgs off the ground to a height of 1m in 1sec you have power = 1hp?"
i say that cause i read 10N= 102gms x (9.8m/s^2) which is apprx. 1kg.
so, 10Nm done in 1 sec = 1Watt.
and 746Watts = 1 Hp.

so i am understanding the above idea to do with lifting a body of mass from off the ground...
NOW...
but what if i have a 10kg car, how fast must i be able to push it to have 1hp?
Am i suppose to be calculating hp from the speed i generate(velocity)... or calculating hp from its acceleration achieved??

I am basically trying to understand the link between Mass, Force, Hp, Acceleration, Speed.
We can ignore drag or friction

thanx, for the help guys!

2. Mar 30, 2015

### Staff: Mentor

Moving the car horizontally in the complete absence of friction and drag, you'd look at its acceleration to determine power. (It takes zero power to keep a vehicle travelling at a constant speed on level ground in the absence of friction.)

3. Mar 30, 2015

### gleem

Yes, 1 HP is 746 watts but 1watt is 1 Nm/sec!

Power is the work done OR energy used per unit time.

Work = Force need to move the object times the distance over which the force is applied
Force = mass time the acceleration
Power then can be written as the force applied times the velocity that is maintained with this force.

How fast do you have to push a 10 Kg car (toy car?) to attain 1 HP. that question is not answerable for I have no way of knowing the force unless you tell me.

4. Mar 30, 2015

### lgoptimus

hi gleem,
Yes 1Watt is 1Nm/s.
Now i wanted to understand the magnitude of 1Hp(or 5hp or 10hp). but not in respect to lifting a weight from the ground. That i kinda got.

so lets take a small weight on wheels , say a car for example... or simply say the car weighed 10kg. what must be its acceleration or velocity if its engine power is ..say..10 or 5Hp ?
basicially some logical way that could help me go about understanding the way i am suppose to go about calculating this? Just simple

5. Mar 30, 2015

### gleem

With a 10 hp engine you are using energy at a rate of 7460 Nt m /sec (10x746 ) What does that translate into the motion of the car? First let us assume that the 10 HP is the power used to propel the car, the actual HP of the engine must be greater to compensate for frictional loses in the transmission, drive shaft etc.

If the 10 hp is supplying energy to get the car going to a certain speed V and maintain it at that speed V might be anything from a small value to an arbitrarily large velocity depending on the mass and how much of that energy is used to accelerate the car. You are supplying energy at a constant rate and the car will continue to accelerate indefinitely until say air resistance or rough road forces stop the acceleration or until the drive shaft rotation and the axle rotation are the same speed at which point there will be no more additional force applied to the axle. At this point the acceleration is zero although and the speed is constant . So the affect of HP on a given mass is not uniquely determined. If as in a rocket you could maintain the HP constant until you ran out of fuel you would continue to accelerate and gain speed until that point. P = m*a*v you gave me P and m and all I can determine is a*v !! Now if the acceleration is constant then we can say v=a*t where t is the time the rocket was being accelerated and we can find a and v if you are given t.

So the question you should as is if a car of 10 KG is powered by a 10 HP engine for 10 sec what is its speed?

6. Mar 30, 2015

### lgoptimus

Hey Gleem that's a great answer.
What if the question is - "In how much time can a 10kg car, with a 10hp engine reach 100km/hr"?
This should be a benchmark answer!

7. Mar 31, 2015

### gleem

OK this is answerable. If the energy is delivered to the car over the time interval we are seeking at a rate of 7460 Ntm/sec and If that energy goes fully into accelerating the car to 100 Km/hr.(27.7 m/sec). then we can equate the total energy input to its final kinetic energy and we can write

P*t =½ m v2

substituting in for P, v and m we get

t= 0.52 secs so the acceleration is 53.3 m/sec2or 5.4 G's

Of course it's mass is only 10 Kg. At 1000Kg the acceleration would be only 0.054 G's with 10hp

8. Mar 31, 2015

### lgoptimus

Hi gleem, absolutely what I needed. And you explained brilliantly!
I did the same for my car that is 980kgs.. Gives 139hp at wheel(not crank) for reaching 100km/hr. It gave me 3.05s. That's a bout too fast cz it actually hits above 8.
Now as u said earlier it must be cz of friction.. Drag .. Etc
From here on .. How could you guide me or give me something to read... Formula... Logic.. etc.. So I could approx calculate this this loss..for my self.
Thanks for all ... Your amazing man!

9. Apr 1, 2015

### gleem

I'm not an automotive engineer , and the forces acting on a car are complex. But you can probably estimate some of the effects that use up some of that hp. You have air resistance that depends on the projected frontal area of the car, the shape of the car, and the speed squared of the car. you have rolling friction of the tires and that varies with the surface they are on and the tire tread pattern inflation pressure, surface temperature. and the weight of the car. I think these are the main resistive forces. Also importantly is the fact that the engine is not always delivering the max hp. In fact that depends on the gear you are in and the rpm. I think you could assume that the Hp is proportional to the rpm. So you might find an average hp for the acceleration period which would be more appropriate for your calculation.

But you can see that since the air resistance force also depend on the speed which is constantly changing so the calculations would be very complex..for this estimate you might determine the energy used by the wind resistance by adding the ave wind force at some ave velocity in the acceleration period times the average velocity times the time you have that velocity. Symbolically Work = Σ Fi(v,t) ⋅ vi(t) ⋅ ti where i is the interval that F , v , t are defined.

You could consider the rolling friction constant.

Below are a few places you can start for estimating these effects.

http://en.wikipedia.org/wiki/Drag_(physics)

http://en.wikipedia.org/wiki/Rolling_resistance